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Papers by farhad ali

Research paper thumbnail of Explication of the conserved quantities corresponding to the spacetimes carrying 10 Noether symmetries

International Journal of Geometric Methods in Modern Physics, Jan 25, 2021

The continuously decreasing curvature of spacetime has been proposed to be due to the phenomenon ... more The continuously decreasing curvature of spacetime has been proposed to be due to the phenomenon like Hawking radiation, the collapse of black holes and neutron stars. It has been found that during these phenomena, energy of source (black hole and neutron stars) decreases. In this paper, we explore this loss in energy of the source by introducing a time conformal factor in the corresponding spacetime in order to get a nonstatic metric without violating its symmetry structure. This technique gives us information about the loss of momentum and energy of the source. We also consider some novel nonstatic classes of the plane-symmetric spacetime containing 10 Noether symmetries and 7 isometries.

Research paper thumbnail of Complete classification of spherically symmetric static space-times via Noether symmetries

Theoretical and Mathematical Physics, Jul 1, 2015

In this paper we give a complete classification of spherically symmetric static spacetimes by the... more In this paper we give a complete classification of spherically symmetric static spacetimes by their Noether symmetries. The determining equations for Noether symmetries are obtained by using the usual Lagrangian of a general spherically symmetric static spacetime which are integrated for each case. In particular we observe that spherically symmetric static spacetimes are categorized into six distinct classes corresponding to Noether algebra of dimensions 5, 6, 7, 9, 11 and 17. Using Noether's theorem we also write down the first integrals for each class of such spacetimes corresponding to their Noether symmetries.

Research paper thumbnail of Dynamics of a particle around AdS Schwarzschild black hole environed by quintessence

Canadian Journal of Physics, May 1, 2021

The field of point particle dynamics is correlated with the particle dynamics around a black hole... more The field of point particle dynamics is correlated with the particle dynamics around a black hole, and one can initiate the investigation of a more complex motion of extended bodies or celestial bodies. In this article, we study the dynamics of neutral and charged particles around the AdS Schwarzschild black hole surrounded by quintessence. At the foot of Noether symmetries and the conservation laws of the proposed spacetime, we discuss the effect of the cosmological constant, angular momentum, quintessence parameter, and magnetic field on the dynamics of neutral and charged particles in the form of the effective potential, effective force, and escape velocity. Finally, we investigate the orbit stability of spacetime with the help of the Lyapunov exponent.

Research paper thumbnail of Dynamics of a particle around AdS Schwarzschild black hole environed by quintessence

Canadian Journal of Physics

The field of point particle dynamics is correlated with the particle dynamics around a black hole... more The field of point particle dynamics is correlated with the particle dynamics around a black hole, and one can initiate the investigation of a more complex motion of extended bodies or celestial bodies. In this article, we study the dynamics of neutral and charged particles around the AdS Schwarzschild black hole surrounded by quintessence. At the foot of Noether symmetries and the conservation laws of the proposed spacetime, we discuss the effect of the cosmological constant, angular momentum, quintessence parameter, and magnetic field on the dynamics of neutral and charged particles in the form of the effective potential, effective force, and escape velocity. Finally, we investigate the orbit stability of spacetime with the help of the Lyapunov exponent.

Research paper thumbnail of Dynamics of particles around the time conformal quantum corrected Schwarzschild black hole

Physics of the Dark Universe, 2020

In this paper, we explore the dynamics of neutral and charged particles in presence/absence of ma... more In this paper, we explore the dynamics of neutral and charged particles in presence/absence of magnetic field around the quantum corrected-Schwarzschild black hole as well as the time conformal quantum corrected-Schwarzschild black hole. We investigate the conditions under which the particles move towards or away from the vicinity of black hole when they collide with other particles. We study the effective potential and effective force in presence/absence of magnetic field graphically. Recently many researchers took interest in point particle dynamics and one can initiate the study of a more complex motion of extended celestial bodies. A major area of interest among these important fields, is the particle motions (neutral and charged) around black hole and naked singularities. In this work we want to show that the quantum corrected-Schwarzschild black hole admits the time conformal factor e ϵg(t) without violating the symmetry structure of the black hole, where ϵ is a small parameter that causes perturbation in the proposed spacetime and g(t) is a function of time t. The inception of time conformal factor, re-scales all the conservation laws that hold in the given spacetime. This type of study is important because it tells about the formation of gravitational waves and Hawking radiation. The study of thermal stability, horizons and energy conditions corresponding to the time conformal quantum corrected Schwarzschild spacetime is also explored. Furthermore, we analyze and compare the dynamics of charged and neutral particle around time conformal quantum corrected-Schwarzschild black hole with the time conformal Schwarzschild black hole. The effective force and effective potential with magnetic field and angular momentum are given graphically. The stability of the proposed spacetime is also discussed with the help of Lyapunov exponent.

