Effective field theory of black hole quasinormal modes in scalar-tensor theories

Abstract

The final ringdown phase in a coalescence process is a valuable laboratory to test General Relativity and potentially constrain additional degrees of freedom in the gravitational sector. We introduce here an effective description for perturbations around spherically symmetric spacetimes in the context of scalar-tensor theories, which we apply to study quasinormal modes for black holes with scalar hair. We derive the equations of motion governing the dynamics of both the polar and the axial modes in terms of the coefficients of the effective theory. Assuming the deviation of the background from Schwarzschild is small, we use the WKB method to introduce the notion of "light ring expansion". This approximation is analogous to the slow-roll expansion used for inflation, and it allows us to express the quasinormal mode spectrum in terms of a small number of parameters. This work is a first step in describing, in a model independent way, how the scalar hair can affect the ringdown stage and leave signatures on the emitted gravitational wave signal. Potential signatures include the shifting of the quasi-normal spectrum, the breaking of isospectrality between polar and axial modes, and the existence of scalar radiation. arXiv:1810.07706v3 [hep-th] 1 Feb 2019 F The Regge-Wheeler equations 44 G Isolating the gravitational waves -the large radius limit 44 H Bianchi identities 46 -1 -out. The non-invariance under shifts of the Hamiltonian constraints, responsible for this fact, is at the core of the construction of shift-symmetric adiabatic modes on FLRW spacetimes [33, 34]. 6In other words, the relevant potential for the odd modes depends exclusively on the background metric components, with exactly the same functional dependence as in GR. This still leaves open the possibility of a modification to the odd QNM spectrum if the metric is different from Schwarzschild.

Parametrized ringdown spin expansion coefficients: A data-analysis framework for black-hole spectroscopy with multiple events

“…Going beyond these consistency tests requires modeling the BH ringdown beyond GR, for instance to perform a Bayesian model selection between GR and any proposed extension of the theory. This is a challenging task and, despite recent progress [37][38][39][40][41][42][43][44], all current attempts have significant limitations: they are based on particular classes of theories, they use geometric-optics approximations for the QNMs, or they neglect the spin of the remnant.…”

Stable wormholes in scalar-tensor theories

“…We will also briefly comment on tachyonic instabilities in the odd sector. To pursue such a program, we will use the Effective Field Theory (EFT) for static, spherically symmetric spacetimes recently introduced in [22]. This framework has the advantage of being completely model-independent: it does not rely on any specific assumption regarding the explicit form of the covariant Lagrangian that defines the microscopic theory.…”

“…In Sec. 2 we briefly review the EFT for perturbations introduced in [22]. We then discuss the background Einstein equations for a generic wormhole metric in Sec.…”

Black hole ringdown as a probe for dark energy

“…The variety of possible sources of new effects in the gravitational waveform emitted during the ringdown suggests that, instead of studying each and every case separately, it would be useful to adopt a more model independent approach, like the one recently proposed in [52], to compute the QNM spectrum.…”