Scalar fields and parametrized spherically symmetric black holes: Can one hear the shape of space-time?

Abstract

In this work we study whether parametrized spherically symmetric black hole solutions in metric theories of gravity can appear to be isospectral when studying perturbations. From a theory agnostic point of view, the test scalar field wave equation is the ideal starting point to approach the quasinormal mode spectrum in alternative black hole solutions. We use a parametrization for the metric proposed by Rezzolla and Zhidenko, as well as the the higher order WKB method in the determination of the quasi-normal mode spectra. We look for possible degeneracies in a tractable subset of the parameter space with respect to the Schwarzschild quasi-normal modes. Considering the frequencies and damping times of the expected observationally most relevant quasi-normal modes, we find such degeneracies. We explicitly demonstrate that the leading Schwarzschild quasi-normal modes can be approximated by alternative black hole solutions when their mass is treated as free parameter. In practice, we conclude that the mass has to be known with extremely high precision in order to restrict the leading terms in the metric expansion to currently known limits coming from the PPN expansion. Possible limitations of using the quasi-normal mode ringdown to investigate black hole space-times are being discussed.

Exact theory for the Rezzolla-Zhidenko metric and self-consistent calculation of quasinormal modes

“…This stresses the necessity of having multiple QNM measurements in placing constraints on BH behaviour and strong gravity simultaneously (see also Refs. [14,15,63]). 5 Note, however, it may be the case that that particular branch is Ostrogradsky-unstable [42] or does not respect independent constraints coming from cosmology [36,37], neutron-star astrophysics [40], or Solar-system dynamics [66].…”

“…In particular, Völkel and Barausse [20] have shown how ringdown data can be used to reconstruct the local spacetime metric given a theory of gravity (see also Refs. [14,15,63]). In that work, however, a solution to the inverse problem was not available, and so various approximations for the EOM describing QNMs had to be used.…”

“…A so that vacuum perturbations can be modeled self-consistently. In addition to being of theoretical interest in its own right, this allows, in principle, for a quantification of the accuracy of various widely-used approximations involving test fields [63][64][65] or mild deviations at the level of the EOM [14,15,20]. Where appropriate, we keep track of the relative difference between QNMs computed using the approach presented here and that of the 'GR-like' approximation discussed in Sec.…”

Eikonal quasinormal modes of black holes beyond general relativity. II. Generalized scalar-tensor perturbations

“…A violation of this hypothesis would hint towards new physics beyond GR [17]. This has motivated considerable effort in modeling the QNM spectrum of black holes outside the Kerr paradigm, ranging from model-independent parametrisations [18][19][20][21][22][23] to calculations done in specific beyond-GR theories, e.g. [24][25][26][27][28][29][30][31].…”

Rotating tensor-multiscalar black holes with two scalars

“…The newly emerging field of gravitational wave astronomy is gathering more and more momentum and it is offering completely new possibilities to probe the nature of black holes and the strong field regime of gravity in general [1,2]. A careful and high precision observation of the gravitational wave signal, including higher order modes, can tell apart the Kerr black hole from its generalizations [3][4][5][6][7][8][9]. It is not trivial, though, to identify the theories that allow for the existence of non-Kerr black holes and to actually construct such solutions analytically or numerically.…”