Patrick Dasgupta | University of Delhi (original) (raw)

Papers by Patrick Dasgupta

Research paper thumbnail of The Cosmological Constant: A Tutorial

Springer eBooks, 1997

A pedagogical treatment to the effect of cosmological constant in the big-bang model is presented... more A pedagogical treatment to the effect of cosmological constant in the big-bang model is presented. It is argued that quantum fluctuations of the vacuum contributes to the cosmological constant and, essentially, leads to the cosmological constant problem. The equation of state corresponding to the cosmological constant is derived using the conservation of energy-momentum tensor in the Friedman models. The epoch after which the cosmological constant starts dominating over the non-relativistic matter is calculated. The evolution of the expansion factor as a function of cosmic time is discussed for the flat model case when A is positive. The ensuing age of the universe since the birth of high redshift QSOs is compared with the ages of the globular clusters. Collapse of a spherical dust ball and its virialization is considered. The flatness problem in the presence of a non-zero cosmological constant is discussed.

Research paper thumbnail of Effects of nonlinear membrane capacitance in the Hodgkin-Huxley model of action potential on the spike train patterns of a single neuron

EPL, Jun 1, 2023

The membrane capacitance has been shown to have a nonlinear dependence on the cell membrane poten... more The membrane capacitance has been shown to have a nonlinear dependence on the cell membrane potential in various types of cells. But the role of the nonlinear membrane capacitance in neurons has not been studied in detail. Herein, by considering the membrane capacitance to be a nonlinear parameter, we have explored the behavior of the cell membrane in three different types of neurons, i.e., squid giant neuron, rodent hippocampal interneuron, and rodent cortical neuron. The Hodgkin-Huxley equation of action potential was modified accordingly and simulated computationally. Our simulated results suggest that the action potential amplitude of a neuron almost remains the same for some duration when the voltage dependence parameter of the nonlinear capacitance increases up to a certain range, the initiation of the next action potential is delayed and the reduction in spike frequencies occurs in comparison to constant membrane capacitance. This indicates the importance of nonlinearity in membrane capacitance. Simultaneously the inter-spike interval (ISI) changes with the nonlinear membrane capacitance parameter. The gating dynamics show changes mainly in the activation current while the membrane capacitance is considered to be nonlinear. The above-mentioned computational results are primarily predictive pending experimental verification.

Research paper thumbnail of Effects of nonlinear membrane capacitance in the Hodgkin-Huxley model of action potential on the spike train patterns of a single neuron

Europhysics Letters

The membrane capacitance has been shown to have a nonlinear dependence on the cell membrane poten... more The membrane capacitance has been shown to have a nonlinear dependence on the cell membrane potential in various types of cells. But the role of the nonlinear membrane capacitance in neurons has not been studied in detail. Herein, by considering the membrane capacitance to be a nonlinear parameter, we have explored the behavior of the cell membrane in three different types of neurons, e.g., squid giant neuron, rodent hippocampal interneuron, and rodent cortical neuron. Hodgkin-Huxley's equation of action potential was modified accordingly and simulated computationally. Our simulated results suggest that the action potential amplitude of a neuron almost remains the same for some duration when the voltage dependence parameter of the nonlinear capacitance increases up to a certain range, the initiation of the next Action Potential is delayed and the reduction in spike frequencies occurs in comparison to constant membrane capacitance. This indicates the importance of nonlinearity in...

Research paper thumbnail of On the possibility of generating Supermassive Black Holes from self-gravitating Bose-Einstein Condensates comprising of Bosonic Dark Matter

Observed active galactic nuclei at redshifts of about 6 strongly suggest that supermassive black ... more Observed active galactic nuclei at redshifts of about 6 strongly suggest that supermassive black holes (SMBHs) had formed early on. Accretion of matter onto remnants of Population III stars leading to SMBHs is a very slow process, and therefore the model faces difficulties in explaining quasars detected at $ z \gtrsim 6$. In this paper we invoke Bose-Einstein condensation of dark bosons to demonstrate that existence of very light ($m \sim 10^{-23} \ \mbox{eV}$) spinless dark matter particles can not only lead to SMBHs of mass gtrsim1010Modot\gtrsim 10^{10} \ M_\odotgtrsim1010Modot at $ z \gtrsim 6$ but also such particles can masquerade as dark matter as well as dark energy.