Research paper thumbnail of Analysis of a mathematical model for the pine wilt disease using a graph theoretic approach

In this paper, we study a vector–host mathematical model for the pine wilt disease, considering i... more In this paper, we study a vector–host mathematical model for the pine wilt disease, considering indirect and direct transmission of the disease. An explicit formula for the basic reproduction number (R0) is obtained. The global stability of the DFE is proved using a graph theoretic approach and a matrix theoretic method. We show that when R0 is less than one, the DFE always exists and it is globally asymptotically stable, and the disease persists at an endemic level. Finally, local sensitivity analysis of parameters and numerical experiments are carried out to illustrate the theoretical bases for the prevention and control of the disease. M.S.C. 2010: 34D20; 92B05.

Research paper thumbnail of Dynamics of Particles in Time Conformal Reissner-Nordström Black Hole

Transylvanian Review, 2018

In this work, we use Noether symmetries to discuss the dynamics of neutral as well as charged par... more In this work, we use Noether symmetries to discuss the dynamics of neutral as well as charged particles in the absence/presence of a magnetic field around the Reissner Nordstrom black hole as well as the time conformal Reissner–Nordstrom black hole. We investigate the circumstances under which the particle can escape from the vicinity of a black hole after collision with another particle. We analyze the effective potential and effective force of a particle without the magnetic field and in the presence of a magnetic field with angular momentum graphically. Point particle dynamics is very important in the sense that from this type of study one can initiate the study of a more complex motion of extended bodies/celestial bodies. A major area of interest, especially in recent times, is the motion of particles (neutral and charge) in the presence of black holes and naked singularities. Initially, we find the Noether symmetries and the corresponding conservation laws of geodesics of the R...

Research paper thumbnail of New cylindrically symmetric solution of Einstein field equations their conservation laws and the particles dynamics

Indian Journal of Physics, 2021

The study explores the particle dynamics, asymptotic behavior, and flatness in Riemann curvature ... more The study explores the particle dynamics, asymptotic behavior, and flatness in Riemann curvature corresponding to the solutions obtained from the Ricci tensor of cylindrical spacetimes. Since these solutions are non-Minkowskian and are proposed to have curvature in almost all the cases, that is why some cylindrically symmetric static vacuum solutions of Einstein Field Equations have been worked out. We explore the Noether symmetries along with their conservation laws of the corresponding static-spacetime and calculate the equation of motions by taking into account Noether symmetries. We study the dynamics of particle in the form of effective potential, effective force.

Research paper thumbnail of Cylindrically symmetric gravitational-wavelike space–times

Theoretical and Mathematical Physics, 2017

We present Noether symmetries of a geodetic Lagrangian for a time-conformal cylindrically symmetr... more We present Noether symmetries of a geodetic Lagrangian for a time-conformal cylindrically symmetric space-time. We introduce a time-conformal factor in the general cylindrically symmetric space-time to make it nonstatic and then find approximate Noether symmetries of the action of the corresponding Lagrangian. Taking the perturbation up to the first order, we find all Lagrangians for cylindrically symmetric space-times for which approximate Noether symmetries exist.

Research paper thumbnail of Dynamics of particles around time conformal Schwarzschild black hole

The European Physical Journal C, 2016

In this work, we present the new technique for discussing the dynamical motion of neutral as well... more In this work, we present the new technique for discussing the dynamical motion of neutral as well as charged particles in the absence/presence of a magnetic field around the time conformal Schwarzschild black hole. Initially, we find the numerical solutions of geodesics of the Schwarzschild black hole and the time conformal Schwarzschild black hole. We observe that the Schwarzschild spacetime admits the time conformal factor e f (t) , where f (t) is an arbitrary function and is very small, which causes a perturbation in the spacetimes. This technique also re-scales the energy content of spacetime. We also investigate the thermal stability, horizons and energy conditions corresponding to time conformal Schwarzschild spacetime. Also, we examine the dynamics of a neutral and charged particle around a time conformal Schwarzschild black hole. We investigate the circumstances under which the particle can escape from the vicinity of a black hole after collision with another particle. We analyze the effective potential and effective force of a particle in the presence of a magnetic field with angular momentum graphically.

