Black hole solutions in shift-symmetric degenerate higher-order scalar-tensor theories

Minamitsuji, Masato; Edholm, James

doi:10.1103/physrevd.100.044053

Cited by 57 publications

(58 citation statements)

References 55 publications

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“…were also found for nonshift-symmetric Horndeski theory [17]. Stealth black holes in DHOST theories have been attracting much attention recently [18][19][20][21][22]. Stealth solutions may also be used as seed solutions in a certain generating-solution method based on disformal transformations [23].…”

Section: Introductionmentioning

confidence: 99%

Weakly-coupled stealth solution in scordatura degenerate theory

Motohashi

Mukohyama

2020

J. Cosmol. Astropart. Phys.

162

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In scalar-tensor theories we revisit the issue of strong coupling of perturbations around stealth solutions, i.e. backgrounds with the same forms of the metric as in General Relativity but with non-trivial configurations of the scalar field. The simplest among them is a stealth Minkowski (or de Sitter) solution with a constant, timelike derivative of the scalar field, i.e. ghost condensation. In the decoupling limit the effective field theory (EFT) describing perturbations around the stealth Minkowski (or de Sitter) solution shows the universal dispersion relation of the form ω 2 = αk 4 /M 2 , where M is a mass scale characterizing the background scalar field and α is a dimensionless constant. Provided that α is positive and of order unity, a simple scaling argument shows that the EFT is weakly coupled all the way up to M . On the other hand, if the structure of the underlining theory forces the perturbations to follow second-order equations of motion then α = 0 and the dispersion relation loses dependence on the spatial momentum. This not only explains the origin of the strong coupling problem that was recently pointed out in a class of degenerate theories but also provides a hint for a possible solution of the problem. We then argue that a controlled detuning of the degeneracy condition, which we call scordatura, renders the perturbations weakly coupled without changing the properties of the stealth solutions of degenerate theories at astrophysical scales.

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Section: Introductionmentioning

confidence: 99%

Weakly-coupled stealth solution in scordatura degenerate theory

Motohashi

Mukohyama

2020

J. Cosmol. Astropart. Phys.

162

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“…In general, it is very difficult to obtain exact solutions for black holes in alternative theories of gravity because the field equations become more complicated. However, some new black hole solutions in the DHOST theories have emerged these last years [14][15][16][17][18][19][20][21]. These solutions can be classified as the stealth solutions and the non-stealth solutions.…”

Section: Introductionmentioning

confidence: 99%

Shadow of a disformal Kerr black hole in quadratic degenerate higher-order scalar–tensor theories

2020

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We have studied the shadow of a disformal Kerr black hole with an extra deformation parameter, which belongs to non-stealth rotating solutions in quadratic degenerate higher-order scalar–tensor (DHOST) theory. Our result show that the size of the shadow increases with the deformation parameter for the black hole with arbitrary spin parameter. However, the effect of the deformation parameter on the shadow shape depends heavily on the spin parameter of black hole and the sign of the deformation parameter. The change of the shadow shape becomes more distinct for the black hole with the more quickly rotation and the more negative deformation parameter. Especially, for the near-extreme black hole with negative deformation parameter, there exist a “pedicel”-like structure appeared in the shadow, which increases with the absolute value of deformation parameter. The eyebrow-like shadow and the self-similar fractal structures also appear in the shadow for the disformal Kerr black hole in DHOST theory. These features in the black hole shadow originating from the scalar field could help us to understand the non-stealth disformal Kerr black hole and quadratic DHOST theory.

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“…Although of course this does not encompass the most general set of scalar-tensor models, it should be clear that the general lessons we will draw should apply very generically. The case of quadratic DHOST theory is also worth focusing on given its interest in the astrophysical and cosmological literature (see e.g., [35][36][37][38][39][40][41][42][43]). Our analysis also opens the way to a classification based on matter coupling consistencies (in the above terminology) of the different scalar-tensor theories among themselves as well as compared with pure general relativity.…”

Section: Introductionmentioning

confidence: 99%

Degeneracy, matter coupling, and disformal transformations in scalar-tensor theories

Deffayet

García-Sáenz

2020

Phys. Rev. D

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Degenerate scalar-tensor theories of gravity extend general relativity by a single degree of freedom, despite their equations of motion being higher than second order. In some cases, this is a mere consequence of a disformal field redefinition carried out in a nondegenerate theory. More generally, this is made possible by the existence of an additional constraint that removes the would-be ghost. It has been noted that this constraint can be thwarted when the coupling to matter involves time derivatives of the metric, which results in a modification of the canonical momenta of the gravitational sector. In this paper we expand on this issue by analyzing the precise ways in which the extra degree of freedom may reappear upon minimal coupling to matter. Specifically, we study examples of matter sectors that lead either to a direct loss of the special constraint or to a failure to generate a pair of secondary constraints. We also discuss the recurrence of the extra degree of freedom using the language of disformal transformations in particular for what concerns "veiled" gravity. On the positive side, we show that the minimal coupling of spinor fields is healthy and does not spoil the additional constraint. We argue that this virtue of spinor fields to preserve the number of degrees of freedom in the presence of higher derivatives is actually very general and can be seen from the level decomposition of Grassmann-valued classical variables.

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Black hole solutions in shift-symmetric degenerate higher-order scalar-tensor theories

Cited by 57 publications

References 55 publications

Weakly-coupled stealth solution in scordatura degenerate theory

Weakly-coupled stealth solution in scordatura degenerate theory

Shadow of a disformal Kerr black hole in quadratic degenerate higher-order scalar–tensor theories

Degeneracy, matter coupling, and disformal transformations in scalar-tensor theories

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