General Relativity from a Thermodynamic Perspective
  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]
