Alladi Ramakrishnan Hall

The Dynamical Evolution of the Spacetime and Equipartition

Sumanta Chakraborty

IUCAA, Pune

In this talk I will show that in general relativity one can interpret the Noether charge in any bulk region as the heat content of its boundary surface. Further, the time evolution of the spacetime metric in Einstein's theory is due to the difference between suitably defined surface and bulk degrees of freedom. I further establish that this thermodynamic interpretation generalizes in a natural fashion to all Lanczos-Lovelock models of gravity. The Noether charge, related to time evolution vector field, in a bulk region of space is equal to the heat content TS of the boundary surface with proper interpretations for temperature and entropy. Using the Wald entropy to define the surface degrees of freedom and Komar energy density to define the bulk degrees of freedom, I will show that the time evolution of the geometry is sourced by their difference.
When it is possible to choose the foliation of spacetime such that metric is independent of time, the above dynamical equation yields the holographic equipartition for Lanczos-Lovelock gravity. The implications will be discussed.