General invertible transformation and physical degrees of freedom

Takahashi, Kazufumi; Motohashi, Hayato; Suyama, Teruaki; Kobayashi, Tsutomu

doi:10.1103/physrevd.95.084053

Cited by 56 publications

(56 citation statements)

References 33 publications

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“…as long as Ω(Ω − XΩ X − X 2 Γ X ) = 0, so that the transformation is invertible [38,39]. This is consistent with the fact that an invertible transformation does not change the number of DOFs [39,40]. The class Ia of quadratic DHOST theories is known to be recast into the Horndeski class via conformal/disformal transformation [17,32].…”

Section: A the Actionsupporting

confidence: 54%

“…The transformation is invertible unless F 3/2 2 / √ F 2 − XA 1 ∝ X. Therefore, in contrast to generic DHOST theories, this subclass has only two physical DOFs, and the system of EL equations is equivalent to those in general relativity [39]. This means that one cannot determine all A, B, and X in this subclass: Any of them remains an arbitrary function of r. Similarly, there would also be a subtlety in BH solutions in the cuscuton theory [48] and its extension [49] having only two propagating DOFs when φ µ is timelike.…”

Section: B Reduction Of Background Equationsmentioning

confidence: 99%

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Linear stability analysis of hairy black holes in quadratic degenerate higher-order scalar-tensor theories: Odd-parity perturbations

2019

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We study static spherically symmetric black hole solutions with a linearly time-dependent scalar field and discuss their linear stability in the shift-and reflection-symmetric subclass of quadratic degenerate higher-order scalar-tensor (DHOST) theories. We present the explicit forms of the reduced system of background field equations for a generic theory within this subclass. Using the reduced equations of motion, we show that in several cases the solution is forced to be of the Schwarzschild or Schwarzschild-(anti-)de Sitter form. We consider odd-parity perturbations around general static spherically symmetric black hole solutions and derive the concise criteria for the black holes to be stable. Our analysis also covers the case with a static or constant profile of the scalar field.*1 Yet, there have been attempts to further extend the framework by relaxing the requirement so that the degenerate property holds only in the unitary gauge [21][22][23].

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Section: A the Actionsupporting

confidence: 54%

Section: B Reduction Of Background Equationsmentioning

confidence: 99%

Linear stability analysis of hairy black holes in quadratic degenerate higher-order scalar-tensor theories: Odd-parity perturbations

2019

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“…Actually, the extension of our analysis to field theories with arbitrary higher-order derivatives is quite interesting, for example, scalar (and vector) fields in the Minkowski background, scalar-tensor theories, vector-tensor theories, scalar-vector-tensor (TeVeS) theories, and even a theory with fermionic degrees of freedom. Especially, it is challenging to find a healthy theory with higher-order derivative terms, which cannot be transformed to a theory with only up to first order derivatives by invertible transformation [29]. We also leave all of these topics as future work.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Ghost-free theories with arbitrary higher-order time derivatives

Motohashi

Suyama

Yamaguchi

2018

J. High Energ. Phys.

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We construct no-ghost theories of analytic mechanics involving arbitrary higher-order derivatives in Lagrangian. It has been known that for theories involving at most second-order time derivatives in the Lagrangian, eliminating linear dependence of canonical momenta in the Hamiltonian is necessary and sufficient condition to eliminate Ostrogradsky ghost. In the previous work we showed for the specific quadratic model involving third-order derivatives that the condition is necessary but not sufficient, and linear dependence of canonical coordinates corresponding to higher time-derivatives also need to be removed appropriately. In this paper, we generalize the previous analysis and establish how to eliminate all the ghost degrees of freedom for general theories involving arbitrary higher-order derivatives in the Lagrangian. We clarify a set of degeneracy conditions to eliminate all the ghost degrees of freedom, under which we also show that the Euler-Lagrange equations are reducible to a second-order system.

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“…In this simple case, one can show that the spin-2 degrees of freedom (the gravitons, perturbations of the metric tensor) do propagate in the initial metric g µν . To simplify this example even further, one may actually consider it in flat spacetime, i.e., without any graviton, while universally 5 References [56][57][58] used similar arguments, and accordingly obtain too restrictive conditions for stability.…”

Section: Causal Cones and Hamiltonian In A General Coordinate Systemmentioning

confidence: 99%

Hamiltonian unboundedness vs stability with an application to Horndeski theory

et al. 2018

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A Hamiltonian density bounded from below implies that the lowest-energy state is stable. We point out, contrary to common lore, that an unbounded Hamiltonian density does not necessarily imply an instability: Stability is indeed a coordinate-independent property, whereas the Hamiltonian density does depend on the choice of coordinates. We discuss in detail the relation between the two, starting from k-essence and extending our discussion to general field theories. We give the correct stability criterion, using the relative orientation of the causal cones for all propagating degrees of freedom. We then apply this criterion to an exact Schwarzschild-de Sitter solution of a beyond-Horndeski theory, while taking into account the recent experimental constraint regarding the speed of gravitational waves. We extract the spin-2 and spin-0 causal cones by analyzing respectively all the odd-parity and the = 0 even-parity modes. Contrary to a claim in the literature, we prove that this solution does not exhibit any kinetic instability for a given range of parameters defining the theory.1 See also [24] for relations between higher dimensional and 4-dimensional scalar-tensor gravity theories. 2 We do not consider here Lorentz-breaking theories [28,29] where equations of motion can be of higher order. Also, in extensions of Horndeski theory [30][31][32][33][34][35][36][37][38][39][40][41][42][43], one may get Euler-Lagrange equations of third order, but by manipulating these equations their order is reduced.

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General invertible transformation and physical degrees of freedom

Cited by 56 publications

References 33 publications

Linear stability analysis of hairy black holes in quadratic degenerate higher-order scalar-tensor theories: Odd-parity perturbations

Linear stability analysis of hairy black holes in quadratic degenerate higher-order scalar-tensor theories: Odd-parity perturbations

Ghost-free theories with arbitrary higher-order time derivatives

Hamiltonian unboundedness vs stability with an application to Horndeski theory

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