Author
Ronald J. Adler
Bio: Ronald J. Adler is an academic researcher from American University. The author has contributed to research in topics: Schwarzschild metric & General relativity. The author has an hindex of 5, co-authored 8 publications receiving 1129 citations.
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TL;DR: In this paper, the interior of a static fluid sphere is solved in closed analytic form, and a physically reasonable equation of state and a maximum mass of 2/5 the fluid radius (in geometric units) are obtained.
Abstract: We solve the Einstein field equations for the interior of a static fluid sphere in closed analytic form. The model sphere obtained has a physically reasonable equation of state, and a maximum mass of 2/5 the fluid radius (in geometric units). As the maximum mass is approached the central density and pressure become infinite, while for masses greater than about 0.35 times the fluid radius the velocity of sound in portions of the fluid exceeds the velocity of light, indicating that the fluid is noncausal in this mass range. In the low mass limit the solution becomes identical to the Schwarzschild interior solution.
109 citations
TL;DR: In this paper, a simple derivation of the Schwarzschild and Kerr geometries by simplifying the Einstein free space field equations for the algebraically special form of metric studied by Kerr is presented.
Abstract: We present a simple derivation of the Schwarzschild and Kerr geometries by simplifying the Einstein free space field equations for the algebraically special form of metric studied by Kerr. This results in a system of two partial differential equations, the Laplace and eikonal equations, for a complex generating function. The metric tensor is a simple explicit functional of this generating function. The simplest solution generates the Schwarzschild geometry, while a displacement of the origin by ia in this solution generates the Kerr geometry.
68 citations
TL;DR: In this article, the authors give a fully relativistic and analytic solution for a slowly rotating neutron star model, which is based on the model described in Fig. 1 : A.
Abstract: We give a fully relativistic and analytic solution representing a slowly rotating neutron-star model.
21 citations
5 citations
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TL;DR: Extended Theories of Gravity as discussed by the authors can be considered as a new paradigm to cure shortcomings of General Relativity at infrared and ultraviolet scales, which is an approach that, by preserving the undoubtedly positive results of Einstein's theory, is aimed to address conceptual and experimental problems recently emerged in astrophysics, cosmology and High Energy Physics.
2,776 citations
01 Dec 1982
1,915 citations
TL;DR: In this paper, it was shown that the matrix elements of the symmetric energy-momentum tensor are cut-off dependent in renormalized perturbation theory for most renormalizable field theories.
1,002 citations
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TL;DR: In this paper, the authors discuss the cosmological and astrophysical implications of extra dimensions, and conclude that none of the three approaches can be ruled out on observational grounds at the present time.
929 citations
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TL;DR: In this paper, it is shown that the exterior Schwarzschild solution itself provides necessary conditions for the types of the density distributions to be considered inside the mass, in order to obtain exact solutions or equations of state compatible with the structure of general relativity.
Abstract: We examine various well known exact solutions available in the literature to investigate the recent criterion obtained in ref. [20] which should be fulfilled by any static and spherically symmetric solution in the state of hydrostatic equilibrium. It is seen that this criterion is fulfilled only by (i) the regular solutions having a vanishing surface density together with the pressure, and (ii) the singular solutions corresponding to a non-vanishing density at the surface of the configuration . On the other hand, the regular solutions corresponding to a non-vanishing surface density do not fulfill this criterion. Based upon this investigation, we point out that the exterior Schwarzschild solution itself provides necessary conditions for the types of the density distributions to be considered inside the mass, in order to obtain exact solutions or equations of state compatible with the structure of general relativity. The regular solutions with finite centre and non-zero surface densities which do not fulfill the criterion [20], in fact, can not meet the requirement of the `actual mass' set up by exterior Schwarzschild solution. The only regular solution which could be possible in this regard is represented by uniform (homogeneous) density distribution.
The criterion [20] provides a necessary and sufficient condition for any static and spherical configuration (including core-envelope models) to be compatible with the structure of general relativity. Thus, it may find application to construct the appropriate core-envelope models of stellar objects like neutron stars and may be used to test various equations of state for dense nuclear matter and the models of relativistic stellar structures like star clusters.
791 citations