Interior dynamics of neutral and charged black holes in f(R) gravity

Abstract

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 $f^{\prime }$ 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 $\varphi$, transformed from $f^{\prime }$, plays a similar role as a physical scalar field in general relativity. Regarding the physical scalar field in $f(R)$ case, when $d\varphi /dt$ is negative (positive), the physical scalar field is suppressed (magnified) by $\varphi$, where $t$ is the coordinate time. For dark energy $f(R)$ gravity, inside black holes, gravity can easily push $f^{\prime }$ 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 $f^{\prime }$ 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, $f^{\prime }$ 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.

35 pages, 22 figures. (Special Issue. Modified Gravity Cosmology: From Inflation to Dark Energy). Minor change. arXiv admin note: substantial text overlap with arXiv:1507.01806

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Cited by in corpus (1)

• Interior dynamics of neutral and charged black holes