General Relativity from a Thermodynamic Perspective

Abstract

I show that the gravitational dynamics in a bulk region of space can be connected to a thermodynamic description in the boundary of that region, thereby providing clear physical interpretations of several mathematical features of classical general relativity: (1) The Noether charge contained in a bulk region, associated with a specific time evolution vector field, has a direct thermodynamic interpretation as the gravitational heat content of the boundary surface. (2) This result, in turn, shows that all static spacetimes maintain holographic equipartition; in these spacetimes, the number of degrees of freedom in the boundary is equal to the number of degrees of freedom in the bulk. (3) In a general, evolving spacetime, the rate of change of gravitational momentum is related to the difference between the number of bulk and boundary degrees of freedom. It is this departure from the holographic equipartition which drives the time evolution of the spacetime. (4) When the equations of motion hold, the (naturally defined) total energy of the gravity plus matter within a bulk region, will be equal to the boundary heat content. (5) After motivating the need for an alternate description of gravity (if we have to solve the cosmological constant problem), I describe a thermodynamic variational principle based on null surfaces to achieve this goal. The concept of gravitational heat density of the null surfaces arises naturally from the Noether charge associated with the null congruence. The null surface variational principle, in fact, extremises the total heat content of the matter plus gravity system. Several variations on this theme and implications are described. [Abridged]

ver3: minor corrections; 54 pages

References in corpus (7)

• Dark Energy and Gravity
• Entropy of Null Surfaces and Dynamics of Spacetime
• Holography of Gravitational Action Functionals
• Entropy density of spacetime and the Navier-Stokes fluid dynamics of null surfaces
• Noether current from the surface term of gravitational action, Virasoro algebra and horizon entropy
• Thermodynamic structure of Lanczos-Lovelock field equations from near-horizon symmetries
• Holography in Action

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