Collapse in f(R) gravity and the method of R matching View Full Text


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DATE

2020-09-29

AUTHORS

Sandip Chowdhury, Kunal Pal, Kuntal Pal, Tapobrata Sarkar

ABSTRACT

Collapsing solutions in f(R) gravity are restricted due to junction conditions that demand continuity of the Ricci scalar and its normal derivative across the time-like collapsing hypersurface. These are obtained via the method of R-matching, which is ubiquitous in f(R) collapse scenarios. In this paper, we study spherically symmetric collapse with the modification term αR2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha R^2$$\end{document}, and use R-matching to exemplify a class of new solutions. After discussing some mathematical preliminaries by which we obtain an algebraic relation between the shear and the anisotropy in these theories, we consider two metric ansatzes. In the first, the collapsing metric is considered to be a separable function of the co-moving radius and time, and the collapse is shear-free, and in the second, a non-separable interior solution is considered, that represents gravitational collapse with non-zero shear viscosity. We arrive at novel solutions that indicate the formation of black holes or locally naked singularities, while obeying all the necessary energy conditions. The separable case allows for a simple analytic expression of the energy-momentum tensor, that indicates the positivity of the pressures throughout collapse, and is further used to study the heat flux evolution of the collapsing matter, whose analytic solutions are presented under certain approximations. These clearly highlight the role of modified gravity in the examples that we consider. More... »

PAGES

902

References to SciGraph publications

  • 2016-04-08. Spherically symmetric collapse of a perfect fluid in f(R) gravity in GENERAL RELATIVITY AND GRAVITATION
  • 2018-10-26. Conformally flat collapsing stars in f(R) gravity in GENERAL RELATIVITY AND GRAVITATION
  • 1997-05. The Expanding Universe in GENERAL RELATIVITY AND GRAVITATION
  • 1996-02. Kinematics and dynamics off(R) theories of gravity in GENERAL RELATIVITY AND GRAVITATION
  • 2008-02-20. Radiating gravitational collapse with shear viscosity revisited in GENERAL RELATIVITY AND GRAVITATION
  • 2010-06-23. f(R) Theories in LIVING REVIEWS IN RELATIVITY
  • 2010-02-03. On the stability of the shear–free condition in GENERAL RELATIVITY AND GRAVITATION
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    http://scigraph.springernature.com/pub.10.1140/epjc/s10052-020-08459-w

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    http://dx.doi.org/10.1140/epjc/s10052-020-08459-w

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