Non-equilibrium Thermodynamics of Spacetime: the Role of Gravitational Dissipation

Details Non-equilibrium Thermodynamics of Spacetime: the Role of Gravitational Dissipation Non-equilibrium Thermodynamics of Spacetime: the Role of Gravitational Dissipation

2009-09-23

arxiv.org/abs/0909.4194v1

Phys.Rev.D81:024016,2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages, 1 figure

Scientific paper

10.1103/PhysRevD.81.024016

In arXiv:gr-qc/9504004 it was shown that the Einstein equation can be derived as a local constitutive equation for an equilibrium spacetime thermodynamics. More recently, in the attempt to extend the same approach to the case of $f(R)$ theories of gravity, it was found that a non-equilibrium setting is indeed required in order to fully describe both this theory as well as classical GR (arXiv:gr-qc/0602001). Here, elaborating on this point, we show that the dissipative character leading to a non-equilibrium spacetime thermodynamics is actually related -- both in GR as well as in $f(R)$ gravity -- to non-local heat fluxes associated with the purely gravitational/internal degrees of freedom of the theory. In particular, in the case of GR we show that the internal entropy production term is identical to the so called tidal heating term of Hartle-Hawking. Similarly, for the case of $f(R)$ gravity, we show that dissipative effects can be associated with the generalization of this term plus a scalar contribution whose presence is clearly justified within the scalar-tensor representation of the theory. Finally, we show that the allowed gravitational degrees of freedom can be fixed by the kinematics of the local spacetime causal structure, through the specific Equivalence Principle formulation. In this sense, the thermodynamical description seems to go beyond Einstein's theory as an intrinsic property of gravitation.

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