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Evolution of expansion-free spherically symmetric self-gravitating non-dissipative fluids and some analytical solutions

Rajesh Kumar

http://orcid.org/0000-0002-2582-7245

Department of Mathematics & Statistics, DDU Gorakhpur University, Gorakhpur, India

E-mail Address: rkmath09@gmail.com

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and

Sudhir Kumar Srivastava

Department of Mathematics & Statistics, DDU Gorakhpur University, Gorakhpur, India

E-mail Address: sudhirpr66@rediffmail.com

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https://doi.org/10.1142/S0219887818500585Cited by:8 (Source: Crossref)

Abstract

We consider the distribution of spherically symmetric self-gravitating non-dissipative (but anisotropic) fluids under the expansion-free condition which requires the existence of vacuum cavity within the fluid distribution. The Darmois junction condition is investigated for matching the spherically symmetric metric to an internal vacuum cavity (Minkowski space-time). We have studied some analytical models, total of three family of solutions out of which two satisfy the junction conditions over both the hypersurfaces. The models are investigated under some known dynamical assumptions which further provide analytical solution in each family.

Keywords:

AMSC: 83C05, 83F05, 83C75

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