Research paper thumbnail of Complete Classification of Cylindrically Symmetric Static Spacetimes and the Corresponding Conservation Laws

Mathematics, 2016

In this paper we find the Noether symmetries of the Lagrangian of cylindrically symmetric static ... more In this paper we find the Noether symmetries of the Lagrangian of cylindrically symmetric static spacetimes. Using this approach we recover all cylindrically symmetric static spacetimes appeared in the classification by isometries and homotheties. We give different classes of cylindrically symmetric static spacetimes along with the Noether symmetries of the corresponding Lagrangians and conservation laws.

Research paper thumbnail of The Thermodynamics of the Perturbed Schwarzschild Black Hole

International Journal of Theoretical Physics, Jun 2, 2020

The phenomena like gravitational waves, Hawking radiation, and growth of black holes not only cha... more The phenomena like gravitational waves, Hawking radiation, and growth of black holes not only change the curvature of spacetime continuously but also affect the thermodynamical properties of the sources over time. The present study explores the effect of time in the thermodynamical properties of the corresponding spacetime. We define a general time conformal factor e ζ(t) in the Schwarzschild black hole spacetime, where is a small parameter that brings perturbation in the said spacetime. This technique redefines the energy content of spacetime. Moreover, the effect of time is explored in the thermodynamical properties of the perturbed Schwarzschild black hole. We calculate the event horizon of the spacetime as a function of t. Then we study the effect of time in the surface gravity, pressure, volume, and Hawking temperature of the perturbed Schwarzschild black hole and analyze them graphically.

Research paper thumbnail of Analysis of a mathematical model for the pine wilt disease using a graph theoretic approach

In this paper, we study a vector–host mathematical model for the pine wilt disease, considering i... more In this paper, we study a vector–host mathematical model for the pine wilt disease, considering indirect and direct transmission of the disease. An explicit formula for the basic reproduction number (R0) is obtained. The global stability of the DFE is proved using a graph theoretic approach and a matrix theoretic method. We show that when R0 is less than one, the DFE always exists and it is globally asymptotically stable, and the disease persists at an endemic level. Finally, local sensitivity analysis of parameters and numerical experiments are carried out to illustrate the theoretical bases for the prevention and control of the disease. M.S.C. 2010: 34D20; 92B05.

Research paper thumbnail of Comparative Study of the Geodesic Structure of Time-Conformal Quantum-Corrected AdS–Schwarzschild Black Hole

Symmetry

This manuscript reports the dynamics of a time-conformal quantum-corrected AdS–Schwarzschild blac... more This manuscript reports the dynamics of a time-conformal quantum-corrected AdS–Schwarzschild black hole. The quantum-corrected parameter and the time-conformal factors are inserted in the AdS–Schwarzschild black. These insertions in the said space- time are taken to study and understand the phenomena of the formation of gravitational waves and Hawking radiations. The Hawking temperature distributions and Bekenstein–Hawking entropy for the inner and outer horizon of the new developed black hole solution are calculated and discussed. The motion of neutral and charged particles in the orbits of the said black hole is discussed under the influence of effective potential and effective force in the new development of the black hole solution. The escape velocity for the time-conformal black hole is obtained and compared with the escape velocity of the exact black hole. The roles of the quantum-corrected parameter and the effect of the time-conformal factor are high- lighted, and their infl...

Research paper thumbnail of Particles Dynamics in Schwarzschild like Black Hole with Time Contracting Horizon

Axioms

The black holes radiate their mass and energy in the form of gravitational waves and Hawking-radi... more The black holes radiate their mass and energy in the form of gravitational waves and Hawking-radiation, which lead to a decrease in the mass and energy of the black holes. During the formation of gravitational waves and Hawking radiation, the mass and energy of black holes reduce continuously with the passage of time t. For this reason the metric tensor of the black hole should depends on time t. In this work, a time-dependent term is introduced in the horizon of black hole without losing its symmetry structure by using the approximate Noether symmetry equation. The time-dependent term affects the effective potential, effective force, and all the dynamic features of the black hole. They are discussed for neutral and charged particles. Profiles of the escape velocity of colliding particles are also taken into consideration. Lyapunov exponent is used to check the stability of the orbits of the black hole. Hawking temperature, Bekenstein entropy, Komar energy, and specific energy at ho...

