Author
Ramesh Tikekar
Other affiliations: Inter-University Centre for Astronomy and Astrophysics
Bio: Ramesh Tikekar is an academic researcher from Sardar Patel University. The author has contributed to research in topics: General relativity & Spacetime. The author has an hindex of 23, co-authored 41 publications receiving 1257 citations. Previous affiliations of Ramesh Tikekar include Inter-University Centre for Astronomy and Astrophysics.
Papers
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TL;DR: In this article, a static spherically symmetric model based on an exact solution of Einstein's equations is given which will permit densities of the order of 2 × 1014 gm cm-3, radii of a few kilometers and masses up to about four times the solar mass.
Abstract: Assuming that the physical 3-spacet = const in a superdense star is spheroidal, a static spherically symmetric model based on an exact solution of Einstein’s equations is given which will permit densities of the order of 2 × 1014 gm cm-3, radii of the order of a few kilometers and masses up to about four times the solar mass.
183 citations
TL;DR: In this paper, exact Bianchi III cosmological solutions of massive strings in the presence of magnetic field are obtained and their physical features are discussed, and some string solutions in which magnetic fields are absent are also discussed.
Abstract: Following the techniques used by Letelier and Stachel some exact Bianchi III cosmological solutions of massive strings in the presence of magnetic field are obtained and their physical features are discussed. Some string solutions in which magnetic fields are absent are also discussed.
134 citations
TL;DR: In this article, a static spherically symmetric model based on an analytic closed-form solution of Einstein's field equations is presented, assuming the density of the order of 2×1014 g/cm−3.
Abstract: Assuming that the physical three‐space in a relativistic superdense star has the geometry of a three‐spheroid, a static spherically symmetric model based on an analytic closed‐form solution of Einstein’s field equations is presented. Assuming the density of the order of 2×1014 g cm−3, estimates of the total mass and size of the stars of the model are obtained for various values of a density‐variation parameter that is suitably defined. The total mass and the boundary radius of each of these models are of the order of the mass and size of a neutron star.
129 citations
TL;DR: In this article, a new exact closed form solution of Einstein's field equations was described for describing the space-time in the interior of a fluid sphere in equilibrium, and the suitability of this solution for describing a relativistic superdense star is discussed and the stability of the model under radial pulsations is examined.
Abstract: A new exact closed form solution of Einstein's field equations is reported describing the space-time in the interior of a fluid sphere in equilibrium. The physical 3-space,t=constant of its space-time has the geometry of a 3-pseudo spheroid. The suitability of this solution for describing the model of a relativistic superdense star is discussed and the stability of the model under radial pulsations is examined.
65 citations
TL;DR: In this paper, a physically relevant explicit Bianchi VI0 solution of string cosmology with magnetic field is reported, which includes two models describing distributions of Takabayashi strings and geometric strings respectively.
Abstract: Following the techniques used by Letelier and Stachel some new physically relevant explicit Bianchi VI0 solutions of string cosmology with magnetic field are reported. They include two models describing distributions of Takabayashi strings and geometric strings respectively.
59 citations
Cited by
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01 Dec 1982
TL;DR: In this paper, the authors study the solutions of the gravitational field equations which describe the contraction of a heavy star, and give general and qualitative arguments on the behavior of the metrical tensor as the contraction progresses.
Abstract: When all thermonuclear sources of energy are exhausted a sufficiently heavy star will collapse. Unless fission due to rotation, the radiation of mass, or the blowing off of mass by radiation, reduce the star's mass to the order of that of the sun, this contraction will continue indefinitely. In the present paper we study the solutions of the gravitational field equations which describe this process. In I, general and qualitative arguments are given on the behavior of the metrical tensor as the contraction progresses: the radius of the star approaches asymptotically its gravitational radius; light from the surface of the star is progressively reddened, and can escape over a progressively narrower range of angles. In II, an analytic solution of the field equations confirming these general arguments is obtained for the case that the pressure within the star can be neglected. The total time of collapse for an observer comoving with the stellar matter is finite, and for this idealized case and typical stellar masses, of the order of a day; an external observer sees the star asymptotically shrinking to its gravitational radius.
1,052 citations
Journal Article•
TL;DR: In this article, the interior and exterior solutions to the field equations of a uniform density vacuum string were derived and the exterior solution correspond to a conical space while the interior solution is that of a spherical cap.
Abstract: Exact interior and exterior solutions to Einstein's field equations are derived for vacuum strings. The exterior solution for a uniform density vacuum string corresponds to a conical space while the interior solution is that of a spherical cap. For Mu equals 0-1/4 the external metric is ds-squared = -dt-squared + dr-squared + (1-4 Mu)-squared r-squared dphi-squared + dz-squared, where Mu is the mass per unit length in the string in Planck masses per Planck length. A maximum mass per unit length for a string is 6.73 x 10 to the 27th g/cm. It is shown that strings cause temperature fluctuations in the cosmic microwave background and produce equal brightness double QSO images separated by up to several minutes of arc. Formulae for lensing probabilities, image splittings, and time delays are derived for strings in a realistic cosmological setting. String searches using ST, the VLA, and the COBE satellite are discussed.
473 citations
TL;DR: In this paper, interior perfect fluid solutions for the Reissner-nordstrom metric are studied on the basis of a new classification scheme, which specifies which two of the characteristics of the fluid are given functions and accordingly picks up one of the three main field equations, the other two being universal.
Abstract: Interior perfect fluid solutions for the Reissner-Nordstr\"om metric are studied on the basis of a new classification scheme. It specifies which two of the characteristics of the fluid are given functions and accordingly picks up one of the three main field equations, the other two being universal. General formulas are found for charged de Sitter solutions, the case of a constant energy component of the energy-momentum tensor, the case of known pressure (including charged dust), and the case of a linear equation of state. Explicit new global solutions, mainly in elementary functions, are given as illustrations. The known solutions are briefly reviewed and corrected.
311 citations
TL;DR: A detailed study of the singularity theorems is presented in this article, where the authors discuss the plausibility and reasonability of their hypotheses, applicability and implications of singularity theories, as well as the theorem itself.
Abstract: A detailed study of the singularity theorems is presented. I discuss the plausibility and reasonability of their hypotheses, the applicability and implications of the theorems, as well as the theorems themselves. The consequences usually extracted from them, some of them without the necessary rigour, are widely and carefully analysed with many clarifying examples and alternative views.
283 citations
TL;DR: In this article, the authors considered the general situation of a compact relativistic body with anisotropic pressures in the presence of the electromagnetic field and provided exact solutions to the Einstein-Maxwell system.
Abstract: We consider the general situation of a compact relativistic body with anisotropic pressures in the presence of the electromagnetic field The equation of state for the matter distribution is linear and may be applied to strange stars with quark matter Three classes of new exact solutions are found to the Einstein–Maxwell system This is achieved by specifying a particular form for one of the gravitational potentials and the electric field intensity We can regain anisotropic and isotropic models from our general class of solutions A physical analysis indicates that the charged solutions describe realistic compact spheres with anisotropic matter distribution The equation of state is consistent with dark energy stars and charged quark matter distributions The masses and central densities correspond to realistic stellar objects in the general case when anisotropy and charge are present
199 citations