Research paper thumbnail of Sound of Binary Black Holes - the First Direct Detection of Gravitational Waves

It is remarkable that almost exactly after 100 years of theoretical prediction of gravitational w... more It is remarkable that almost exactly after 100 years of theoretical prediction of gravitational waves by Einstein, the dedicated laser interferometric devices at USA directly detected these waves from a coalescing binary black hole event on September 14, 2015. The event GW150914 has also almost directly confirmed the existence of black holes. In this article, I provide a pedagogical introduction to the topic of gravitational waves. I also explore the issue of black hole thermodynamics in connection with the gravitational wave event GW150914, and show that the physical parameters estimated for this source is consistent with Hawking’s black hole area theorem.

Research paper thumbnail of Some exact stationary state solutions of a nonlinear Dirac equation in 2+ 1 dimensions

Research paper thumbnail of Workshop on gravitational waves and relativistic astrophysics

Pramana, 2004

ABSTRACT Discussions related to gravitational wave experiments viz. LIGO and LISA as well as to o... more ABSTRACT Discussions related to gravitational wave experiments viz. LIGO and LISA as well as to observations of supermassive black holes dominated the workshop sessions on gravitational waves and relativistic astrophysics in the ICGC-2004. A summary of seven papers that were presented in these workshop sessions has been provided in this article.

Research paper thumbnail of Comets in Ancient India

The Indo-aryans of ancient India observed stars and constellations for ascertaining auspicious ti... more The Indo-aryans of ancient India observed stars and constellations for ascertaining auspicious times in order to conduct sacrificial rites ordained by vedas. It is but natural that they would have recounted in the vedic texts about comets. In Rigveda (∼ 1700 -1500 BC) and Atharvaveda (∼ 1150 BC), there are references to dhumaketus and ketus, which stand for comets in Sanskrit. Rigveda mentions a fig tree with roots held up in the sky (Parpola 2010). Could it have been inspired by the hirsute appearance of a comet's tail? Varahamihira in 550 AD and Ballal Sena (∼ 1100 -1200 AD) have described a large number of comets recorded by ancient seers such as Parashara, Vriddha Garga, Narada, Garga, etc. In this article, I conjecture that an episode narrated in Mahabharata of a radiant king, Nahusha, ruling the heavens, and later turning into a serpent after he had kicked the seer Agastya (also the star Canopus), is a mythological retelling of a cometary event.

Research paper thumbnail of General Relativity and Compact Objects

Research paper thumbnail of Artificial Intelligence, Free-Will, Physics and All That Useless Ruminations

Research paper thumbnail of General Relativity for Pedestrians -- First 6 lectures

arXiv: Popular Physics, 2016

The 2017 Nobel Prize in physics awarded to Rainer Weiss, Barry C. Barish and Kip S. Thorne has ge... more The 2017 Nobel Prize in physics awarded to Rainer Weiss, Barry C. Barish and Kip S. Thorne has generated unprecedented interest in gravitational waves (GWs). These notes are based on my lectures on various occasions - in the University of Delhi as well as in different GW schools held in India following the exciting direct detection of GWs. I discuss GW flux and luminosity while pointing out a curious aspect associated with the latter - physical dimensions of c5/Gc^5/Gc5/G as well as third time derivative of mass quadrupole moment are that of luminosity. Formation of primordial black holes in the early universe and progenitors of fast radio bursts could have generated GW luminosity comparable to the Planck luminosity, c5/Gc^5/Gc5/G. I also address the issue of black hole thermodynamics in connection with the GW150914 event, demonstrating that this event is consistent with Hawking's black hole area theorem. In the last section, as an illustrative exercise, I estimate the GW amplitude expected...

