Spherical collapse inf(R)gravity and the Belinskii-Khalatnikov-Lifshitz conjecture

Abstract

Spherical scalar collapse in f (R) gravity is studied numerically in double-null coordinates in the Einstein frame. Dynamics in the vicinity of the singularity of the formed black hole is examined via mesh refinement and asymptotic analysis. Before the collapse, the scalar degree of freedom f is coupled to a physical scalar field, and general relativity is restored. During the collapse, the major energy of the physical scalar field moves to the center. As a result, f loses the coupling and becomes light, and gravity transits from general relativity to f (R) gravity. Due to strong gravity from the singularity and the low mass of f , f will cross the minimum of the potential and approach zero. Therefore, the dynamical solution is significantly different from the static solution of the black hole in f (R) gravity-it is not the de Sitter-Schwarzschild solution as one might have expected. f tries to suppress the evolution of the physical scalar field, which is a dark energy effect. As the singularity is approached, metric terms are dominant over other terms. The Kasner solution for spherical scalar collapse in f (R) theory is obtained and confirmed by numerical results. These results support the Belinskii-Khalatnikov-Lifshitz conjecture well.

Spherically symmetric collapse of a perfect fluid in f(R) gravity

“…which is a result of the simplication of the expressions for the density and pressure in equations (17,18). The conclusion that the the density and pressure remaining inhomogeneous strongly supports the result obtained by Goswami et al, which is the only extensive work in f (R) collapse.…”

“…There has been a recent investigation using numerical simulations by Borisov, Jain and Zhang [17]. Guo, Wang and Frolov [18] also used a numerical simulation to investigate an f (R) collapse in Einstein frame, where the nonlinear contribution of the curvature in the action is reduced to a nonminimally coupled scalar field via a conformal transformation. Sharif and Kausar [19] investigated the collapse of a spherical fluid distribution with a constant Ricci curvature.…”

Gravitational collapse in f (R) gravity for a spherically symmetric spacetime admitting a homothetic Killing vector

“…The stability of collapsing models in f (R) theories has been investigated by Sharif and Yousaf [11,12]. Apart from these analytical work, numerical techniques have also been utilized in f (R) gravity collapse by Borisov, Jain and Zhang [13] and also by Guo, Wang and Frolov [14].…”

On the hyperbolicity and stability of $$3+1$$ 3 + 1 formulations of metric f(R) gravity

“…In fact, with the exception of [83], the Cauchy problem of f (R) has mostly been studied by utilizing this equivalence, see [23,44] for examples involving numerical applications. However, such dynamical equivalence should be interpreted with caution [48,20,28,56].…”