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

McManus, Ryan; Berti, Emanuele; Macedo, Caio F. B.; Kimura, Masashi; Maselli, Andrea; Cardoso, Vítor

doi:10.1103/physrevd.100.044061

Cited by 117 publications

(91 citation statements)

References 96 publications

(153 reference statements)

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“…In a similar way, we also showed that δV can be rewritten in terms of (r H /r) j with only low j using the ambiguity of the effective potential. It is also interesting to extend the present discussion to the coupled cases and the higher order cases [6], but we leave them for future work.…”

Section: Summary and Discussionmentioning

confidence: 96%

Note on the parametrized black hole quasinormal ringdown formalism

Kimura

2020

Phys. Rev. D

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The parametrized black hole quasinormal ringdown formalism is useful to compute quasinormal mode (QNM) frequencies if a master equation for the gravitational perturbation around a black hole has a small deviation from the Regge-Wheeler or Zerilli equation. In this formalism, the deviation of QNM frequency from general relativity can be calculated by small deviation parameters and model independent coefficients. In this paper, we derive recursion relations for the model independent coefficients. Using these relations, the higher order coefficients are written only by the lower order coefficients. Thus, we only need the lower order coefficients when we numerically compute the model independent coefficients.

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Section: Summary and Discussionmentioning

confidence: 96%

Note on the parametrized black hole quasinormal ringdown formalism

Kimura

2020

Phys. Rev. D

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“…Finally, let us point that such disformal transformation of the Schwarzschild stealth solution provides a straightforward way to build minimal hairy deformation of vacuum GR solution which are exact solution of a DHOST theory. Up to now, such minimal deformation of the vacuum solutions of GR have been introduced for phenomenological investigation and remain ad hoc [70]. Using the new exact solution (4.35), and performing a linear expansion in term of the parameters A • and B • , our solution generating method allows instead to endow these phenomenologically interesting geometries within the effective approach of DHOST theories.…”

Section: Starting From a Stealth Solutionmentioning

confidence: 99%

Hairy black holes in DHOST theories: exploring disformal transformation as a solution generating method

Achour

Liu

Mukohyama

2020

J. Cosmol. Astropart. Phys.

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Solutions-generating methods based on field redefinitions, such as conformal mapping, play an important role in investigating exact solutions in modified gravity. In this work, we explore the possibility to use disformal field redefinitions to investigate new regions of the solution space of DHOST theories, and present new hairy black holes solutions beyond the stealth sector. The crucial ingredient is to find suitable seed solutions to generate new exact ones for DHOST theories. We first consider a seed solution of the Einstein-Scalar system describing a naked singularity. Under suitable assumptions, we derive a no-go result showing that no black hole solution can be constructed from such a seed GR solution. Then, taking into account the stability of each three degeneracy classes of quadratic DHOST theories under a general disformal mapping, we consider two kinds of known black hole solutions as seed configurations: the Schwarzschild stealth solution and the non-stealth Reissner-Nordstrom like solution. Restricting our considerations to invertible disformal transformations, we show that building new hairy black hole solutions from the stealth solution associated to a constant kinetic term is also quite constrained. We obtain new solutions which either are stealth or describe asymptotically locally flat black holes with a deficit solid angle. However, starting from the non-stealth seed solution associated to a non constant kinetic term, we show that a disformal transformation can introduce rather general modifications of the exterior geometry. Finally, we consider the construction of minimally modified hairy black hole solutions using a small disformal transformation. Further applications of this solution generating method should allow to provide new hairy rotating black hole solutions beyond the stealth sector, as well as minimally modified GR solutions useful for phenomenological investigations of compact objects beyond GR.

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“…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.…”

Section: Introductionmentioning

confidence: 99%

“…The above discussion suggests that a case-by-case analysis is impractical, and that parametrizing directly the observables (i.e., frequencies and damping times) is the most efficient way to perform ringdown tests (see e.g. [22,27,42,43] for work in this direction). Similar observable-based approaches have been very successful to model weak-field effects [73] and the inspiral [74,75].…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2020

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Black-hole spectroscopy is arguably the most promising tool to test gravity in extreme regimes and to probe the ultimate nature of black holes with unparalleled precision. These tests are currently limited by the lack of a ringdown parametrization that is both robust and accurate. We develop an observable-based parametrization of the ringdown of spinning black holes beyond general relativity, which we dub ParSpec (Parametrized Ringdown Spin Expansion Coefficients). This approach is perturbative in the spin, but it can be made arbitrarily precise (at least in principle) through a high-order expansion. It requires O(10) ringdown detections, which should be routinely available with the planned space mission LISA and with third-generation ground-based detectors. We provide a preliminary analysis of the projected bounds on parametrized ringdown parameters with LISA and with the Einstein Telescope, and discuss extensions of our model that can be straightforwardly included in the future. arXiv:1910.12893v1 [gr-qc] 28 Oct 2019where J = 1, 2, ..., q labels the mode; M i and χ i 1 are the detector-frame mass and spin of the i-th source, both measured assuming GR (see below); D is the order of the spin expansion; w (n) J and t (n) J are the dimensionless coefficients of the spin expansion for a Kerr BH in GR (provided in Table I for a few representative modes); γ i are dimensionless coupling constants, which can depend on the source i -see Eq. (6) below -but do not depend 1 The QNMs are identified by three integer numbers: the angular momentum number l, the azimuthal number m ∈ [−l, l], and the overtone number, which we set to zero in this paper, i.e. we only consider fundamental modes. For ease of notation we leave these indices implicit, i.e. ω (J) ≡ ω (0lm) , where J is an index that labels the mode. (n) J and δt (n) J (n) J and δt (n) J (or, equivalently, δW (n) J and δT (n) J ), these corrections depend only on the theory and not on the source.It is easy to check that, to leading order in α, the redefinitionsbring Eqs. (A1) and (A2) to the form in Eqs.(3) and (4) used in the main text. The above redefinitions also show that there is some degeneracy among the beyond-GR parameters, and that one can only constrain the combinations δw (n) J and δt (n) J , which contains the intrinsic mode corrections (δW (n) J and δT (n) J ) and the mass and spin corrections (δm and δχ).(n) J and δt (n) J are unconstrained by the data.

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

Cited by 117 publications

References 96 publications

Note on the parametrized black hole quasinormal ringdown formalism

Note on the parametrized black hole quasinormal ringdown formalism

Hairy black holes in DHOST theories: exploring disformal transformation as a solution generating method

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

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