Investigating the Linearized Second Law in Horndeski Gravity

Abstract

Since the entropy of stationary black holes in Horndeski gravity will be modified by the non-minimally coupling scalar field, a significant issue of whether the Wald entropy still obeys the linearized second law of black hole thermodynamics can be proposed. To investigate this issue, a physical process that the black hole in Horndeski gravity is perturbed by the accreting matter fields and finally settles down to a stationary state is considered. According to the two assumptions that there is a regular bifurcation surface in the background spacetime and that the matter fields always satisfy the null energy condition, one can show that the Wald entropy monotonically increases along the future event horizon under the linear order approximation without any specific expression of the metric. It illustrates that the Wald entropy of black holes in Horndeski gravitational theory still obeys the requirement of the linearized second law. Our work strengthens the physical explanation of Wald entropy in Horndeski gravity and takes a step towards studying the area increase theorem in the gravitational theories with non-minimal coupled matter fields.

arXiv comment6 pages

References in corpus (22)

• Black Hole Entropy is Noether Charge
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• The galileon as a local modification of gravity
• On Black Hole Entropy
• Horndeski theory and beyond: a review
• A 3+1 perspective on null hypersurfaces and isolated horizons
• Quintessence and phantom cosmology with non-minimal derivative coupling
• Increase of Black Hole Entropy in Higher Curvature Gravity
• Asymptotically locally AdS and flat black holes in the presence of an electric field in the Horndeski scenario
• Black Hole Entropy and Viscosity Bound in Horndeski Gravity
• A Second Law for Higher Curvature Gravity
• Unified Dark Matter in Scalar Field Cosmologies
• Second Law Violations in Lovelock Gravity for Black Hole Mergers
• Generalized second law at linear order for actions that are functions of Lovelock densities
• Inflationary Cosmology Connecting Dark Energy and Dark Matter
• The holographic entropy increases in quadratic curvature gravity
• Entropy increase during physical processes for black holes in Lanczos-Lovelock gravity
• Physical process first law and increase of horizon entropy for black holes in Einstein-Gauss-Bonnet gravity
• DC Conductivities with Momentum Dissipation in Horndeski Theories
• On holographic entanglement entropy of Horndeski black holes
• Interacting dark energy: generic cosmological evolution for two scalar fields
• From Prigogine to Raychaudhuri

Cited by in corpus (5)

• Non-minimal coupling of scalar and gauge fields with gravity: an entropy current and linearized second law
• Generalized proof of the linearized second law in general quadric corrected Einstein-Maxwell gravity
• Entropy-current for dynamical black holes in Chern-Simons theories of gravity
• The linearized second law for any higher curvature gravity with the scalar and the electromagnetic fields
• Black Hole Zeroth Law in Horndeski Gravity