Black Holes in an Effective Field Theory Extension of General Relativity

Abstract

Effective field theory methods suggest that some rather-general extensions of General Relativity include, or are mimicked by, certain higher-order curvature corrections, with coupling constants expected to be small but otherwise arbitrary. Thus, the tantalizing prospect to test the fundamental nature of gravity with gravitational-wave observations, in a systematic way, emerges naturally. Here, we build black hole solutions in such a framework and study their main properties. Once rotation is included, we find the first purely gravitational example of geometries without Z2-symmetry. Despite the higher-order operators of the theory, we show that linearized fluctuations of such geometries obey second-order differential equations. We find nonzero tidal Love numbers. We study and compute the quasinormal modes of such geometries. These results are of interest to gravitational-wave science but also potentially relevant for electromagnetic observations of the galactic center or X-ray binaries.

Parametrized black hole quasinormal ringdown. II. Coupled equations and quadratic corrections for nonrotating black holes

“…Note that the coupled QNM frequencies computed by direct integration in Fig. 4 are novel results that were not presented in [46]. FIG.…”

“…For illustration, we now apply the formalism to compute QNM spectra for some classes of modified theories of gravity that are known to lead to coupled perturbation equations. Specifically, we consider two models where the coupling is between scalar and tensor modes (dCS gravity [44] and Horndeski gravity [34]) and a model where the coupling is between axial and polar gravitational perturbations (the EFT inspired model [46] not considered in detail in Paper I), so that the background QNM spectra are degenerate.…”

“…One of the EFT models considered in [46] couples the axial and polar gravitational perturbations. The wave equations map onto Eq.…”

“…where V − and V + were defined in Eqs. (6) and (7), V(r) can be found in Appendix A of [46], and the small dimensionless parameter is inversely related to the UV cutoff scale of the EFT. The spectra of V + and V − are degenerate when = 0, so the coupling should induce linear corrections, as discussed in Section V. This expectation is verified in Figure 5.…”

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

“…These departures can be due to extra charges, a modified theory of gravity, environmental effects, etcetera, and we wish to develop a generic framework that can accommodate various special cases. GR corrections might affect the ringdown in two ways: by predicting a spinning BH other than Kerr [11,12,15,50,51,53,57,66], or (even if GR BHs are still solutions of the theory) by affecting the dynamics of the perturbations [40,[67][68][69][70][71]. In both cases, the ringdown modes will acquire corrections proportional to the fundamental coupling constant(s) of the theory.…”