Although f (R) modification of late time cosmology is successful in explaining present cosmic acceleration, it is difficult to satisfy the fifth-force constraint simultaneously. Even when the fifth-force constraint is satisfied, the effective scalar degree of freedom may move to a point (close to its potential minima) in the field space where the Ricci scalar diverges. We elucidate this point further with a specific example of f (R) gravity that incorporates several viable f (R) gravity models in the literature. In particular, we show that the nonlinear evolution of the scalar field in pressureless contracting dust can easily lead to the curvature singularity, making this theory unviable.
Here, we derive the metric for the spacetime around rotating object for the gravity action having nonlocal correction of R −2 R to the Einstein-Hilbert action. Starting with the generic stationary, axisymmetric metric, we solve the equations of motion in linearized gravity limit for the modified action including energy-momentum tensor of the rotating mass. We also derive the rotating metric from the static metric using the Demanski-Janis-Newmann algorithm. Finally, we obtain the constraint on the value of M by calculating the frame dragging effect in our theory and comparing it with that of General Relativity and Gravity Probe B results, where M is the mass scale of the theory.
f (R) modifications of Einstein's gravity is an interesting possibility to explain the late time acceleration of the Universe. In this work we explore the cosmological viability of one such f (R) modification proposed in [1]. We show that the model violates fifth-force constraints. The model is also plagued with the issue of curvature singularity in a spherically collapsing object, where the effective scalar field reaches to the point of diverging scalar curvature.
The strong gravitational field near massive blackhole is an interesting regime to test General Relativity (GR) and modified gravity theories. The knowledge of spacetime metric around a blackhole is a primary step for such tests. Solving field equations for rotating blackhole is extremely challenging task for the most modified gravity theories. Though the derivation of Kerr metric of GR is also demanding job, the magical Newmann–Janis algorithm does it without actually solving Einstein equation for rotating blackhole. Due to this notable success of Newmann–Janis algorithm in the case of Kerr metric, it has been being used to obtain rotating blackhole solution in modified gravity theories. In this work, we derive the spacetime metric for the external region of a rotating blackhole in a nonlocal gravity theory using Newmann–Janis algorithm. We also derive metric for a slowly rotating blackhole by perturbatively solving field equations of the theory. We discuss the applicability of Newmann–Janis algorithm to nonlocal gravity by comparing slow rotation limit of the metric obtained through Newmann–Janis algorithm with slowly rotating solution of the field equation.
Recently the nonlocal gravity theory has come out to be a good candidate for an effective field theory of quantum gravity and also it can provide rich phenomenology to understand late time accelerating expansion of the universe. For any valid theory of gravity, it has to surmount solar system tests as well as strong field tests. Having motivations to prepare the framework for the strong field test of the modified gravity using Extreme Mass Ratio Inspirals (EMRIs), here we try to obtain the metric for Kerr-like black hole for a nonlocal gravity model known as RR model and calculate the shift in orbital frequencies of a test particle moving around the black hole. We also derive the metric for a rotating object in the weak gravity regime for the same model.
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