Collapse in f ( R ) gravity and the method of R matching
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Regular Article - Theoretical Physics
Collapse in f (R) gravity and the method of R matching Sandip Chowdhurya , Kunal Palb , Kuntal Palc , Tapobrata Sarkard Department of Physics, Indian Institute of Technology, Kanpur 208016, India
Received: 2 December 2019 / Accepted: 10 September 2020 © The Author(s) 2020
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 α R 2 , 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.
1 Introduction Einstein’s general relativity (GR) is the most successful theory of gravity till date, although modifications to GR continue to attract much attention. One of the primary reasons for attempting such modifications has to do with explaina e-mail:
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ing the late time acceleration of the universe. It is known that this phenomenon is compatible with GR in the presence of a dark energy component in the stress tensor. However, much work has been done over the last two decades in trying to explain cosmic acceleration of the universe without invoking dark forms of matter and energy. One such candidate theory is f (R) gravity1 (for a sampling of the literature, see the excellent reviews [1–7]) obtained by modifying the Einstein–Hilbert action to one which includes a regular nonlinear function f (R) of the Ricci scalar R, i.e one in which the Lagrangian density is R + f (R), apart from the matter part. In this paper, we will deal with the specific model f (R) = α R 2 , with α being a positive constant, a model proposed in [8]. While phenomenological studies of f (R) gravity abound in the literature, there has been relatively lesser focus on co
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