L K Patel
Articles written in Pramana – Journal of Physics
Volume 14 Issue 4 April 1980 pp 253-262 General Relativity
Some solutions of the Einstein-Maxwell equations in general relativity
A solution of the Einstein-Maxwell equations corresponding to source-free electromagnetic field plus pure radiation is obtained. The solution is algebraically special. A particular case of the solution is considered which encompasses many known solutions. Among them is a radiating Ruban metric.
Volume 16 Issue 5 May 1981 pp 375-383 General Relativity
A NUT-like electrovac spacetime
A solution of the Einstein-Maxwell equations corresponding to source-free electromagnetic field is obtained. The solution is algebraically special. A particular case of the solution is considered which includes Brill’s solution. The details regarding the solution are also discussed.
Volume 26 Issue 3 March 1986 pp 171-178 General Relativity
A radiating Kerr-Newman solution
A non-static exact solution of Einstein’s equations corresponding to a field of flowing null radiation plus an electromagnetic field is presented. The geometry of the solution is described by the Kerr-Schild metric. The solution admits a shear-free, geodetic null congruence. It has the symmetry of the Kerr-Newman solution and when a certain parameter is put equal to zero the solution becomes static and reduces to the Kerr-Newman solution.
Volume 27 Issue 1-2 July 1986 pp 63-72 Electromagnetics, Statistical Mechanics And General Relativity
Gravitational fields with space-times of Bianchi type IX
Spatially homogeneous space-times of Bianchi type IX are considered. A general scheme for the derivation of exact solutions of Einstein’s equations corresponding to perfect fluid plus pure radiation fields is outlined. Some simple rotating Bianchi type IX cosmological models are presented. The details of these solutions are also discussed.
Volume 28 Issue 2 February 1987 pp 109-115 General Relativity
Kerr-Newman metric in deSitter background
L K Patel Sharda S Koppar P V Bhatt
In addition to the Kerr-Newman metric with cosmological constant several other metrics are presented giving Kerr-Newman type solutions of Einstein-Maxwell field equations in the background of deSitter universe. The electromagnetic field in all the solutions is assumed to be source-free. A new metric of what may be termed as an electrovac rotating de-Sitter space-time—a space-time devoid of matter but containing source-free electromagnetic field and a null fluid with twisting rays—has been presented. In the absence of the electromagnetic field, our solutions reduce to those discussed by Vaidya.
Volume 32 Issue 6 June 1989 pp 731-739 General Relativity And Gravitation
Radiating Kerr particle in Einstein universe
A generalized Kerr-NUT type metric is considered in connection with Einstein field equations corresponding to perfect fluid plus a pure radiation field. A general scheme for obtaining the exact solutions of these field equations is developed. Two physically meaningful particular cases are investigated in detail. One gives the field of a radiating Kerr particle embedded in the Einstein universe. The other solution may probably represent a deSitter-like universe pervaded by a pure radiation field.
Volume 37 Issue 1 July 1991 pp 1-11
Some new radiating Kerr-Newman solutions
L K Patel S S Koppar Tajinder Singh
Three exact non-static solutions of Einstein-Maxwell equations corresponding to a field of flowing null radiation plus an electromagnetic field are presented. These solutions are non-static generalizations of the well known Kerr-Newman solution. The current vector is null in all the three solutions. These solutions are the electromagnetic generalizations of the three generalized radiating Kerr solutions discussed by Vaidya and Patel. The solutions discussed by us describe the exterior gravitational fields of rotating radiating charged bodies. Many known solutions are derived as particular cases.
Volume 39 Issue 1 July 1992 pp 17-25 Research Articles
Non-adiabatic gravitational collapse of charged radiating fluid spheres
Dynamical equations governing the non-adiabatic collapse of a shear-free spherical distribution of unisotropic matter in the presence of charge are obtained. A brief outline of constructing a model describing collapse of a charged radiating fluid sphere in the set up developed is given.
