A no-hair theorem for stars in Horndeski theories

Lehébel, Antoine; Babichev, Eugeny; Charmousis, Christos

doi:10.1088/1475-7516/2017/07/037

Cited by 46 publications

(40 citation statements)

References 40 publications

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“…To guarantee the uniqueness of GR solutions, one may need to impose some additional conditions, for instance, symmetries of spacetime, ansatz for scalar field, and/or internal symmetry of the theory. Indeed, theories satisfying the conditions 1-3 include Brans-Dicke theory, the shift-symmetric Horndeski theory, and the shift-symmetric GLPV theory as a subclass, for which no-hair theorems in the four-dimensional spacetime have been proven [64][65][66]115].…”

Section: Classificationmentioning

confidence: 99%

General Relativity solutions in modified gravity

Motohashi

Minamitsuji

2018

Physics Letters B

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Recent gravitational wave observations of binary black hole mergers and a binary neutron star merger by LIGO and Virgo Collaborations associated with its optical counterpart constrain deviation from General Relativity (GR) both on strong-field regime and cosmological scales with high accuracy, and further strong constraints are expected by near-future observations. Thus, it is important to identify theories of modified gravity that intrinsically possess the same solutions as in GR among a huge number of theories. We clarify the three conditions for theories of modified gravity to allow GR solutions, i.e., solutions with the metric satisfying the Einstein equations in GR and the constant profile of the scalar fields. Our analysis is quite general, as it applies a wide class of single-/multi-field scalar-tensor theories of modified gravity in the presence of matter component, and any spacetime geometry including cosmological background as well as spacetime around black hole and neutron star, for the latter of which these conditions provide a necessary condition for no-hair theorem. The three conditions will be useful for further constraints on modified gravity theories as they classify general theories of modified gravity into three classes, each of which possesses i) unique GR solutions (i.e., no-hair cases), ii) only hairy solutions (except the cases that GR solutions are realized by cancellation between singular coupling functions in the Euler-Lagrange equations), and iii) both GR and hairy solutions, for the last of which one of the two solutions may be selected dynamically.

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Section: Classificationmentioning

confidence: 99%

General Relativity solutions in modified gravity

Motohashi

Minamitsuji

2018

Physics Letters B

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“…solutions that are regular everywhere in the spacetime and possess no horizon). In [25,34] it was shown that stars in shift-symmetric Horndeski theories obey a no-hair theorem and thus have a zero scalar charge. A similar conclusion was made earlier in [35] where it was found that there is no emission of dipolar radiation in such theories.…”

Section: Introductionmentioning

confidence: 99%

Equivalence principle on cosmological backgrounds in scalar–tensor theories

Alberte¹

2019

Class. Quantum Grav.

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We study the extent up to which the equivalence principle is obeyed in models of modified gravity and dark energy involving a single scalar degree of freedom. We focus on the effective field theories of dark energy describing the late time acceleration in the presence of ordinary matter species. In their covariant form these coincide with the Horndeski theories on a cosmological background with a slowly varying Hubble rate and a time-dependent scalar field. We show that in the case of an exactly de Sitter universe both the weak and strong equivalence principles hold. This occurs due to the combination of the shift symmetry of the scalar and the time translational invariance of de Sitter space. When generalized to Friedmann-Robertson-Walker cosmologies (FRW) we show that the weak equivalence principle is obeyed for test particles and extended objects in the quasi-static subhorizon limit. We do this by studying the field created by an extended object moving in an FRW background as well as its equation of motion in an external gravitational field. We also estimate the corrections to the geodesic equation of the extended object due to the approximations made.

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“…However, one of the key assumption of [34] is that the norm of the Noether current be finite on the horizon and it was further demonstrated in [39] that with the assumption of vanishing radial Noether current, black hole solutions do not exist in these class of models. However, modifying the scalar-tensor gravity model allows for black hole solutions with finite norm of the Noether current [41].…”

Section: Introductionmentioning

confidence: 99%

Charged black holes in a generalized scalar–tensor gravity model

Brihaye

Hartmann

2017

Physics Letters B

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We study 4-dimensional charged and static black holes in a generalized scalar-tensor gravity model, in which a shift symmetry for the scalar field exists. For vanishing scalar field the solution corresponds to the Reissner-Nordström (RN) solution, while solutions of the full scalar-gravity model have to be constructed numerically. We demonstrate that these black holes support galilean scalar hair up to a maximal value of the scalar-tensor coupling that depends on the value of the charge and can be up to roughly twice as large as that for uncharged solutions. The Hawking temperature TH of the hairy black holes at maximal scalar-tensor coupling decreases continuously with the increase of the charge and reaches TH = 0 for the highest possible charge that these solutions can carry. However, in this limit, the scalar-tensor coupling needs to vanish. The limiting solution hence corresponds to the extremal RN solution, which does not support regular galilaen scalar hair due to its AdS2 × S 2 near-horizon geometry.

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A no-hair theorem for stars in Horndeski theories

Cited by 46 publications

References 40 publications

General Relativity solutions in modified gravity

General Relativity solutions in modified gravity

Equivalence principle on cosmological backgrounds in scalar–tensor theories

Charged black holes in a generalized scalar–tensor gravity model

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