NDLI: Exact Solutions of Einstein's Field Equations

Content Provider	Springer Nature Link
Author	Negi, P. S.
Copyright Year	2006
Abstract	We examine various well known exact solutions available in the literature to investigate the recent criterion obtained in Negi and Durgapal [Gravitation and Cosmology 7, 37 (2001)] 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 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 state of hydrostatic equilibrium in general relativity. The regular solutions with finite centre and non-zero surface densities which do not fulfill the criterion given by Negi and Durgapal (2001), in fact, cannot 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. This criterion 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 [that is, the state of hydrostatic equilibrium in 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 star clusters with arbitrary large central redshifts.
Starting Page	1684
Ending Page	1702
Page Count	19
File Format	PDF
ISSN	00207748
Journal	International Journal of Theoretical Physics
Volume Number	45
Issue Number	9
e-ISSN	15729575
Language	English
Publisher	Kluwer Academic Publishers-Plenum Publishers
Publisher Date	2006-07-07
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mathematical and Computational Physics Elementary Particles, Quantum Field Theory Quantum Physics Physics
Content Type	Text
Resource Type	Article
Subject	Physics and Astronomy Mathematics

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