Gravitational wave signatures of the absence of an event horizon: Nonradial oscillations of a thin-shell gravastar

Abstract

Gravitational waves from compact objects provide information about their structure, probing deep into strong-gravity regions. Here we illustrate how the presence or absence of an event horizon can produce qualitative differences in the gravitational waves emitted by ultracompact objects. In order to set up a straw-man ultracompact object with no event horizon, but which is otherwise almost identical to a black hole, we consider a nonrotating thin-shell model inspired by Mazur and Mottola's gravastar, which has a Schwarzschild exterior, a de Sitter interior and an infinitely thin shell with finite tension separating the two regions. As viewed from the external space-time, the shell can be located arbitrarily close to the Schwarzschild radius, so a gravastar might seem indistinguishable from a black hole when tests are only performed on its external metric. We study the linearized dynamics of the system, and, in particular, the junction conditions connecting internal and external gravitational perturbations. As a first application of the formalism we compute polar and axial oscillation modes of a thin-shell gravastar. We show that the quasinormal mode spectrum is completely different from that of a black hole, even in the limit when the surface redshift becomes infinite. Polar quasinormal modes depend on the equation of state of matter on the shell and can be used to distinguish between different gravastar models. Our calculations suggest that low-compactness gravastars could be unstable when the sound speed on the shell v s =c * 0:92.

Implications of the gravitational wave event GW150914

“…As an illustrative example of a class of objects that can be nearly ruled out using the GW150914 data, [87] explore the possibility that the merging objects formed a gravastar, which is an object that combines an exterior Schwarzschild spacetime with an interior de Sitter spacetime, with a layer of exotic matter in between [88,89,90]. It is important to recognize that even before the gravitational wave detection, such objects were not considered probable; there is no known mechanism to produce them, and the concatenation of spacetimes is arbitrary even if it is formally a solution to Einstein's equations.…”

Application of the confluent Heun functions for finding the quasinormal modes of nonrotating black holes

“…For example, by comparing the theoretically obtained gravitational QNMs with the frequencies of the gravitational waves, one can confirm or refute the nature of the central engines of many astrophysical objects, since those modes differ for the different types of objects -black holes, superspinars (naked singularities), neutron stars, black hole mimickers etc. [8][9][10][11][12][13].…”

“…For example, by comparing the theoretically obtained gravitational QNMs with the frequencies of the gravitational waves, one can confirm or refute the nature of the central engines of many astrophysical objects, since those modes differ for the different types of objects -black holes, superspinars (naked singularities), neutron stars, black hole mimickers etc. [8][9][10][11][12][13].To find the QNMs, one needs to solve the second-order linear differential equations describing the linearized perturbations of the metric: the Regge-Wheeler equation (RWE) and the Zerilli equation for the Schwarzschild metric or the Teukolsky radial equation (TRE) for the Kerr metric and to impose the appropriate boundary conditions -the so-called black hole boundary conditions (waves going simultaneously into the horizon and into infinity) [1,3]. Additionally, one requires a regularity condition for the angular part of the solutions.…”

A recipe for echoes from exotic compact objects

“…Standard tests of the nature of the final merged object call for the black hole's resonant frequencies [31][32][33], known as quasinormal mode (QNM) frequencies, to be extracted from the ringdown portion of the waveform and compared to theoretical calculations [34][35][36][37][38][39]. Working in the test particle limit, Cardoso et al [40] pointed out that in the case of highly compact wormholes, the ringdown of the final ECO is initially nearly identical to that of a BH despite the fact that QNM spectrum is radically changed [41][42][43]. A naive application of the QNM based tests would be fooled by a highly compact ECO.…”