2018
DOI: 10.1103/physrevd.97.044021
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General theories of linear gravitational perturbations to a Schwarzschild black hole

Abstract: We use the covariant formulation proposed in [1] to analyse the structure of linear perturbations about a spherically symmetric background in different families of gravity theories, and hence study how quasi-normal modes of perturbed black holes may be affected by modifications to General Relativity. We restrict ourselves to single-tensor, scalar-tensor and vector-tensor diffeomorphism-invariant gravity models in a Schwarzschild black hole background. We show explicitly the full covariant form of the quadratic… Show more

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Cited by 55 publications
(73 citation statements)
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“…orbiting stars around BHs [5][6][7], or BH imaging [8][9][10]), QNM carry information on the dynamical regime of gravity and thus provide crucial new information. In particular, in the case of a massive scalar field conformally coupled to gravity, the BH stationary solution is a Kerr metric, as in GR, while the QNM spectrum will generically be given by a linear superposition of the normal GR spectrum and the scalar field spectrum [11]. Studying this scalar field spectrum then will help understand one of the possible deviations from GR that can be tested in the future with a detection of QNM.…”
Section: Introductionmentioning
confidence: 99%
“…orbiting stars around BHs [5][6][7], or BH imaging [8][9][10]), QNM carry information on the dynamical regime of gravity and thus provide crucial new information. In particular, in the case of a massive scalar field conformally coupled to gravity, the BH stationary solution is a Kerr metric, as in GR, while the QNM spectrum will generically be given by a linear superposition of the normal GR spectrum and the scalar field spectrum [11]. Studying this scalar field spectrum then will help understand one of the possible deviations from GR that can be tested in the future with a detection of QNM.…”
Section: Introductionmentioning
confidence: 99%
“…The resulting eikonal expressions, although somewhat unwieldy and markedly more complicated than those of Paper I, should encompass a large class of black holes beyond GR. The algebraic complexity of our results is the main reason we have not attempted a similar analysis (although such analysis should be feasible) for the coupled system of three black hole perturbation equations that appear in generalised vector-tensor [19] and in Einstein-Maxwell-dilaton theories [29]. As was the case for the perturbation equations of Paper I, we have been able to show that the eikonal QNM can be associated with the peak of an effective potential although no correspondence to a geodesic photon ring appears to exist (this issue was explored in detail in [32]).…”
Section: Discussionmentioning
confidence: 99%
“…We consider perturbed non-GR black holes described by a general system of wave equations with two coupled scalar-tensor field degrees of freedom {Θ, ψ}. Our equations are supposed to be theory-agnostic but they do include, for instance, the perturbation equations of Schwarzschild black holes within the framework of the generalised class of scalar-tensor theories discussed in [19]. Although we assume spherically symmetric black holes, we can also allow for the possibility of first-order rotational corrections.…”
Section: The Coupled Wave Equationsmentioning
confidence: 99%
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“…We will assume that the UV cutoff of the dark energy EFT, and 3 Note that the frequencies of the LIGO measurement of GW170817 are close to Λ 3 , so additional assumptions about the UV physics are implicitly made when using this measurement to constrain such 'cosmological' operators suppressed by Λ 3 [19]. 4 The exact definition of the operators is given below in Eq. (6), here we are just keeping track schematically of the number of fields and derivatives.…”
Section: Introduction and Setupmentioning
confidence: 99%