
TL;DR
This paper explores a holographic relationship in gravitational actions, linking surface and bulk terms to entropy and energy, supporting the view of gravity as an emergent thermodynamic phenomenon.
Contribution
It introduces an alternative decomposition of gravitational actions into surface and bulk terms with thermodynamic interpretations, reinforcing the emergent gravity perspective.
Findings
Surface term equals Wald entropy on horizons.
Bulk term corresponds to energy density (ADM Hamiltonian).
Holographic relation relates energy and entropy descriptions.
Abstract
Einstein-Hilbert action and its natural generalizations to higher dimensions (like the Lanczos-Lovelock action) have certain peculiar features. All of them can be separated into a bulk and a surface term, with a specific ("holographic") relationship between the two, so that either term can be used to extract information about the other. Further, the surface term leads to entropy of the horizons on-shell. It has been argued in the past that these features are impossible to understand in the conventional approach but find a natural explanation if we consider gravity as an emergent phenomenon. We provide further support for this point of view in this paper. We describe an alternative decomposition of the Einstein-Hilbert action and Lanczos-Lovelock action into a new pair of surface and bulk terms, such that the surface term becomes Wald entropy on a horizon and the bulk term is the energy…
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