Research paper thumbnail of Comets, Historical Records and Vedic Literature

arXiv: History and Philosophy of Physics, 2019

A verse in Book One of the Rigveda mentions a cosmic tree with rope-like aerial roots held up in ... more A verse in Book One of the Rigveda mentions a cosmic tree with rope-like aerial roots held up in the sky. Such an imagery might have ensued from the appearance of a comet having a ‘tree stem’-like tail, with branched out portions resembling aerial roots. Interestingly, a comet referred to as ‘heavenly tree’ was seen in 162 BC, as reported by old Chinese records. Because of weak surface gravity, cometary appendages may possibly assume strange shapes depending on factors like rotation, structure and composition of the comet as well as solar wind patterns. Varāhamihira and Ballala Sena listed several comets having strange forms as reported originally by ancient seers such as Parashara, Vriddha Garga, Narada and Garga.

Research paper thumbnail of Aspects of Black Hole Physics and Formation of Super-massive Black Holes from Ultra-light Dark Bosons

arXiv: General Relativity and Quantum Cosmology, 2018

First, we verify that the physical parameters estimated for the four directly detected gravitatio... more First, we verify that the physical parameters estimated for the four directly detected gravitational wave (GW) events involving coalescence of binary black holes (BHs) indeed uphold the second law of BH thermodynamics, strengthening further the case for BH physics. Non-spherical gravitational collapse leading to BH formation may entail very high GW luminosities during the final phase of implosion, reaching non-negligible fraction of Dyson luminosity simc5/G\sim c^5/G simc5/G. Most galaxies harbor supermassive black holes (SMBHs) in their nuclear regions. Several bright quasars detected at redshifts gtrsim\gtrsimgtrsim 6 are powered by accreting SMBHs of mass gtrsim109Modot\gtrsim 10^9 M_\odotgtrsim109Modot when the universe was only sim109\sim 10^9sim109 yrs old. We posit that creation of SMBHs occurs due to collapse (on dynamical time scales sim108\sim 10^8sim108 yrs) of ultra-light bosonic dark matter (DM) particles that have undergone Bose-Einstein condensation. Furthermore, oscillations in DM Bose-Einstein condensates (BECs) triggered by tidal f...

Research paper thumbnail of Collapsing supra-massive magnetars: FRBs, the repeating FRB121102 and GRBs

Journal of Astrophysics and Astronomy

Research paper thumbnail of Gravity, Bose-Einstein Condensates and Gross-Pitaevskii Equation

Research paper thumbnail of Can the wave function of a single system be measured?

The problem of two interacting simple harmonic oscillators is analysed in the frame work of the a... more The problem of two interacting simple harmonic oscillators is analysed in the frame work of the adiabatic approximation. It is shown that even when the interaction is weak and switched on slowly, the wave function of the combined system is not separable in terms of the respective coordinates. This has serious repercussion on the recently proposed protective measurements.

Research paper thumbnail of Periodic Gravitational and Electromagnetic Radiation from a highly magnetized, spinning White Dwarf

A spinning white dwarf (WD) endowed with a misaligned magnetic field in excess of 101010^{10}1010 G may... more A spinning white dwarf (WD) endowed with a misaligned magnetic field in excess of 101010^{10}1010 G may develop sufficient ellipticity so as to lose rotational energy and angular momentum by emitting not only electromagnetic waves but also gravitational radiation. Discovery of RX J0648.0-4418 system, a WD in a binary with mass slightly over 1.2 $ M_{\dotcirc}$, and rotating with a short spin period of 13.2 s has provided an impetus to revisit the problem of WD spin evolution due to rotational energy loss. In this work, we have estimated the electromagnetic and gravitational wave luminosities from a rigidly rotating, magnetized WD by taking into consideration the change in its radius by employing scalar virial theorem. As regards equilibrium configurations of WD, we have shown that our analytical results agree well with detailed numerical models of Yoon & Langer (2005).

