Exact black hole solutions in shift-symmetric quadratic degenerate higher-order scalar-tensor theories

Motohashi, Hayato; Minamitsuji, Masato

doi:10.1103/physrevd.99.064040

Cited by 71 publications

(126 citation statements)

References 49 publications

(124 reference statements)

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“…We note that for Λ = 0 the solution exactly corresponds to the stealth Schwarzschild solution with X = −q 2 and is consistent with the conditions for "Case 1" in Ref. [17], and for r |ζ/Λ|, the solution can be well approximated by the Schwarzschild solution. Thus, on distance scales much shorter than |ζ/Λ| the gravitational force law can be approximated by the Newtonian one.…”

Section: Model A-qsupporting

confidence: 85%

“…By choosing C 1 appropriately, it is possible to make A = B. This solution described the Schwarzschild-(anti-) de Sitter-type solution with the effective cosmological constant Λ [17,21]. The deficit solid angle is absent (κ = 1) in the case of A 1 = 0, namely in the case that the difference between c gw , the speed of GWs and c, the speed of light is absent, i.e.…”

Section: Discussionmentioning

confidence: 99%

“…In order to keep the independent EL equations after varying the action (3), we start with the general gauge of the static and spherically symmetric spacetime metric [17,21,53] ds 2 = −A(r)dt 2 + dr 2 B(r) + 2D(r)dtdr + r 2 (dθ 2 + sin 2 θdϕ 2 ).…”

Section: A Solving the Equations Of Motionmentioning

confidence: 99%

“…[17,[20][21][22]. Another nontrivial solution is the Schwarzschild-(anti-) de Sitter solution with the same properties of the scalar field [17][18][19][20][21][22][23]. Kerr-(anti-) de Sitter solutions with a constant X were obtained in Ref.…”

mentioning

confidence: 99%

“…[9,[12][13][14][15].The application of modern scalar-tensor theories to BH physics has attracted great interest. Besides the Schwarzschild or Kerr solutions in General Relativity (GR) with or without a constant scalar field [16,17], i.e. GR BH solutions, they also allow BH solutions which are absent in GR.…”

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Black holes with a nonconstant kinetic term in degenerate higher-order scalar tensor theories

Minamitsuji

Edholm

2020

Phys. Rev. D

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We investigate static and spherically symmetric black hole (BH) solutions in shift-symmetric quadratic-order degenerate higher-order scalar-tensor (DHOST) theories. We allow a nonconstant kinetic term X = g µν ∂µφ∂ν φ for the scalar field φ and assume that φ is, like the spacetime, a pure function of the radial coordinate r, namely φ = φ(r). First, we find analytic static and spherically symmetric vacuum solutions in the so-called Class Ia DHOST theories, which include the quartic Horndeski theories as a subclass. We consider several explicit models in this class and apply our scheme to find the exact vacuum BH solutions. BH solutions obtained in our analysis are neither Schwarzschild or Schwarzschild (anti-) de Sitter. We show that a part of the BH solutions obtained in our analysis are free of ghost and Laplacian instabilities and are also mode stable against the oddparity perturbations. Finally, we argue the case that the scalar field has a linear time dependence φ = qt + ψ(r) and show several simple examples of nontrivial BH solutions with a nonconstant kinetic term obtained analytically and numerically. I. INTRODUCTIONScalar-tensor theories have provided the unified mathematical description of modified gravity theories [1]. In classic scalar-tensor theories, whose Lagrangian density depends on the metric g µν , the scalar field φ, and its first-order derivative φ µ := ∇ µ φ, L = L(g µν , φ, φ µ ), the Euler-Lagrange (EL) equations are given by the second-order differential equations. However, the Lagrangian density of modern scalar-tensor theories may also contain the second-order derivatives of the scalar field φ µν := ∇ µ ∇ ν φ. Although generically the EL equations in such theories contain higher derivative terms, the appearance of Ostrogradsky ghosts [2] can be avoided using certain degeneracy conditions [3]. Degenerate higher-order scalar-tensor (DHOST) theories [4-9] (see also [10,11]) provide the most general framework of scalar-tensor theories which are free from Ostrogradsky instabilities [2], and hence the system contains only three degrees of freedom (DOFs), namely, two tensorial and one scalar polarizations (See § II for details). Applications of DHOST theories to cosmological and astrophysical problems have been investigated in Refs. [9,[12][13][14][15].The application of modern scalar-tensor theories to BH physics has attracted great interest. Besides the Schwarzschild or Kerr solutions in General Relativity (GR) with or without a constant scalar field [16,17], i.e. GR BH solutions, they also allow BH solutions which are absent in GR. A typical nontrivial BH solution is the stealth Schwarzschild solution [18,19] obtained in shift-symmetric Horndeski theories with the assumptions of a linearly time-dependent scalar field φ = qt + ψ(r) and a constant kinetic term X = const, where t and r are the time and radial coordinates of the static and spherically symmetric spacetime and X := g µν φ µ φ ν represents the canonical kinetic term of the scalar field. In stealth solutions, the spacetime geometry ...

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Section: Model A-qsupporting

confidence: 85%

Section: Discussionmentioning

confidence: 99%

Section: A Solving the Equations Of Motionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Black holes with a nonconstant kinetic term in degenerate higher-order scalar tensor theories

Minamitsuji

Edholm

2020

Phys. Rev. D

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Spherical inhomogeneous solutions of Einstein and scalar–tensor gravity: A map of the land

2021

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Stealth black hole perturbations in kinetic gravity braiding

Bernardo

Vega

2021

Journal of Mathematical Physics

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We study stealth black hole perturbations in shift symmetric kinetic gravity braiding and obtain its analogous Regge–Wheeler and Zerilli master equations for the odd and even parity sectors. We show that the nontrivial hair of static and spherically symmetric stealth black holes contributes only an additional source term to the even parity master equation. Furthermore, we derive exact solutions to the monopolar and dipolar perturbations and show that they are generally pathological non-gauge modes or else reduce to the pure-gauge low-order multipoles of general relativity.

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Exact black hole solutions in shift-symmetric quadratic degenerate higher-order scalar-tensor theories

Cited by 71 publications

References 49 publications

Black holes with a nonconstant kinetic term in degenerate higher-order scalar tensor theories

Black holes with a nonconstant kinetic term in degenerate higher-order scalar tensor theories

Spherical inhomogeneous solutions of Einstein and scalar–tensor gravity: A map of the land

Stealth black hole perturbations in kinetic gravity braiding

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