Spacetime thermodynamics in the presence of torsion

Abstract

It was shown by Jacobson in 1995 that the Einstein equation can be derived as a local constitutive equation for an equilibrium spacetime thermodynamics. With the aim to understand if such thermodynamical description is an intrinsic property of gravitation, many attempts have been done so far to generalise this treatment to a broader class of gravitational theories. Here we consider the case of the Einstein-Cartan theory as a prototype of theories with non-propagating torsion. In doing so, we study the properties of Killing horizons in the presence of torsion, establish the notion of local causal horizon in Riemann-Cartan spacetimes, and derive the generalised Raychaudhuri equation for this kind of geometries. Then, starting with the entropy that can be associated to these local causal horizons, we derive the Einstein-Cartan equation by implementing the Clausius equation. We outline two ways of proceeding with the derivation depending on whether we take torsion as a geometric field or as a matter field. In both cases we need to add internal entropy production terms to the Clausius equation as the shear and twist cannot be taken to be zero a priori for our setup. This fact implies the necessity of a non-equilibrium thermodynamics treatment for the local causal horizon. Furthermore, it implies that a non-zero twist at the horizon will in general contribute to the Hartle-Hawking tidal heating for black holes with possible implications for future observations.

18 pages

References in corpus (4)

• Emergent Gravity Paradigm: Recent Progress
• Hydrodynamics of spacetime and vacuum viscosity
• Coarse graining flow of spin foam intertwiners
• Raychaudhuri equation in spacetimes with torsion

Cited by in corpus (19)

• Noether charge and black hole entropy in teleparallel gravity
• Raychaudhuri equations and gravitational collapse in Einstein-Cartan theory
• Thermodynamic structure of a generic null surface and the zeroth law in scalar-tensor theory
• Relativistic cosmology and intrinsic spin of matter: Results and theorems in Einstein-Cartan theory
• Revisiting wormhole energy conditions in Riemann-Cartan spacetimes and under Weyl transformations
• Singularity theorems and the inclusion of torsion in affine theories of gravity
• Covariant approach to the thermodynamic structure of a generic null surface
• Kinematics and dynamics of null hypersurfaces in the Einstein-Cartan spacetime and related thermodynamic interpretation
• Lorentzian quantum cosmology with torsion
• Kinematics in Metric-Affine Geometry
• Focusing conditions for extended teleparallel gravity theories
• Lagrangian Formulation of the Raychaudhuri Equation in Non-Riemannian Geometry
• Recovering semiclassical Einstein's equation using generalized entropy
• Tidal heating in a Riemann-Cartan spacetime
• Jacobson's thermodynamic approach to classical gravity applied to non-Riemannian geometries: remarks on the simplicity of Nature
• Possible fluid interpretation and tidal force equation on a generic null hypersurface in Einstein-Cartan theory
• Off-Shell ADT Conserved Quantities in Palatini Gravity
• Black Holes as a Gateway to the Quantum: Classical and Semi-Classical Explorations
• Near-horizon geometry with torsion: Kerr-AdS black hole