Black Hole Zeroth Law in Horndeski Gravity

Abstract

The four laws of black hole mechanics have been put forward for a long time. However, the zeroth law, which states that the surface gravity of a stationary black hole is a constant on the event horizon, still lacks universal proof in various modified gravitational theories. In this paper, we study the zeroth law {in a special Horndeski gravity}, which is an interesting gravitational theory with a nonminimally coupled scalar field. After assuming that {the nonminimally coupled scalar field has the same symmetries with the spacetime,} the minimally coupled matter fields satisfy the dominant energy condition and the Horndeski gravity has a smooth limit to Einstein gravity when the coupling constant approaches zero, we prove the zeroth law based on the gravitational equation in Horndeski gravity without any assumption to the spacetime symmetries.

arXiv comment6 pages, and this paper has been accepted by PRD

References in corpus (23)

• Planck 2015 results. XIII. Cosmological parameters
• The Cosmological Constant and Dark Energy
• Particle Dark Matter: Evidence, Candidates and Constraints
• The galileon as a local modification of gravity
• Generalized G-inflation: Inflation with the most general second-order field equations
• From k-essence to generalised Galileons
• General second order scalar-tensor theory, self tuning, and the Fab Four
• Dressing a black hole with a time-dependent Galileon
• Quintessence and phantom cosmology with non-minimal derivative coupling
• Black holes and stars in Horndeski theory
• Black Hole Entropy and Viscosity Bound in Horndeski Gravity
• Global Extensions of Spacetimes Describing Asymptotic Final States of Black Holes
• Neutron stars in Horndeski gravity
• Thermodynamics of Charged Black Holes in Einstein-Horndeski-Maxwell Theory
• Causality in gravitational theories with second order equations of motion
• On Black Hole Temperature in Horndeski Gravity
• Intrinsic and extrinsic geometries of a tidally deformed black hole
• P-V criticality in the extended phase space of black holes in Einstein-Horndeski gravity
• Cosmological Evolution and Solar System Consistency of Massive Scalar-Tensor Gravity
• Thermodynamics of Horndeski black holes with non-minimal derivative coupling
• Black Hole Zeroth Law in Higher Curvature Gravity
• The issue of zeroth law for Killing horizons in Lanczos-Lovelock gravity
• Investigating the Linearized Second Law in Horndeski Gravity

Cited by in corpus (6)

• The zeroth law of black hole thermodynamics in arbitrary higher derivative theories of gravity
• Superradiant energy extraction from rotating hairy Horndeski black holes
• Non-minimal coupling of scalar and gauge fields with gravity: an entropy current and linearized second law
• Noether charge formalism for Weyl invariant theories of gravity
• The linearized second law for any higher curvature gravity with the scalar and the electromagnetic fields
• Scalar-hairy Lovelock gravity respects zeroth law