Research paper thumbnail of S. Chandrasekhar: White Dwarfs, H��� ion,.., Black holes, Gravitational waves

Research paper thumbnail of Rise and decay time of subpeaks in short duration bursts

AIP Conference Proceedings, 2000

Temporal profiles of subpeaks detected in GRBs, belonging to a sample of 65 short duration bursts... more Temporal profiles of subpeaks detected in GRBs, belonging to a sample of 65 short duration bursts selected from the 3B catalog, have been studied by fitting the former with lognormal functions since most subpeaks exhibit fast rise and slow decay. We present statistical evidence for a systematic increase in the ratio of rise to decay time with peak position. Using

Research paper thumbnail of Morphological properties of short duration Gamma Ray Bursts

Research paper thumbnail of The Cosmological Constant: A Tutorial

Springer eBooks, 1997

A pedagogical treatment to the effect of cosmological constant in the big-bang model is presented... more A pedagogical treatment to the effect of cosmological constant in the big-bang model is presented. It is argued that quantum fluctuations of the vacuum contributes to the cosmological constant and, essentially, leads to the cosmological constant problem. The equation of state corresponding to the cosmological constant is derived using the conservation of energy-momentum tensor in the Friedman models. The epoch after which the cosmological constant starts dominating over the non-relativistic matter is calculated. The evolution of the expansion factor as a function of cosmic time is discussed for the flat model case when A is positive. The ensuing age of the universe since the birth of high redshift QSOs is compared with the ages of the globular clusters. Collapse of a spherical dust ball and its virialization is considered. The flatness problem in the presence of a non-zero cosmological constant is discussed.

Research paper thumbnail of Effects of nonlinear membrane capacitance in the Hodgkin-Huxley model of action potential on the spike train patterns of a single neuron

EPL, Jun 1, 2023

The membrane capacitance has been shown to have a nonlinear dependence on the cell membrane poten... more The membrane capacitance has been shown to have a nonlinear dependence on the cell membrane potential in various types of cells. But the role of the nonlinear membrane capacitance in neurons has not been studied in detail. Herein, by considering the membrane capacitance to be a nonlinear parameter, we have explored the behavior of the cell membrane in three different types of neurons, i.e., squid giant neuron, rodent hippocampal interneuron, and rodent cortical neuron. The Hodgkin-Huxley equation of action potential was modified accordingly and simulated computationally. Our simulated results suggest that the action potential amplitude of a neuron almost remains the same for some duration when the voltage dependence parameter of the nonlinear capacitance increases up to a certain range, the initiation of the next action potential is delayed and the reduction in spike frequencies occurs in comparison to constant membrane capacitance. This indicates the importance of nonlinearity in membrane capacitance. Simultaneously the inter-spike interval (ISI) changes with the nonlinear membrane capacitance parameter. The gating dynamics show changes mainly in the activation current while the membrane capacitance is considered to be nonlinear. The above-mentioned computational results are primarily predictive pending experimental verification.

Research paper thumbnail of Effects of nonlinear membrane capacitance in the Hodgkin-Huxley model of action potential on the spike train patterns of a single neuron

Europhysics Letters

The membrane capacitance has been shown to have a nonlinear dependence on the cell membrane poten... more The membrane capacitance has been shown to have a nonlinear dependence on the cell membrane potential in various types of cells. But the role of the nonlinear membrane capacitance in neurons has not been studied in detail. Herein, by considering the membrane capacitance to be a nonlinear parameter, we have explored the behavior of the cell membrane in three different types of neurons, e.g., squid giant neuron, rodent hippocampal interneuron, and rodent cortical neuron. Hodgkin-Huxley's equation of action potential was modified accordingly and simulated computationally. Our simulated results suggest that the action potential amplitude of a neuron almost remains the same for some duration when the voltage dependence parameter of the nonlinear capacitance increases up to a certain range, the initiation of the next Action Potential is delayed and the reduction in spike frequencies occurs in comparison to constant membrane capacitance. This indicates the importance of nonlinearity in...

