Salah Haggag - Academia.edu (original) (raw)

Papers by Salah Haggag

ERU Research Journal, Oct 28, 2023

Physica Scripta

A new approach to construct relativistic stellar models is presented. The problem is formulated a... more A new approach to construct relativistic stellar models is presented. The problem is formulated as an optimal control problem, with an objective function to be optimized. As illustration, the problem is formulated and solved, with the rest mass as the objective function to be minimized, in three cases. First, if the density is piece-wise continuous the optimal solution is the spherical shell. Second, if the density gradient is piece-wise continuous the optimal solution has constant density. Third, if the speed of sound does not exceed that of light, the optimal solution has a linear equation of state. Thus, using this new approach, the equation of state is determined by a physical motivation. Results support the suggestion that the linear equation of state could represent a relativistic incompressible fluid. Extensions to some other configurations are explored.

General Relativity and Gravitation, 1999

Kramer' s formulation of Einstein' s ® eld equations for static perfect¯uid cylinders is co nside... more Kramer' s formulation of Einstein' s ® eld equations for static perfect¯uid cylinders is co nsidered. Three approac hes are followed in seeking solutions of Kramer' s equations. First, a particular integral is found which repro duces a previously known class of four solutions. Secon d, a fairly general ansatz is suggested, whereb y a class of six new solutions is deriv ed. Finally, the problem for an incompressible p erfect¯uid, with constan t energy densit y, is redu ced to a single second order equ ation. All solutions are regular ev erywhere. Constrain ts are imp osed on the solutions parameters such that energy conditions are satis® ed and hence the solutions are physically reasonable.

Astrophysics and Space Science, 2003

The condition of hydrostatic equilibrium of relativistic stellar models is formulated as an optim... more The condition of hydrostatic equilibrium of relativistic stellar models is formulated as an optimal control problem. Application of Pontryagin's maximum principle leads directly to the Tolman-Oppenheimer-Volkoff equation.

Classical and Quantum Gravity, 1996

A class of four static cylindrically symmetric perfect-fluid solutions is derived using a formula... more A class of four static cylindrically symmetric perfect-fluid solutions is derived using a formulation given by Kramer. The solutions are regular and satisfy energy conditions inside cylinders of bounded radii at which the pressure vanishes. Matching to the exterior Levi-Civita metric is achieved and thus the solutions could represent cylindrical sources of gravitational fields.

Astrophysics and Space Science, 1995

Einstein field equations for a static and spherically symmetric perfect fluid are considered. A f... more Einstein field equations for a static and spherically symmetric perfect fluid are considered. A formulation given by Patiño and Rago is used to obtain a class of nine solutions, two of them are Tolman solutions I, IV and the remaining seven are new. The solutions are the correct ones corresponding to expressions derived by Patiño and Rago which have been

Astrophysics and Space Science, 1990

Einstein's interior field equations in general relativity are considered when spacetime is static... more Einstein's interior field equations in general relativity are considered when spacetime is static and axisymmetric and the energy-momentum tensor represents an anisotropic fluid. After imposing a set of simplifying assumptions a two-parameter solution is derived and its properties are discussed. The solution is found to be physically reasonable in a certain range of the parameters in which case the metric could represent a core of anisotropie matter.

A closed universe with maximum life-time is constructed using optimal control. Einstein's fie... more A closed universe with maximum life-time is constructed using optimal control. Einstein's field equations are used with varying cosmological "constant". The second time derivative of the Hubble parameter acts as the control function in the optimal control model.

The problem of static incompressible perfect fluid cylinders in general relativity is considered.... more The problem of static incompressible perfect fluid cylinders in general relativity is considered. A power series solution is obtained using a single second order equation in Kramer’s formulation. Convergence of the solution is demonstrated. The metric is matched to the exterior Levi-Civita (LC) metric. Regularity and energy conditions are satisfied, and hence the solution is a physically reasonable source for the LC spacetime.

This paper presents a review of the use of Computer Algebra Systems in General Relativity researc... more This paper presents a review of the use of Computer Algebra Systems in General Relativity research and teaching. On one hand, the impact of using Computer Algebra Systems in General Relativity research is illustrated by pointing out some important achievements in the field. In particular, by using Computer Algebra Systems, the present author has been able to obtain results that would have been almost impossible otherwise. On the other hand, Computer Algebra Systems can be a very helpful tool in teaching and learning GR. Some reports on using Computer Algebra Systems in teaching General Relativity are outlined.

It is shown that, for the Curzon metric, there exists no perfect-fluid source for which the equip... more It is shown that, for the Curzon metric, there exists no perfect-fluid source for which the equipressure surfaces are coordinate spheres.

arXiv: General Relativity and Quantum Cosmology, 2019

The problem of a static cylindrically symmertic incompressible perfect fluid in general relativit... more The problem of a static cylindrically symmertic incompressible perfect fluid in general relativity is considered. Using Kramer's formulation of the field equations, the problem is reduced into the single nonlinear second order differential equation [ 4 (z^2 - 2 z y - z^3 y + y^2 + 2 z^2 y^2 - z y^3) y'' + (8 z + 16 y

Gravitation and Cosmology

Cosmological inflationary models based on a self-interacting scalar field are considered. A slow-... more Cosmological inflationary models based on a self-interacting scalar field are considered. A slow-roll model is formulated as an optimal control problem. Application of Pontryagin’s maximum principle leads to an exact solution.

General Relativity and Gravitation Volume 1, Jul 1, 1983

Il Nuovo Cimento B, Apr 1, 2001

Il Nuovo Cimento B, 2003