Interior Dynamics of Neutral and Charged Black Holes in f(R) Gravity

摘要

In this paper, we explore the interior dynamics of neutral and charged black holes in f ( R ) gravity. We transform f ( R ) gravity from the Jordan frame into the Einstein frame and simulate scalar collapses in flat, Schwarzschild, and Reissner-Nordström geometries. In simulating scalar collapses in Schwarzschild and Reissner-Nordström geometries, Kruskal and Kruskal-like coordinates are used, respectively, with the presence of f ′ and a physical scalar field being taken into account. The dynamics in the vicinities of the central singularity of a Schwarzschild black hole and of the inner horizon of a Reissner-Nordström black hole is examined. Approximate analytic solutions for different types of collapses are partially obtained. The scalar degree of freedom ϕ, transformed from f ′ , plays a similar role as a physical scalar field in general relativity. Regarding the physical scalar field in f ( R ) case, when d ϕ / d t is negative (positive), the physical scalar field is suppressed (magnified) by ϕ, where t is the coordinate time. For dark energy f ( R ) gravity, inside black holes, gravity can easily push f ′ to 1. Consequently, the Ricci scalar R becomes singular, and the numerical simulation breaks down. This singularity problem can be avoided by adding an R 2 term to the original f ( R ) function, in which case an infinite Ricci scalar is pushed to regions where f ′ is also infinite. On the other hand, in collapse for this combined model, a black hole, including a central singularity, can be formed. Moreover, under certain initial conditions, f ′ and R can be pushed to infinity as the central singularity is approached. Therefore, the classical singularity problem, which is present in general relativity, remains in collapse for this combined model.