Research paper thumbnail of On the possibility of generating Supermassive Black Holes from self-gravitating Bose-Einstein Condensates comprising of Bosonic Dark Matter

Observed active galactic nuclei at redshifts of about 6 strongly suggest that supermassive black ... more Observed active galactic nuclei at redshifts of about 6 strongly suggest that supermassive black holes (SMBHs) had formed early on. Accretion of matter onto remnants of Population III stars leading to SMBHs is a very slow process, and therefore the model faces difficulties in explaining quasars detected at $ z \gtrsim 6$. In this paper we invoke Bose-Einstein condensation of dark bosons to demonstrate that existence of very light ($m \sim 10^{-23} \ \mbox{eV}$) spinless dark matter particles can not only lead to SMBHs of mass gtrsim1010Modot\gtrsim 10^{10} \ M_\odotgtrsim1010Modot at $ z \gtrsim 6$ but also such particles can masquerade as dark matter as well as dark energy.

Research paper thumbnail of Sound of Binary Black Holes - the First Direct Detection of Gravitational Waves

It is remarkable that almost exactly after 100 years of theoretical prediction of gravitational w... more It is remarkable that almost exactly after 100 years of theoretical prediction of gravitational waves by Einstein, the dedicated laser interferometric devices at USA directly detected these waves from a coalescing binary black hole event on September 14, 2015. The event GW150914 has also almost directly confirmed the existence of black holes. In this article, I provide a pedagogical introduction to the topic of gravitational waves. I also explore the issue of black hole thermodynamics in connection with the gravitational wave event GW150914, and show that the physical parameters estimated for this source is consistent with Hawking’s black hole area theorem.

Research paper thumbnail of Some exact stationary state solutions of a nonlinear Dirac equation in 2+ 1 dimensions

Research paper thumbnail of Workshop on gravitational waves and relativistic astrophysics

Pramana, 2004

ABSTRACT Discussions related to gravitational wave experiments viz. LIGO and LISA as well as to o... more ABSTRACT Discussions related to gravitational wave experiments viz. LIGO and LISA as well as to observations of supermassive black holes dominated the workshop sessions on gravitational waves and relativistic astrophysics in the ICGC-2004. A summary of seven papers that were presented in these workshop sessions has been provided in this article.

Research paper thumbnail of Comets in Ancient India

The Indo-aryans of ancient India observed stars and constellations for ascertaining auspicious ti... more The Indo-aryans of ancient India observed stars and constellations for ascertaining auspicious times in order to conduct sacrificial rites ordained by vedas. It is but natural that they would have recounted in the vedic texts about comets. In Rigveda (∼ 1700 -1500 BC) and Atharvaveda (∼ 1150 BC), there are references to dhumaketus and ketus, which stand for comets in Sanskrit. Rigveda mentions a fig tree with roots held up in the sky (Parpola 2010). Could it have been inspired by the hirsute appearance of a comet's tail? Varahamihira in 550 AD and Ballal Sena (∼ 1100 -1200 AD) have described a large number of comets recorded by ancient seers such as Parashara, Vriddha Garga, Narada, Garga, etc. In this article, I conjecture that an episode narrated in Mahabharata of a radiant king, Nahusha, ruling the heavens, and later turning into a serpent after he had kicked the seer Agastya (also the star Canopus), is a mythological retelling of a cometary event.

Research paper thumbnail of General Relativity and Compact Objects

Research paper thumbnail of Artificial Intelligence, Free-Will, Physics and All That Useless Ruminations

Research paper thumbnail of General Relativity for Pedestrians -- First 6 lectures

arXiv: Popular Physics, 2016

The 2017 Nobel Prize in physics awarded to Rainer Weiss, Barry C. Barish and Kip S. Thorne has ge... more The 2017 Nobel Prize in physics awarded to Rainer Weiss, Barry C. Barish and Kip S. Thorne has generated unprecedented interest in gravitational waves (GWs). These notes are based on my lectures on various occasions - in the University of Delhi as well as in different GW schools held in India following the exciting direct detection of GWs. I discuss GW flux and luminosity while pointing out a curious aspect associated with the latter - physical dimensions of c5/Gc^5/Gc5/G as well as third time derivative of mass quadrupole moment are that of luminosity. Formation of primordial black holes in the early universe and progenitors of fast radio bursts could have generated GW luminosity comparable to the Planck luminosity, c5/Gc^5/Gc5/G. I also address the issue of black hole thermodynamics in connection with the GW150914 event, demonstrating that this event is consistent with Hawking's black hole area theorem. In the last section, as an illustrative exercise, I estimate the GW amplitude expected...

