On the stability and deformability of top stars

Abstract

Topological stars, or top stars for brevity, are smooth horizonless static solutions of Einstein-Maxwell theory in 5-d that reduce to spherically symmetric solutions of Einstein-Maxwell-Dilaton theory in 4-d. We study linear scalar perturbations of top stars and argue for their stability and deformability. We tackle the problem with different techniques including WKB approximation, numerical analysis, Breit-Wigner resonance method and quantum Seiberg-Witten curves. We identify three classes of quasi-normal modes corresponding to prompt-ring down modes, long-lived meta-stable modes and what we dub ‘highly-damped’ modes. All mode frequencies we find have negative imaginary parts, thus suggesting linear stability of top stars. Moreover we determine the tidal Love and dissipation numbers encoding the response to tidal deformations and, similarly to black holes, we find zero value in the static limit but, contrary to black holes, we find non-trivial dynamical Love numbers and vanishing dissipative effects at linear order. For the sake of illustration in a simpler context, we also consider a toy model with a piece-wise constant potential and a centrifugal barrier that captures most of the above features in a qualitative fashion.

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.…”

“…In this paper, we apply these ideas to the study of the tidal response for D1D5 [61], Topological Star [62,63] and D1D5p superstrata geometries of type (1,0,s) [64,65]. Perturbations around these geometries are described by a differential equation of the Heun type and can be mapped to a SU(2) gauge theory with matter transforming in the fundamental representation [44,45,52,54]. The crucial difference with respect to the case of BH's is the presence of poles in the connection matrix associated to the real frequencies where the argument of a Gamma function, in the tidal function, becomes a negative integer.…”

“…In this section we illustrate the ideas of tidal resonances and their connection with QNM's in a toy model of the wave dynamics introduced in [54]. We consider the quantum mechanics of a particle moving in a piecewise constant potential V (x) with different values in the intervals (0, L], [L, L + ∆] and [L + ∆, ∞], see figure 1.…”