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On the hyperbolicity of the most general Horndeski theory · Around

2017

On the hyperbolicity of the most general Horndeski theory

Papallo, Giuseppe

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In this paper we study the hyperbolicity of the equations of motion for the most general Horndeski theory of gravity in a generic "weak field" background.

We first show that a special case of this theory, namely Einstein-dilaton-Gauss-Bonnet gravity, fails to be strongly hyperbolic in any generalised harmonic gauge.
We then complete the proof that the most general Horndeski theory which, for weak fields, is strongly hyperbolic in a generalised harmonic gauge is simply a "k-essence" theory coupled to Einstein gravity and that adding any more general Horndeski term will result in a weakly, but not strongly, hyperbolic theory.

Built on

R. Arnowitt, S. Deser and C. W. Misner, Dynamical Structure and Definition of Energy in General Relativity , Phys. Rev. 116
1959
Earlier work this paper cites.
G. W. Horndeski, Second-order scalar-tensor field equations in a four-dimensional space , Int. J. Theor. Phys. 10
1974
Earlier work this paper cites.
P. Kanti, N. E. Mavromatos, J. Rizos, K. Tamvakis and E. Winstanley, Dilatonic Black Holes in Higher Curvature String Gravity , Phys. Rev. D 54
1995
Earlier work this paper cites.

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Then

O. Sarbach and M. Tiglio, Continuum and Discrete Initial-Boundary Value Problems and Einstein’s Field Equations , Living Rev. Relativ. 15
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2012
Later among the works it cites.
D. Bettoni and S. Liberati, Disformal invariance of second order scalar-tensor theories: Framing the Horndeski action , Phys. Rev. D 88
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2013
Later among the works it cites.
G. Papallo and H. S. Reall, On the local well-posedness of Lovelock and Horndeski theories , Phys. Rev. D 96
Original
2017
Closest in time.

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