Research paper thumbnail of Approximate Symmetries Analysis and Conservation Laws Corresponding to Perturbed Korteweg–de Vries Equation

Journal of Mathematics, 2021

The Korteweg–de Vries (KdV) equation is a weakly nonlinear third-order differential equation whic... more The Korteweg–de Vries (KdV) equation is a weakly nonlinear third-order differential equation which models and governs the evolution of fixed wave structures. This paper presents the analysis of the approximate symmetries along with conservation laws corresponding to the perturbed KdV equation for different classes of the perturbed function. Partial Lagrange method is used to obtain the approximate symmetries and their corresponding conservation laws of the KdV equation. The purpose of this study is to find particular perturbation (function) for which the number of approximate symmetries of perturbed KdV equation is greater than the number of symmetries of KdV equation so that explore something hidden in the system.

Research paper thumbnail of Полная классификация сферически-симметричных статических пространств-времен с помощью симметрий Нeтер

Теоретическая и математическая физика, 2015

Приведена полная классификация сферически-симметричных статических пространств-времен по их симме... more Приведена полная классификация сферически-симметричных статических пространств-времен по их симметриям Нётер. Уравнения, определяющие симметрии Нётер, получены с помощью обычного лагранжиана общего сферически-симметричного пространства-времени и интегрируются в каждом рассмотренном случае. В частности, обнаружено, что сферически-симметричные статические пространства-времена можно распределить по шести различным классам, соответствующим алгебрам Нётер размерностей 5, 6, 7, 9, 11 и 17. С помощью теоремы Нётер найдены также первые интегралы, соответствующие каждой симметрии. Кроме того, получены некоторые новые сферическисимметричные статические решения.

Research paper thumbnail of Sensitivity analysis and optimal control of COVID-19 dynamics based on SEIQR model

Results in Physics, 2021

It is of great curiosity to observe the effects of prevention methods and the magnitudes of the o... more It is of great curiosity to observe the effects of prevention methods and the magnitudes of the outbreak including epidemic prediction, at the onset of an epidemic. To deal with COVID-19 Pandemic, an SEIQR model has been designed. Analytical study of the model consists of the calculation of the basic reproduction number and the constant level of disease absent and disease present equilibrium. The model also explores number of cases and the predicted outcomes are in line with the cases registered. By parameters calibration, new cases in Pakistan are also predicted. The number of patients at the current level and the permanent level of COVID-19 cases are also calculated analytically and through simulations. The future situation has also been discussed, which could happen if precautionary restrictions are adopted.

Research paper thumbnail of Dynamics in the Charged Time Conformal Schwarzschild Black Hole

arXiv: General Physics, 2016

In this work, we present the new technique for discussing the dynamical motion of neutral as well... more In this work, we present the new technique for discussing the dynamical motion of neutral as well as charged particles in the absence/presence of magnetic field around the time conformal Schwarzschild black hole. Initially, we find the numerical solutions of geodesics of Schwarzschild black hole and the time conformal Schwarzschild black hole. We observe that the Schwarzschild spacetime admits the time conformal factor eepsilonf(t)e^{\epsilon f(t)}eepsilonf(t), where f(t)f(t)f(t) is an arbitrary function and epsilon\epsilonepsilon is very small which causes the perturbation in the spacetimes. This technique also re-scale the energy content of spacetime. We also investigate the thermal stability, horizons and energy conditions corresponding time conformal Schwarzschild spacetime. Also, we examine the dynamics of neutral and charged particle around time conformal Schwarzschild black hole. We investigate the circumstances under which the particle can escape from vicinity of black hole after collision with another particle. W...

Research paper thumbnail of M ar 2 02 0 N-extended Chern-Simons Carrollian supergravities in 2 + 1 spacetime dimensions

In this work we present the ultra-relativistic N -extended AdS Chern-Simons supergravity theories... more In this work we present the ultra-relativistic N -extended AdS Chern-Simons supergravity theories in three spacetime dimensions invariant under N -extended AdS Carroll superalgebras. We first consider the (2, 0) and (1, 1) cases; subsequently, we generalize our analysis to N = (N , 0), with N even, and to N = (p, q), with p, q > 0. The N -extended AdS Carroll superalgebras are obtained through the Carrollian (i.e., ultra-relativistic) contraction applied to an so(2) extension of osp(2|2) ⊗ sp(2), to osp(2|1) ⊗ osp(2, 1), to an so(N ) extension of osp(2|N ) ⊗ sp(2), and to the direct sum of an so(p) ⊕ so(q) algebra and osp(2|p) ⊗ osp(2, q), respectively. We also analyze the flat limit (l→ ∞, being l the length parameter) of the aforementioned N -extended Chern-Simons AdS Carroll supergravities, in which we recover the ultrarelativistic N -extended (flat) Chern-Simons supergravity theories invariant under N -extended super-Carroll algebras. The flat limit is applied at the level of...

