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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.

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In this paper, we revisit the solar system tests of f (R) gravity. When the Sun sits in a vacuum, the field f is light, which leads to a metric different from the observations. We reobtain this result in a simpler way by directly focusing on the equations of motion for f (R) gravity in the Jordan frame. The discrepancy between the metric in the f (R) gravity and the observations can be alleviated by the chameleon mechanism. The implications from the chameleon mechanism on the functional form f (R) are discussed. Considering the analogy of the solar system tests to the false vacuum decay problem, the effective potentials in different cases are also explored. The combination of analytic and numerical approaches enables us to ascertain whether an f (R) model can pass the solar system tests or not.

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In this paper, we explore an idea of having Newton's constant change its value depending on the curvature scale involved. Such modification leads to a particular scalar-tensor gravity theory, with the Lagrangian derived from renormalization group (RG) flow arguments. Several of the well-known f (R) modified gravity models have remarkably simple description in terms of the infrared renormalization group, but not the "designer" types in general. We find that de Sitter-like accelerated expansion can be generated even in the absence of cosmological constant term, entirely due to running of the Newton's constant. In hopes of tackling the problem of cosmological constant's smallness, we explore the flows which are capable of generating exponential hierarchy between infrared and ultraviolet scales, and investigate cosmological evolution in the models thus derived.

In this paper, we explore the interior dynamics of neutral and charged black holes. Scalar collapses in flat, Schwarzschild, and Reissner-Nordström geometries are simulated. We examine 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. In simulating scalar collapses in Schwarzschild and ReissnerNordström geometries, Kruskal and Kruskal-like coordinates are used, respectively, with the presence of a scalar field being taken into account. It is found that, besides near the inner horizons of ReissnerNordström and Kerr black holes, mass inflation also takes place near the central singularity in neutral scalar collapse. Approximate analytic expressions for different types of mass inflation are partially obtained via a close interplay between numerical and analytical approaches and an examination of the connections between Schwarzschild black holes, Reissner-Nordström black holes, neutral collapse, and charge scattering. We argue that the mass inflations near the central singularity and the inner horizon are related to the localness of the dynamics in strong gravity regions. This is in accord with the Belinskii, Khalatnikov, and Lifshitz conjecture.

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