Exorcising the Ostrogradsky ghost in coupled systems

Klein, Remko; Roest, Diederik

doi:10.1007/jhep07(2016)130

Cited by 76 publications

(78 citation statements)

References 59 publications

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“…We found Models A, B, and C given by Eqs. (31), (33), and (35), which could provide the analytic BH solutions whose metrics are given by Eqs. (38), (42), and (45), respectively.…”

Section: Discussionmentioning

confidence: 99%

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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“…We found Models A, B, and C given by Eqs. (31), (33), and (35), which could provide the analytic BH solutions whose metrics are given by Eqs. (38), (42), and (45), respectively.…”

Section: Discussionmentioning

confidence: 99%

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

Minamitsuji

Edholm

2020

Phys. Rev. D

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“…As a second example, let us consider another case with n = 3 and couple a scalar field π with a mixed-symmetry tensor N with degree (7,1). By counting, the relevant action is one in 10 dimensions and it reads as…”

Section: Jhep03(2017)070mentioning

confidence: 99%

Tensor Galileons and gravity

Chatzistavrakidis

Khoo

Roest

et al. 2017

J. High Energ. Phys.

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The particular structure of Galileon interactions allows for higher-derivative terms while retaining second order field equations for scalar fields and Abelian p-forms. In this work we introduce an index-free formulation of these interactions in terms of two sets of Grassmannian variables. We employ this to construct Galileon interactions for mixedsymmetry tensor fields and coupled systems thereof. We argue that these tensors are the natural generalization of scalars with Galileon symmetry, similar to p-forms and scalars with a shift-symmetry. The simplest case corresponds to linearised gravity with Lovelock invariants, relating the Galileon symmetry to diffeomorphisms. Finally, we examine the coupling of a mixed-symmetry tensor to gravity, and demonstrate in an explicit example that the inclusion of appropriate counterterms retains second order field equations.

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“…We follow the results of [12,22,23] and underline some difficulties to extend them to diff invariant theories (see also [24] as an alternative way to deal with Ostrogradsky modes). In general there is a potential Ostrogradsky mode for each field in the action appearing with second time derivatives.…”

Section: A Ostrogradsky Instabilities and Constraintsmentioning

confidence: 99%

“…The Ostrogradsky problem and the notion of degeneracy (necessary to avoid such a problem) were systematically studied in the context of classical mechanics in [22,23] and later in the context of higher order field theories without gauge symmetries in [12]. A similarly rigorous analysis however is still missing for field theories that possess gauge symmetries, such as gravity theories enjoying diff invariance.…”

Section: Introductionmentioning

confidence: 99%

Beyond Lovelock gravity: Higher derivative metric theories

et al. 2018

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We consider theories describing the dynamics of a four-dimensional metric, whose Lagrangian is diffeomorphism invariant and depends at most on second derivatives of the metric. Imposing degeneracy conditions we find a set of Lagrangians that, apart form the Einstein-Hilbert one, are either trivial or contain more than 2 degrees of freedom. Among the partially degenerate theories, we recover Chern-Simons gravity, endowed with constraints whose structure suggests the presence of instabilities. Then, we enlarge the class of parity violating theories of gravity by introducing new "chiral scalar-tensor theories." Although they all raise the same concern as Chern-Simons gravity, they can nevertheless make sense as low energy effective field theories or, by restricting them to the unitary gauge (where the scalar field is uniform), as Lorentz breaking theories with a parity violating sector.

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Exorcising the Ostrogradsky ghost in coupled systems

Cited by 76 publications

References 59 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

Tensor Galileons and gravity

Beyond Lovelock gravity: Higher derivative metric theories

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