Research paper thumbnail of Comets, Historical Records and Vedic Literature

arXiv: History and Philosophy of Physics, 2019

A verse in Book One of the Rigveda mentions a cosmic tree with rope-like aerial roots held up in ... more A verse in Book One of the Rigveda mentions a cosmic tree with rope-like aerial roots held up in the sky. Such an imagery might have ensued from the appearance of a comet having a ‘tree stem’-like tail, with branched out portions resembling aerial roots. Interestingly, a comet referred to as ‘heavenly tree’ was seen in 162 BC, as reported by old Chinese records. Because of weak surface gravity, cometary appendages may possibly assume strange shapes depending on factors like rotation, structure and composition of the comet as well as solar wind patterns. Varāhamihira and Ballala Sena listed several comets having strange forms as reported originally by ancient seers such as Parashara, Vriddha Garga, Narada and Garga.

Research paper thumbnail of Aspects of Black Hole Physics and Formation of Super-massive Black Holes from Ultra-light Dark Bosons

arXiv: General Relativity and Quantum Cosmology, 2018

First, we verify that the physical parameters estimated for the four directly detected gravitatio... more First, we verify that the physical parameters estimated for the four directly detected gravitational wave (GW) events involving coalescence of binary black holes (BHs) indeed uphold the second law of BH thermodynamics, strengthening further the case for BH physics. Non-spherical gravitational collapse leading to BH formation may entail very high GW luminosities during the final phase of implosion, reaching non-negligible fraction of Dyson luminosity simc5/G\sim c^5/G simc5/G. Most galaxies harbor supermassive black holes (SMBHs) in their nuclear regions. Several bright quasars detected at redshifts gtrsim\gtrsimgtrsim 6 are powered by accreting SMBHs of mass gtrsim109Modot\gtrsim 10^9 M_\odotgtrsim109Modot when the universe was only sim109\sim 10^9sim109 yrs old. We posit that creation of SMBHs occurs due to collapse (on dynamical time scales sim108\sim 10^8sim108 yrs) of ultra-light bosonic dark matter (DM) particles that have undergone Bose-Einstein condensation. Furthermore, oscillations in DM Bose-Einstein condensates (BECs) triggered by tidal f...

Research paper thumbnail of Collapsing supra-massive magnetars: FRBs, the repeating FRB121102 and GRBs

Journal of Astrophysics and Astronomy

Research paper thumbnail of Gravity, Bose-Einstein Condensates and Gross-Pitaevskii Equation

Research paper thumbnail of Can the wave function of a single system be measured?

The problem of two interacting simple harmonic oscillators is analysed in the frame work of the a... more The problem of two interacting simple harmonic oscillators is analysed in the frame work of the adiabatic approximation. It is shown that even when the interaction is weak and switched on slowly, the wave function of the combined system is not separable in terms of the respective coordinates. This has serious repercussion on the recently proposed protective measurements.

Research paper thumbnail of Periodic Gravitational and Electromagnetic Radiation from a highly magnetized, spinning White Dwarf

A spinning white dwarf (WD) endowed with a misaligned magnetic field in excess of 101010^{10}1010 G may... more A spinning white dwarf (WD) endowed with a misaligned magnetic field in excess of 101010^{10}1010 G may develop sufficient ellipticity so as to lose rotational energy and angular momentum by emitting not only electromagnetic waves but also gravitational radiation. Discovery of RX J0648.0-4418 system, a WD in a binary with mass slightly over 1.2 $ M_{\dotcirc}$, and rotating with a short spin period of 13.2 s has provided an impetus to revisit the problem of WD spin evolution due to rotational energy loss. In this work, we have estimated the electromagnetic and gravitational wave luminosities from a rigidly rotating, magnetized WD by taking into consideration the change in its radius by employing scalar virial theorem. As regards equilibrium configurations of WD, we have shown that our analytical results agree well with detailed numerical models of Yoon & Langer (2005).

