On the physical process first law for dynamical black holes

Abstract

Physical process version of the first law of black hole mechanics relates the change in entropy of a perturbed Killing horizon, between two asymptotic cross sections, to the matter flow into the horizon. Here, we study the mathematical structure of the physical process first law for a general diffeomorphism invariant theory of gravity. We analyze the effect of ambiguities in the Wald's definition of entropy on the physical process first law. We show that for linearized perturbations, the integrated version of the physical process law, which determines the change of entropy between two asymptotic cross-sections, is independent of these ambiguities. In case of entropy change between two intermediate cross sections of the horizon, we show that it inherits additional contributions, which coincide with the membrane energy associated with the horizon fluid. Using this interpretation, we write down a physical process first law for entropy change between two arbitrary non-stationary cross sections of the horizon for both general relativity and Lanczos-Lovelock gravity.

v3; Minor revision; Published version

References in corpus (7)

• Entropy density of spacetime and the Navier-Stokes fluid dynamics of null surfaces
• A Novel Formula for Bulk Viscosity from the Null Horizon Focusing Equation
• Variational Principle for Gravity with Null and Non-null boundaries: A Unified Boundary Counter-term
• The Physical Process First Law for Bifurcate Killing Horizons
• Entropy of a generic null surface from its associated Virasoro algebra
• Physical process first law and caustic avoidance for Rindler horizon
• Black Hole Entropy production and Transport coefficients in Lovelock Gravity

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• A new formula for conserved charges of Lovelock gravity in AdS spacetimes and its generalization
• Iyer-Wald ambiguities and gauge covariance of Entropy current in Higher derivative theories of gravity
• Physical Process First Law and the Entropy Change of Rindler Horizons
• An entropy current and the second law in higher derivative theories of gravity
• Thermodynamics and phase transitions of $\kappa$-deformed Schwarzschild-AdS black holes