In this paper, the metric approach of f(R) theory of gravity is used to investigate the exact vacuum solutions of spatially homogeneous rotating spacetimes. For this purpose, R is replaced by f(R) in the standard Einstein-Hilbert action and the set of modified Einstein field equations reduce to a single equation. We adopt the assumption of constant Ricci scalar which maybe zero or non-zero. Moreover, the energy density of the non-trivial solution has been evaluated by using the generalized Landau-Lifshitz energy-momentum complex in the perspective of f(R) gravity for some appropriate f(R) model, which turns out to be a constant quantity.

# Category Archives: General Relativity

# Approximate Black Hole Binary Spacetime via Asymptotic Matching

We construct a fully-analytic, general relativistic, non-spinning black hole binary spacetime that approximately solves the vacuum Einstein equations everywhere in space and time for black holes sufficiently well-separated. The metric is constructed by asymptotically matching perturbed Schwarzschild metrics near each black hole to a two-body post-Newtonian metric far from them, and a two-body post-Minkowskian metric farther still. Asymptotic matching is done without linearizing about a particular time slice, and thus it is valid dynamically and for all times, provided the binary is sufficiently well-separated. This approximate global metric can be used for long dynamical evolutions of relativistic magnetohydrodynamical, circumbinary disks around inspiraling supermassive black holes to study a variety of phenomena.

# Jebsen-Birkhoff theorem and its stability in f(R) gravity

We prove a Jebsen-Birkhoff like theorem for f(R) theories of gravity in order to to find the necessary conditions required for the existence of the Schwarzschild solution in these theories and demonstrate that the rigidity of such solutions of f(R) gravity is valid even in the perturbed scenario.

# On the thermodynamic stability of rotating black holes in higher dimensions — a comparison of thermodynamic ensembles

Thermodynamic potentials relevant to the micro-canonical, the canonical and the grand-canonical ensembles, associated with rotating black holes in D-dimensions, are analysed and compared. Such black holes are known to be thermodynamically unstable, but the instability is a consequence of a subtle interplay between specific heats and the moments of inertia and it manifests itself differently in the different ensembles. A simple relation between the product of the specific heat and the determinant of the moment of inertia in both the canonical and the grand-canonical ensembles is derived. Myers-Perry black holes in arbitrary dimension are studied in detail. All temperature extrema in the micro-canonical ensemble are determined and classified. The specific heat and the moment of inertia tensor are evaluated in both the canonical and the grand-canonical ensembles in any dimension. All zeros and poles of the specific heats, as a function of the angular momenta, are determined and the eigenvalues of the isentropic moment of inertia tensor are also found and classified. It is further shown that many of the thermodynamic properties of a Myers-Perry black hole in D-2 dimensions can be obtained from those of a black hole in D dimensions by sending one of the angular momenta to infinity.

# Thermodynamics of the polymeric quantized Schwarzschild black hole

Polymer representation of quantum mechanics is an effective approach to loop quantum gravity. In this paper we develop statistical mechanics in the polymer framework. While to obtain energies of microstates one needs usually to solve the polymer-modified Schr\”{o}dinger equation, we have not adopted this strategy here since it is not an easy task due to the complicated form of the Schr\”{o}dinger equation in the polymer picture. Instead, we formulate the ensemble theory in polymer framework in a semi-classical regime through deformed density of states. We show that our results are in good agreement with those arising from quantum mechanical considerations. Applying this method to thermodynamics of quantum Schwarzschild black hole, we obtain corrections to the Bekenstein-Hawking entropy due to loop quantum gravity effects.

# A perturbative and gauge invariant treatment of gravitational wave memory

We present a perturbative treatment of gravitational wave memory. The coordinate invariance of Einstein’s equations leads to a type of gauge invariance in perturbation theory. As with any gauge invariant theory, results are more clear when expressed in terms of manifestly gauge invariant quantities. Therefore we derive all our results from the perturbed Weyl tensor rather than the perturbed metric. We derive gravitational wave memory for the Einstein equations coupled to a general energy-momentum tensor that reaches null infinity.

# Higher Spin Resolution of a Toy Big Bang

Diffeomorphisms preserve spacetime singularities, whereas higher spin symmetries need not. Since three dimensional de Sitter space has quotients that have big-bang/big-crunch singularities and since dS_3-gravity can be written as an SL(2,C) Chern-Simons theory, we investigate SL(3,C) Chern-Simons theory as a higher-spin context in which these singularities might get resolved. As in the case of higher spin black holes in AdS_3, the solutions are invariantly characterized by their holonomies. We show that the dS_3 quotient singularity can be de-singularized by an SL(3,C) gauge transformation that preserves the holonomy: this is a higher spin resolution the cosmological singularity. Our work deals exclusively with the bulk theory, and is independent of the subtleties involved in defining a CFT_2 dual to dS_3 in the sense of dS/CFT.