Research paper thumbnail of S. Chandrasekhar: White Dwarfs, H��� ion,.., Black holes, Gravitational waves

Research paper thumbnail of Rise and decay time of subpeaks in short duration bursts

AIP Conference Proceedings, 2000

Temporal profiles of subpeaks detected in GRBs, belonging to a sample of 65 short duration bursts... more Temporal profiles of subpeaks detected in GRBs, belonging to a sample of 65 short duration bursts selected from the 3B catalog, have been studied by fitting the former with lognormal functions since most subpeaks exhibit fast rise and slow decay. We present statistical evidence for a systematic increase in the ratio of rise to decay time with peak position. Using

Research paper thumbnail of Morphological properties of short duration Gamma Ray Bursts

Research paper thumbnail of Creation of Supermassive Kerr Black Holes from the Gravitational Collapse of the Rotating BECs of Ultra-light Scalars

Supermassive Black Holes (SMBHs) have been detected in the nuclei of majority of galaxies. The re... more Supermassive Black Holes (SMBHs) have been detected in the nuclei of majority of galaxies. The red-shift observed for quasars and other Active Galactic Nuclei(AGNs) is very high so that the associated SMBHs have formed very early on. Conventional technique of accretion of baryonic matter/dark matter is too slow to be a viable model for the formation of these BHs in the early epoch. In recent years, there has been active research works concerning cosmological structure formation that involve coherent, ultra-light bosons in a dark fluid-like or fuzzy cold DM state. It has been shown recently that SMBHs can be generated at early times on dynamical time scales from collapsing Bose-Einstein Condensates (BECs) of ultra-light scalars that constitute portions of dark matter galactic halos. In this work, we extend the analysis to investigate the possibility of forming Kerr SMBHs from excited states of BECs associated with non-zero angular momenta. GP equation is used to know the evolution of the condensate via time-dependent variational method and different mass constraints are obtained for the identical bosons to form Kerr SMBHs of higher angular momenta. The collapse of the halo BEC clusters can emit Gravitational Waves(GW) and, amplitude, luminosity and frequency of the condensate GW are investigated. Finally, the validity of Hawking Area Theorem for black-hole binaries in the recent four GW events is also analyzed.

Research paper thumbnail of COMETS, HISTORICAL RECORDS AND VEDIC LITERATURE

A verse in book one of Rigveda mentions a cosmic tree with rope-like aerial roots held up in the ... more A verse in book one of Rigveda mentions a cosmic tree with rope-like aerial roots held up in the sky. Such an imagery might have ensued from the appearance of a comet having`tree stem' like tail, with branched out portions resembling aerial roots. Interestingly enough, a comet referred to as " heavenly tree " was seen in 162 BC, as reported by old Chinese records. Because of weak surface gravity, cometary appendages may possibly assume strange shapes depending on factors like rotation, structure and composition of the comet as well as solar wind pattern. Varahamihira and Ballala Sena listed several comets having strange forms as reported originally by ancient seers such as Parashara, Vriddha Garga, Narada and Garga. Mahabharata speaks of a mortal king Nahusha who ruled the heavens when Indra, king of gods, went into hiding. Nahusha became luminous and egoistic after absorbing radiance from gods and seers. When he kicked Agastya (southern star Canopus), the latter cursed him to become a serpent and fall from the sky. We posit arguments to surmise that this Mahabharata lore is a mythical recounting of a cometary event wherein a comet crossed Ursa Major, moved southwards with an elongated tail in the direction of Canopus and eventually went out of sight. In order to check whether such a conjecture holds water, a preliminary list of comets (that could have or did come close to Canopus) drawn from various historical records is presented and discussed.