Research paper thumbnail of Explication of the conserved quantities corresponding to the spacetimes carrying 10 Noether symmetries

International Journal of Geometric Methods in Modern Physics, Jan 25, 2021

The continuously decreasing curvature of spacetime has been proposed to be due to the phenomenon ... more The continuously decreasing curvature of spacetime has been proposed to be due to the phenomenon like Hawking radiation, the collapse of black holes and neutron stars. It has been found that during these phenomena, energy of source (black hole and neutron stars) decreases. In this paper, we explore this loss in energy of the source by introducing a time conformal factor in the corresponding spacetime in order to get a nonstatic metric without violating its symmetry structure. This technique gives us information about the loss of momentum and energy of the source. We also consider some novel nonstatic classes of the plane-symmetric spacetime containing 10 Noether symmetries and 7 isometries.

Research paper thumbnail of Complete classification of spherically symmetric static space-times via Noether symmetries

Theoretical and Mathematical Physics, Jul 1, 2015

In this paper we give a complete classification of spherically symmetric static spacetimes by the... more In this paper we give a complete classification of spherically symmetric static spacetimes by their Noether symmetries. The determining equations for Noether symmetries are obtained by using the usual Lagrangian of a general spherically symmetric static spacetime which are integrated for each case. In particular we observe that spherically symmetric static spacetimes are categorized into six distinct classes corresponding to Noether algebra of dimensions 5, 6, 7, 9, 11 and 17. Using Noether's theorem we also write down the first integrals for each class of such spacetimes corresponding to their Noether symmetries.

Research paper thumbnail of Dynamics of a particle around AdS Schwarzschild black hole environed by quintessence

Canadian Journal of Physics, May 1, 2021

The field of point particle dynamics is correlated with the particle dynamics around a black hole... more The field of point particle dynamics is correlated with the particle dynamics around a black hole, and one can initiate the investigation of a more complex motion of extended bodies or celestial bodies. In this article, we study the dynamics of neutral and charged particles around the AdS Schwarzschild black hole surrounded by quintessence. At the foot of Noether symmetries and the conservation laws of the proposed spacetime, we discuss the effect of the cosmological constant, angular momentum, quintessence parameter, and magnetic field on the dynamics of neutral and charged particles in the form of the effective potential, effective force, and escape velocity. Finally, we investigate the orbit stability of spacetime with the help of the Lyapunov exponent.

Research paper thumbnail of Dynamics of a particle around AdS Schwarzschild black hole environed by quintessence

Canadian Journal of Physics

The field of point particle dynamics is correlated with the particle dynamics around a black hole... more The field of point particle dynamics is correlated with the particle dynamics around a black hole, and one can initiate the investigation of a more complex motion of extended bodies or celestial bodies. In this article, we study the dynamics of neutral and charged particles around the AdS Schwarzschild black hole surrounded by quintessence. At the foot of Noether symmetries and the conservation laws of the proposed spacetime, we discuss the effect of the cosmological constant, angular momentum, quintessence parameter, and magnetic field on the dynamics of neutral and charged particles in the form of the effective potential, effective force, and escape velocity. Finally, we investigate the orbit stability of spacetime with the help of the Lyapunov exponent.

Research paper thumbnail of Dynamics of particles around the time conformal quantum corrected Schwarzschild black hole

Physics of the Dark Universe, 2020

In this paper, we explore the dynamics of neutral and charged particles in presence/absence of ma... more In this paper, we explore the dynamics of neutral and charged particles in presence/absence of magnetic field around the quantum corrected-Schwarzschild black hole as well as the time conformal quantum corrected-Schwarzschild black hole. We investigate the conditions under which the particles move towards or away from the vicinity of black hole when they collide with other particles. We study the effective potential and effective force in presence/absence of magnetic field graphically. Recently many researchers took interest in point particle dynamics and one can initiate the study of a more complex motion of extended celestial bodies. A major area of interest among these important fields, is the particle motions (neutral and charged) around black hole and naked singularities. In this work we want to show that the quantum corrected-Schwarzschild black hole admits the time conformal factor e ϵg(t) without violating the symmetry structure of the black hole, where ϵ is a small parameter that causes perturbation in the proposed spacetime and g(t) is a function of time t. The inception of time conformal factor, re-scales all the conservation laws that hold in the given spacetime. This type of study is important because it tells about the formation of gravitational waves and Hawking radiation. The study of thermal stability, horizons and energy conditions corresponding to the time conformal quantum corrected Schwarzschild spacetime is also explored. Furthermore, we analyze and compare the dynamics of charged and neutral particle around time conformal quantum corrected-Schwarzschild black hole with the time conformal Schwarzschild black hole. The effective force and effective potential with magnetic field and angular momentum are given graphically. The stability of the proposed spacetime is also discussed with the help of Lyapunov exponent.

