Black hole perturbation theory and multiple polylogarithms

Abstract

We study black hole linear perturbation theory in a four-dimensional Schwarzschild (anti) de Sitter background. When dealing with a positive cosmological constant, the corresponding spectral problem is solved systematically via the Nekrasov-Shatashvili functions or, equivalently, classical Virasoro conformal blocks. However, this approach can be more complicated to implement for certain perturbations if the cosmological constant is negative. For these cases, we propose an alternative method to set up perturbation theory for both small and large black holes in an analytical manner. Our analysis reveals a new underlying recursive structure that involves multiple polylogarithms. We focus on gravitational, electromagnetic, and conformally coupled scalar perturbations subject to Dirichlet and Robin boundary conditions. The low-lying modes of the scalar sector of gravitational perturbations and its hydrodynamic limit are studied in detail.

Post Newtonian emission of gravitational waves from binary systems: a gauge theory perspective

“…GW signals coming from a binary system can be described in analytic terms in the ringdown and inspiral phases. In [13][14][15][16][17][18][19][20], novel techniques capitalizing on recent advances in quantum field theories have been exploited to study the QNM's characterising the ringdown phase of the GW emission. More traditional analytical approaches to the dynamics of gravitationally interacting binary systems [21][22][23][24] have been successfully compared against gauge inspired scattering amplitude techniques [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43], effective field theories [44][45][46][47] in the description of the inspiral phase.…”

Tidal resonances for fuzzballs

“…The study of TLN resonances will be the central focus of this paper. To carry on this task we will exploit the gravity/Seiberg-Witten correspondence (GSW) recently developed in [42][43][44][45][46][47] that relates gravity to N = 2 supersymmetric SU(2) gauge theories and/or two-dimensional conformal field theories (CFT), see also [48][49][50][51][52][53][54][55]. This correspondence exploits the results of Seiberg-Witten (SW) [56], localization [57][58][59] and AGT duality [60], to provide a combinatorial description of the wave functions describing the gravity systems at linear order.…”