Research paper thumbnail of Three Faces of the Aharanov-Bohm Phase - An Elementary Exposition

Beginning with the basic notions of quantum theory, impossibility of `trajectory' description f... more Beginning with the basic notions of quantum theory, impossibility of `trajectory' description for particles that ensues from uncertainty principle is discussed. Why the observed tracks in bubble/cloud chambers are not really the `trajectories' of high energy particles, rather they are simply the trails of the atoms/molecules excited or ionized in the direction of the high momenta of the incoming particles, are highlighted.

Thereafter, the notion of symmetry and its application to the non-relativistic Schrodinger equation have been delineated. The demand for U(1) gauge invariance and the resulting `gauge miracle', that automatically leads to the correct interaction terms describing the electromagnetic force between the charge particles and the field, have been elaborated upon.

A simple treatment, but with explicit derivation, of the Aharanov-Bohm effect, is presented, that underlines a strange phenomena - sites, impenetrable by charge particles but are threaded with magnetic field lines, conspire with a `Trojan Horse', namely the magnetic vector potential outside, to cause measurable shift in the double-slit interference fringes. This shift in the interference pattern is non-classical since the charge particles move in field-free regions.

The crucial Aharonov-Bohm (AB) phase that makes its entry in the above bizarre effect is also deployed to derive the observed magnetic flux quantisation in superconductors as well as the Dirac result which implies that the existence of a single magnetic monopole anywhere in the universe would entail quantisation of the product of a particle's electric charge and the monopole's magnetic charge. Nontrivial consequences of AB phase follow whenever the physical region accessible, from the point of view of the wavefunction of a charge particle, is multiply-connected.

Research paper thumbnail of The Puzzle of Fast Radio Bursts

This is a popular level article on an exciting variety of cosmic source. This new class of tran... more This is a popular level article on an exciting variety of cosmic source. This new class of transient radio sources is creating waves among the astronomers these days. These are bursts of radio waves detected around 1 GHz band, coming from random directions away from the Galactic plane, spread over a time interval of only few milli-seconds. Termed as Fast Radio Bursts (FRBs), by now about 30 such FRBs have been detected, with one of them (FRB 121102) displaying sporadic repetitions. Although the first FRB was discovered by Duncan Lorimer in 2007, one still does not know the real physical nature of these transient radio sources.

Research paper thumbnail of On Reasonable Effectiveness of Pedagogy in Mathematical Physics

It is an established fact that advanced mathematics is indispensable not only to physical science... more It is an established fact that advanced mathematics is indispensable not only to physical sciences but also to technology and economics. A thought-provoking article by Eugene Wigner, titled `The unreasonable effectiveness of mathematics in the Natural sciences' (1960), had essentially underscored this point.

Ironically, a large fraction of students in Indian universities are unable to cope well with subjects that are mathematics driven. Moreover, it is a double irony, since from time immemorial, India has produced several outstanding mathematicians - Pingala, Aryabhatta, Ramanujan, Harish-Chandra, etc. and also the recent Fields Medalists Manjula Bhargava and Akshay Venkatesh, two brilliant mathematicians of Indian origin.

From the point of view of epistemology, science relies on controlled measurements whose outcomes are numbers and therefore, for building a logical as well as consistent model to explain the results of experiments, the inherent framework must indeed be mathematical in nature. Furthermore, pure and abstract mathematics provide us that sixth sense which navigate us beyond our five senses employed to discover new scientific laws. Perhaps, if systems with artificial intelligence are made to learn abstract mathematics in the future, discovering fundamental laws of Nature would become easier.

To overcome the `maths-phobia' among the young, I suggest remedial measures like introducing recreational mathematics at the school level, as well as making basic concepts of mathematical physics more visual and exciting by employing mathematics based magic tricks in the bachelor’s program. The science museums across the country should also display interesting tricks and surprising outcomes that are based on mathematics and its applications.