Research paper thumbnail of Analysis of a mathematical model for the pine wilt disease using a graph theoretic approach

In this paper, we study a vector–host mathematical model for the pine wilt disease, considering i... more In this paper, we study a vector–host mathematical model for the pine wilt disease, considering indirect and direct transmission of the disease. An explicit formula for the basic reproduction number (R0) is obtained. The global stability of the DFE is proved using a graph theoretic approach and a matrix theoretic method. We show that when R0 is less than one, the DFE always exists and it is globally asymptotically stable, and the disease persists at an endemic level. Finally, local sensitivity analysis of parameters and numerical experiments are carried out to illustrate the theoretical bases for the prevention and control of the disease. M.S.C. 2010: 34D20; 92B05.

Research paper thumbnail of Dynamics of Particles in Time Conformal Reissner-Nordström Black Hole

Transylvanian Review, 2018

In this work, we use Noether symmetries to discuss the dynamics of neutral as well as charged par... more In this work, we use Noether symmetries to discuss the dynamics of neutral as well as charged particles in the absence/presence of a magnetic field around the Reissner Nordstrom black hole as well as the time conformal Reissner–Nordstrom black hole. We investigate the circumstances under which the particle can escape from the vicinity of a black hole after collision with another particle. We analyze the effective potential and effective force of a particle without the magnetic field and in the presence of a magnetic field with angular momentum graphically. Point particle dynamics is very important in the sense that from this type of study one can initiate the study of a more complex motion of extended bodies/celestial bodies. A major area of interest, especially in recent times, is the motion of particles (neutral and charge) in the presence of black holes and naked singularities. Initially, we find the Noether symmetries and the corresponding conservation laws of geodesics of the R...

Research paper thumbnail of New cylindrically symmetric solution of Einstein field equations their conservation laws and the particles dynamics

Indian Journal of Physics, 2021

The study explores the particle dynamics, asymptotic behavior, and flatness in Riemann curvature ... more The study explores the particle dynamics, asymptotic behavior, and flatness in Riemann curvature corresponding to the solutions obtained from the Ricci tensor of cylindrical spacetimes. Since these solutions are non-Minkowskian and are proposed to have curvature in almost all the cases, that is why some cylindrically symmetric static vacuum solutions of Einstein Field Equations have been worked out. We explore the Noether symmetries along with their conservation laws of the corresponding static-spacetime and calculate the equation of motions by taking into account Noether symmetries. We study the dynamics of particle in the form of effective potential, effective force.

Research paper thumbnail of Cylindrically symmetric gravitational-wavelike space–times

Theoretical and Mathematical Physics, 2017

We present Noether symmetries of a geodetic Lagrangian for a time-conformal cylindrically symmetr... more We present Noether symmetries of a geodetic Lagrangian for a time-conformal cylindrically symmetric space-time. We introduce a time-conformal factor in the general cylindrically symmetric space-time to make it nonstatic and then find approximate Noether symmetries of the action of the corresponding Lagrangian. Taking the perturbation up to the first order, we find all Lagrangians for cylindrically symmetric space-times for which approximate Noether symmetries exist.

Research paper thumbnail of Dynamics of particles around time conformal Schwarzschild black hole

The European Physical Journal C, 2016

In this work, we present the new technique for discussing the dynamical motion of neutral as well... more In this work, we present the new technique for discussing the dynamical motion of neutral as well as charged particles in the absence/presence of a magnetic field around the time conformal Schwarzschild black hole. Initially, we find the numerical solutions of geodesics of the Schwarzschild black hole and the time conformal Schwarzschild black hole. We observe that the Schwarzschild spacetime admits the time conformal factor e f (t) , where f (t) is an arbitrary function and is very small, which causes a perturbation in the spacetimes. This technique also re-scales the energy content of spacetime. We also investigate the thermal stability, horizons and energy conditions corresponding to time conformal Schwarzschild spacetime. Also, we examine the dynamics of a neutral and charged particle around a time conformal Schwarzschild black hole. We investigate the circumstances under which the particle can escape from the vicinity of a black hole after collision with another particle. We analyze the effective potential and effective force of a particle in the presence of a magnetic field with angular momentum graphically.

