Spacetime Evolution and Equipartition in Lanczos-Lovelock Gravity

  • Sumanta ChakrabortyEmail author
Part of the Springer Theses book series (Springer Theses)


In the case of general relativity it is possible to interpret the Noether charge in any bulk region of spacetime as the heat content of its boundary surface. Further, the time evolution of spacetime metric in Einstein’s theory arises due to the difference between suitably defined surface and bulk degrees of freedom. In this chapter we demonstrate that this thermodynamic interpretation can be generalized in a natural fashion to all Lanczos-Lovelock theories of gravity. The Noether charge, related to time evolution vector field, in Lanczos-Lovelock gravity evaluated in a bulk region of space is equal to the heat content of the boundary surface. Here the temperature is defined using local Rindler observers and the entropy identified as the Wald entropy. Defining the surface degrees of freedom using Wald entropy and Komar energy density to define the bulk degrees of freedom, we can also show that the time evolution of the geometry is sourced by their difference. If the spacetime admits a timelike Killing vector field the holographic equipartition for Lanczos-Lovelock gravity follows.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Theoretical PhysicsIndian Association for the Cultivation of ScienceJadavpur, KolkataIndia

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