Volume 42 Issue 6 June 1994 pp 483-489
Some exact solutions in Bianchi VI_{0} string cosmology
Following the techniques used by Letelier and Stachel some new physically relevant explicit Bianchi VI_{0} solutions of string cosmology with magnetic field are reported. They include two models describing distributions of Takabayashi strings and geometric strings respectively.
Volume 44 Issue 4 April 1995 pp 303-316
On singularity-free spacetimes
Naresh Dadhich L K Patel R Tikekar
We consider here the metric for the singularity-free family of fluid models. The metric is unique for cylindrically symmetric space-time with metric potentials being separable functions of radial and time coordinates in the comoving coordinates. It turns out that fluid models separate out into two classes, with
Volume 46 Issue 5 May 1996 pp 331-339
Cosmic strings in Bianchi II, VIII and IX spacetimes: Integrable cases
L K Patel S D Maharaj P G L Leach
We investigate the integrability of cosmic strings in Bianchi II, VIII and IX space-times using a Lie symmetry analysis. The behaviour of the gravitational field is governed by solutions of a single second order nonlinear differential equation. We demonstrate that this equation is integrable and admits an infinite family of physically reasonable solutions. Particular solutions obtained by other authors are shown to be special cases of our class of solutions.
Volume 46 Issue 5 May 1996 pp 341-348
A spherically symmetric gravitational collapse-field with radiation
An interior spherically symmetric solution of Einstein’s field equations corresponding to perfect fluid plus a flowing radiation-field is presented. The physical 3-space
Volume 47 Issue 1 July 1996 pp 33-39 Research Articles
Stationary rotating string world models with a magnetic field
Following the techniques used by Letelier and Stachel some new physically relevant stationary solutions of string cosmology with magnetic field are presented. In these solutions, the flow vector of matter has non-zero rotation and the cosmological constant is taken to be non-zero. Previously known solutions are derived as particular cases from our class of solutions. Some string models with vanishing cosmological constant are also discussed.
Volume 47 Issue 5 November 1996 pp 387-392
A class of stationary rotating string cosmological models
We obtain a one parameter class of stationary rotating string cosmological models of which the well-known Gödel universe is a particular case. By suitably choosing the free parameter function, it is always possible to satisfy the energy conditions. The rotation of the model hinges on the cosmological constant which turns out to be negative. String-dust distribution in Gödel-type universes is also briefly discussed.
Volume 48 Issue 3 March 1997 pp 819-824
Higher dimensional Vaidya metric in Einstein and de Sitter background
Spherically symmetric non-static higher dimensional metrics are considered in connection with Einstein’s field equations. Two exact solutions are derived. One of them corresponds to a mixture of perfect fluid and pure radiation field and represents higher dimensional Vaidya metric in the cosmological background of Einstein static universe. The other corresponds to a pure radiation field and represents higher dimensional Vaidya metric in the background de Sitter universe. For both of these solutions, the cosmological constant is taken to be non-zero. Many known solutions are derived as particular cases.
Volume 49 Issue 2 August 1997 pp 213-224 Research Articles
Inhomogeneous cosmological models with heat flux
L K Patel Ramesh Tikekar Naresh Dadhich
We present a general class of inhomogeneous cosmological models filled with non-thermalized perfect fluid by assuming that the background spacetime admits two space-like commuting Killing vectors and has separable metric coefficients. The singularity structure of these models depends on the choice of the parameters and the metric functions. A number of previously known perfect fluid models follow as particular cases of this general class. Physical and geometrical features of these models are studied and the general expression for temperature distribution is given.
Volume 55 Issue 3 September 2000 pp 361-368 Research Articles
Rotating cylindrically symmetric Kaluza-Klein fluid model
Kaluza-Klein field equations for stationary cylindrically symmetric fluid models in standard Einstein theory are formulated and a set of physically viable solutions is reported. This set is believed to be the first such Kaluza-Klein solutions and it includes the Kaluza-Klein counterpart of Davidson’s solution describing spacetime of a perfect fluid in rigid rotation about a regular axis.
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