Research paper thumbnail of Complete Classification of Cylindrically Symmetric Static Spacetimes and the Corresponding Conservation Laws

Mathematics, 2016

In this paper we find the Noether symmetries of the Lagrangian of cylindrically symmetric static ... more In this paper we find the Noether symmetries of the Lagrangian of cylindrically symmetric static spacetimes. Using this approach we recover all cylindrically symmetric static spacetimes appeared in the classification by isometries and homotheties. We give different classes of cylindrically symmetric static spacetimes along with the Noether symmetries of the corresponding Lagrangians and conservation laws.

Research paper thumbnail of The Thermodynamics of the Perturbed Schwarzschild Black Hole

International Journal of Theoretical Physics, Jun 2, 2020

The phenomena like gravitational waves, Hawking radiation, and growth of black holes not only cha... more The phenomena like gravitational waves, Hawking radiation, and growth of black holes not only change the curvature of spacetime continuously but also affect the thermodynamical properties of the sources over time. The present study explores the effect of time in the thermodynamical properties of the corresponding spacetime. We define a general time conformal factor e ζ(t) in the Schwarzschild black hole spacetime, where is a small parameter that brings perturbation in the said spacetime. This technique redefines the energy content of spacetime. Moreover, the effect of time is explored in the thermodynamical properties of the perturbed Schwarzschild black hole. We calculate the event horizon of the spacetime as a function of t. Then we study the effect of time in the surface gravity, pressure, volume, and Hawking temperature of the perturbed Schwarzschild black hole and analyze them graphically.

Research paper thumbnail of Analysis of a mathematical model for the pine wilt disease using a graph theoretic approach

In this paper, we study a vector–host mathematical model for the pine wilt disease, considering i... more In this paper, we study a vector–host mathematical model for the pine wilt disease, considering indirect and direct transmission of the disease. An explicit formula for the basic reproduction number (R0) is obtained. The global stability of the DFE is proved using a graph theoretic approach and a matrix theoretic method. We show that when R0 is less than one, the DFE always exists and it is globally asymptotically stable, and the disease persists at an endemic level. Finally, local sensitivity analysis of parameters and numerical experiments are carried out to illustrate the theoretical bases for the prevention and control of the disease. M.S.C. 2010: 34D20; 92B05.

Research paper thumbnail of Comparative Study of the Geodesic Structure of Time-Conformal Quantum-Corrected AdS–Schwarzschild Black Hole

Symmetry

This manuscript reports the dynamics of a time-conformal quantum-corrected AdS–Schwarzschild blac... more This manuscript reports the dynamics of a time-conformal quantum-corrected AdS–Schwarzschild black hole. The quantum-corrected parameter and the time-conformal factors are inserted in the AdS–Schwarzschild black. These insertions in the said space- time are taken to study and understand the phenomena of the formation of gravitational waves and Hawking radiations. The Hawking temperature distributions and Bekenstein–Hawking entropy for the inner and outer horizon of the new developed black hole solution are calculated and discussed. The motion of neutral and charged particles in the orbits of the said black hole is discussed under the influence of effective potential and effective force in the new development of the black hole solution. The escape velocity for the time-conformal black hole is obtained and compared with the escape velocity of the exact black hole. The roles of the quantum-corrected parameter and the effect of the time-conformal factor are high- lighted, and their infl...

Research paper thumbnail of Particles Dynamics in Schwarzschild like Black Hole with Time Contracting Horizon

Axioms

The black holes radiate their mass and energy in the form of gravitational waves and Hawking-radi... more The black holes radiate their mass and energy in the form of gravitational waves and Hawking-radiation, which lead to a decrease in the mass and energy of the black holes. During the formation of gravitational waves and Hawking radiation, the mass and energy of black holes reduce continuously with the passage of time t. For this reason the metric tensor of the black hole should depends on time t. In this work, a time-dependent term is introduced in the horizon of black hole without losing its symmetry structure by using the approximate Noether symmetry equation. The time-dependent term affects the effective potential, effective force, and all the dynamic features of the black hole. They are discussed for neutral and charged particles. Profiles of the escape velocity of colliding particles are also taken into consideration. Lyapunov exponent is used to check the stability of the orbits of the black hole. Hawking temperature, Bekenstein entropy, Komar energy, and specific energy at ho...

