Non-minimal coupling of scalar and gauge fields with gravity: an entropy current and linearized second law

Abstract

This work extends the proof of a local version of the linearized second law involving an entropy current with non-negative divergence by including the arbitrary non-minimal coupling of scalar and $U(1)$ gauge fields with gravity. In recent works, the construction of entropy current to prove the linearized second law rested on an important assumption about the possible matter couplings to gravity: the corresponding matter stress tensor was assumed to satisfy the null energy conditions. However, the null energy condition can be violated, even classically, when the non-minimal coupling of matter fields to gravity is considered. Considering small dynamical perturbations around stationary black holes in diffeomorphism invariant theories of gravity with non-minimal coupling to scalar or gauge fields, we prove that an entropy current with non-negative divergence can still be constructed. The additional non-minimal couplings that we have incorporated contribute to the entropy current, which may even survive in the equilibrium limit. We also obtain a spatial current on the horizon apart from the entropy density in out-of-equilibrium situations. We achieve this by using a boost symmetry of the near horizon geometry, which constraints the off-shell structure of a specific component of the equations of motion with newer terms due to the non-minimal couplings. The final expression for the entropy current is $U(1)$ gauge-invariant for gauge fields coupled to gravity. We explicitly check that the entropy current obtained from our abstract arguments is consistent with the expressions already available in the literature for specific model theories involving non-minimal coupling of matter with higher derivative theories of gravity. Finally, we also argue that the physical process version of the first law holds for these theories with arbitrary non-minimal matter couplings.

arXiv comment31 pages + appendices. Section 7 on the physical process version of the first law with non-minimal interactions has been added. Version to appear in JHEP

References in corpus (33)

• Black Hole Entropy is Noether Charge
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• On Black Hole Entropy
• Entropy of Lovelock Black Holes
• Does backreaction enforce the averaged null energy condition in semiclassical gravity?
• A proof of the generalized second law for rapidly changing fields and arbitrary horizon slices
• Scalar fields, energy conditions, and traversable wormholes
• Increase of Black Hole Entropy in Higher Curvature Gravity
• The "physical process" version of the first law and the generalized second law for charged and rotating black holes
• A Second Law for Higher Curvature Gravity
• Global Extensions of Spacetimes Describing Asymptotic Final States of Black Holes
• The First Law of Black Hole Mechanics for Fields with Internal Gauge Freedom
• First law of black hole mechanics in Einstein-Maxwell and Einstein-Yang-Mills theories
• Generalized second law at linear order for actions that are functions of Lovelock densities
• 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
• The second law of black hole mechanics in effective field theory
• Causality in gravitational theories with second order equations of motion
• The Physical Process First Law for Bifurcate Killing Horizons
• Black Hole Thermodynamics: General Relativity and Beyond
• Square Peg in a Circular Hole: Choosing the Right Ansatz for Isolated Black Holes in Generic Gravitational Theories
• Black Hole Zeroth Law in Higher Curvature Gravity
• An entropy current for dynamical black holes in four-derivative theories of gravity
• Entropy functionals and c-theorems from the second law
• Towards a second law for Lovelock theories
• The zeroth law of black hole thermodynamics in arbitrary higher derivative theories of gravity
• On the physical process first law for dynamical black holes
• Physical process first law and caustic avoidance for Rindler horizon
• On Coupling NEC-Violating Matter to Gravity
• Investigating the Linearized Second Law in Horndeski Gravity
• Generalized proof of the linearized second law in general quadric corrected Einstein-Maxwell gravity
• Black Hole Zeroth Law in Horndeski Gravity

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• Nonlinear Einstein-Power-Yang-Mills AdS Black Holes: From Quantum Tunneling to Aschenbach Effect
• Linearised Second Law for Higher Curvature Gravity and Non-Minimally Coupled Vector Fields
• Entropy Current and Fluid-Gravity Duality in Gauss-Bonnet theory
• Entropy-current for dynamical black holes in Chern-Simons theories of gravity
• Dynamical entropy of charged black objects
• Iyer-Wald ambiguities and gauge covariance of Entropy current in Higher derivative theories of gravity
• Apparent Horizons Associated with Dynamical Black Hole Entropy
• Generalized Second Law for Non-minimally Coupled Matter Theories
• Noether gauge symmetry approach applying for the non-minimally coupled gravity to the Maxwell field