New results on the physical interpretation of black-brane gravitational perturbations

Abstract

The linear perturbation theory applied to the study of black holes is a traditional and powerful tool to investigate some of the basic properties of these objects, such as the stability of the event horizon, the spectra of quasinormal modes, the scattering and the production of waves in a process of gravitational collapse. Since long ago, the physical interpretation of the linear fluctuations in the metric of spherically symmetric black holes has been established. In a multipolar expansion, it is known that polar perturbations of a monopole type (l = 0) can only increase the black-hole mass, axial perturbations of a dipole type (l = 1) induce a slow rotation in the system, and perturbations with l ≥ 2 always lead to the production of gravitational waves. However, in relation to the planar Schwarzschild anti-de Sitter black holes (or black branes, for short), there is still no conclusive study on some aspects of the physical meaning of these perturbations. In particular, there is some controversy concerning the polar sector of fluctuations with zero wave numbers (k = 0). Some authors claim that this kind of perturbation causes only a small variation in the black-brane mass parameter, while others obtained also evidence for the existence of gravitational waves associated to such modes. The present study aims to contribute to the resolution of this controversy by revealing the physical meaning of the gravitational perturbations of anti-de Sitter black branes. In this work we use the Chandrasekhar's gauge formalism to evaluate the linear variations in the complex Weyl scalars in terms of the Regge-Wheeler-Zerilli gauge-invariant quantities. Then we use the Szekeres' proposal for the meaning of the Weyl scalars and the Pirani's criterion for the existence of gravitational radiation in order to give a physical interpretation of the black-brane perturbations with arbitrary wave number values.

The timbre of Hawking gravitons: an effective description of energy transport from holography

“…Nevertheless, for the sake of completeness, we include an analysis of the homogeneous solution space. We demonstrate that it can be understood as the space of large diffeomorphisms, and moreover demarcate the part which is captured by our designer field in appendix E (see [26] for an earlier analysis).…”

“…Irrespective of this we will quote here the full counterterm action accurate to fourth order in boundary derivatives. 26 The gravitational dynamics we consider is governed by 27…”

“…Our first task will be to identify the diffeomorphism invariant combinations of the metric perturbations for the ansatz (3.1). A natural way to capture this information is to look at 26 The fourth order counterterms will turn out to be the leading regularization for Z which receives no corrections at lower orders. 27 We eschew the overall normalization by 1 16πG N to keep the expressions simple.…”

Third-order relativistic hydrodynamics: dispersion relations and transport coefficients of a dual plasma

“…The fact that makes this solution important for applications in AdS/CFT is the non-spherical topology of the horizon, which may be planar (R × R), cylindrical (S 1 × R) or toroidal (S 1 × S 1 ). The gravitational and electromagnetic perturbations of these objects have been extensively studied in the last two decades [33][34][35][36][37][38][39]. In ref.…”

The timbre of Hawking gravitons: an effective description of energy transport from holography

“…We can interpret Y S and Y ab in terms of metric components in the scalar sector in a Debye gauge. 26 This is a coordinate chart such that metric has no derivatives of scalar plane waves under plane wave decomposition, viz., the perturbation can be recast into the form…”