Research paper thumbnail of Approximate Symmetries Analysis and Conservation Laws Corresponding to Perturbed Korteweg–de Vries Equation

Journal of Mathematics, 2021

The Korteweg–de Vries (KdV) equation is a weakly nonlinear third-order differential equation whic... more The Korteweg–de Vries (KdV) equation is a weakly nonlinear third-order differential equation which models and governs the evolution of fixed wave structures. This paper presents the analysis of the approximate symmetries along with conservation laws corresponding to the perturbed KdV equation for different classes of the perturbed function. Partial Lagrange method is used to obtain the approximate symmetries and their corresponding conservation laws of the KdV equation. The purpose of this study is to find particular perturbation (function) for which the number of approximate symmetries of perturbed KdV equation is greater than the number of symmetries of KdV equation so that explore something hidden in the system.

Research paper thumbnail of Полная классификация сферически-симметричных статических пространств-времен с помощью симметрий Нeтер

Теоретическая и математическая физика, 2015

Приведена полная классификация сферически-симметричных статических пространств-времен по их симме... more Приведена полная классификация сферически-симметричных статических пространств-времен по их симметриям Нётер. Уравнения, определяющие симметрии Нётер, получены с помощью обычного лагранжиана общего сферически-симметричного пространства-времени и интегрируются в каждом рассмотренном случае. В частности, обнаружено, что сферически-симметричные статические пространства-времена можно распределить по шести различным классам, соответствующим алгебрам Нётер размерностей 5, 6, 7, 9, 11 и 17. С помощью теоремы Нётер найдены также первые интегралы, соответствующие каждой симметрии. Кроме того, получены некоторые новые сферическисимметричные статические решения.

Research paper thumbnail of Sensitivity analysis and optimal control of COVID-19 dynamics based on SEIQR model

Results in Physics, 2021

It is of great curiosity to observe the effects of prevention methods and the magnitudes of the o... more It is of great curiosity to observe the effects of prevention methods and the magnitudes of the outbreak including epidemic prediction, at the onset of an epidemic. To deal with COVID-19 Pandemic, an SEIQR model has been designed. Analytical study of the model consists of the calculation of the basic reproduction number and the constant level of disease absent and disease present equilibrium. The model also explores number of cases and the predicted outcomes are in line with the cases registered. By parameters calibration, new cases in Pakistan are also predicted. The number of patients at the current level and the permanent level of COVID-19 cases are also calculated analytically and through simulations. The future situation has also been discussed, which could happen if precautionary restrictions are adopted.

Research paper thumbnail of Dynamics in the Charged Time Conformal Schwarzschild Black Hole

arXiv: General Physics, 2016

In this work, we present the new technique for discussing the dynamical motion of neutral as well... more In this work, we present the new technique for discussing the dynamical motion of neutral as well as charged particles in the absence/presence of magnetic field around the time conformal Schwarzschild black hole. Initially, we find the numerical solutions of geodesics of Schwarzschild black hole and the time conformal Schwarzschild black hole. We observe that the Schwarzschild spacetime admits the time conformal factor eepsilonf(t)e^{\epsilon f(t)}eepsilonf(t), where f(t)f(t)f(t) is an arbitrary function and epsilon\epsilonepsilon is very small which causes the perturbation in the spacetimes. This technique also re-scale the energy content of spacetime. We also investigate the thermal stability, horizons and energy conditions corresponding time conformal Schwarzschild spacetime. Also, we examine the dynamics of neutral and charged particle around time conformal Schwarzschild black hole. We investigate the circumstances under which the particle can escape from vicinity of black hole after collision with another particle. W...

Research paper thumbnail of M ar 2 02 0 N-extended Chern-Simons Carrollian supergravities in 2 + 1 spacetime dimensions

In this work we present the ultra-relativistic N -extended AdS Chern-Simons supergravity theories... more In this work we present the ultra-relativistic N -extended AdS Chern-Simons supergravity theories in three spacetime dimensions invariant under N -extended AdS Carroll superalgebras. We first consider the (2, 0) and (1, 1) cases; subsequently, we generalize our analysis to N = (N , 0), with N even, and to N = (p, q), with p, q > 0. The N -extended AdS Carroll superalgebras are obtained through the Carrollian (i.e., ultra-relativistic) contraction applied to an so(2) extension of osp(2|2) ⊗ sp(2), to osp(2|1) ⊗ osp(2, 1), to an so(N ) extension of osp(2|N ) ⊗ sp(2), and to the direct sum of an so(p) ⊕ so(q) algebra and osp(2|p) ⊗ osp(2, q), respectively. We also analyze the flat limit (l→ ∞, being l the length parameter) of the aforementioned N -extended Chern-Simons AdS Carroll supergravities, in which we recover the ultrarelativistic N -extended (flat) Chern-Simons supergravity theories invariant under N -extended super-Carroll algebras. The flat limit is applied at the level of...