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Register a new userPerturbations of Cosmological and Black Hole Solutions in Massive gravity and Bi-gravity
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We investigate perturbations of a class of spherically symmetric solutions in massive gravity and bi-gravity. The background equations of motion for the particular class of solutions we are interested in reduce to a set of the Einstein equations with a cosmological constant. Thus, the solutions in this class include all the spherically symmetric solutions in general relativity, such as the Friedmann-Lema^{i}tre-Robertson-Walker solution and the Schwarzschild (-de Sitter) solution, though the one-parameter family of two parameters of the theory admits such a class of solutions. We find that the equations of motion for the perturbations of this class of solutions also reduce to the perturbed Einstein equations at first and second order. Therefore, the stability of the solutions coincides with that of the corresponding solutions in general relativity. In particular, these solutions do not suffer from non-linear instabilities which often appear in the other cosmological solutions in massive gravity and bi-gravity.
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We present a detailed study of the static spherically symmetric solutions in de Rham-Gabadadze-Tolley (dRGT) theory. Since the diffeomorphism invariance can be restored by introducing the St{u}ckelberg fields $phi^a$, there is new invariant $I^{ab}=g^{mu u}partial_{mu}phi^apartial_ uphi^b$ in the massive gravity, which adds to the ones usually encountered in general relativity (GR). In the unitary gauge $phi^a=x^mudelta_mu^a$, any inverse metric $g^{mu u}$ that has divergence including the coordinate singularity in GR would exhibit a singularity in the invariant $I^{ab}$. Therefore, there is no conventional Schwarzschild metric if we choose unitary gauge. In this paper, we obtain a self-consistent static spherically symmetric ansatz in the nonunitary gauge. Under this ansatz, we find that there are seven solutions including the Schwarzschild solution, Reissner-Nordstr{o}m solution and five other solutions. These solutions may possess an event horizon depending upon the physical parameters (Schwarzschild radius $r_s$, scalar charge $S$ and/or electric charge $Q$). If these solutions possess an event horizon, we show that the singularity of $I^{ab}$ is absent at the horizon. Therefore, these solutions may become candidates for black holes in dRGT.
In this paper we continue a study of cosmological perturbations in the conformal gravity theory. In previous work we had obtained a restricted set of solutions to the cosmological fluctuation equations, solutions that were required to be both transverse and synchronous. Here we present the general solution. We show that in a conformal invariant gravitational theory fluctuations around any background that is conformal to flat (backgrounds that include the cosmologically interesting Robertson-Walker and de Sitter geometries) can be constructed from the (known) solutions to fluctuations around a flat background. For this construction to hold it is not necessary that the perturbative geometry associated with the fluctuations itself be conformal to flat. Using this construction we show that in a conformal Robertson-Walker cosmology early universe fluctuations grow as $t^4$. We present the scalar, vector, tensor decomposition of the fluctuations in the conformal theory, and compare and contrast our work with the analogous treatment of fluctuations in the standard Einstein gravity theory.
We study cosmological perturbation theory within the framework of unimodular gravity. We show that the Lagrangian constraint on the determinant of the metric required by unimodular gravity leads to an extra constraint on the gauge freedom of the metric perturbations. Although the main equation of motion for the gravitational potential remains the same, the shift variable, which is gauge artifact in General Relativity, cannot be set to zero in unimodular gravity. This non-vanishing shift variable affects the propagation of photons throughout the cosmological evolution and therefore modifies the Sachs-Wolfe relation between the relativistic gravitational potential and the microwave temperature anisotropies. However, for adiabatic fluctuations the difference between the result in General Relativity and unimodular gravity is suppressed on large angular scales. Thus, no strong constraints on the theory can be derived.
The rapid advancement of gravitational wave astronomy in recent years has paved the way for the burgeoning development of black hole spectroscopy, which enhances the possibility of testing black holes by their quasinormal modes (QNMs). In this paper, the axial gravitational perturbations and the QNM frequencies of black holes in the hybrid metric-Palatini gravity (HMPG) are investigated. The HMPG theory is characterized by a dynamical scalar degree of freedom and is able to explain the late-time accelerating expansion of the universe without introducing any textit{ad hoc} screening mechanism to preserve the dynamics at the Solar System scale. We obtain the master equation governing the axial gravitational perturbations of the HMPG black holes and calculate the QNM frequencies. Moreover, in the scrutiny of the black holes and their QNMs, we take into account the constraints on the model parameters based on the post-Newtonian analysis, and show how the QNM frequencies of the HMPG black holes would be altered in the observationally consistent range of parameter space.
Along this review, we focus on the study of several properties of modified gravity theories, in particular on black-hole solutions and its comparison with those solutions in General Relativity, and on Friedmann-Lemaitre-Robertson-Walker metrics. The thermodynamical properties of fourth order gravity theories are also a subject of this investigation with special attention on local and global stability of paradigmatic f(R) models. In addition, we revise some attempts to extend the Cardy-Verlinde formula, including modified gravity, where a relation between entropy bounds is obtained. Moreover, a deep study on cosmological singularities, which appear as a real possibility for some kind of modified gravity theories, is performed, and the validity of the entropy bounds is studied.
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