Gravity: A New Holographic Perspective

TL;DR

This paper introduces a holographic framework for classical and semiclassical gravity, linking surface and bulk terms in the action, which offers new insights into gravity's nature and the cosmological constant problem.

Contribution

It proposes a universal Lagrangian form for semiclassical gravity based on holography, deriving Einstein-Hilbert and Gauss-Bonnet actions, and explains the invariance of field equations under vacuum energy shifts.

Findings

Gravity equations derive from surface terms, not bulk.

The approach explains the cosmological constant as an integration constant.

Holographic relation between surface and bulk terms in the action.

Abstract

A general paradigm for describing classical (and semiclassical) gravity is presented. This approach brings to the centre-stage a holographic relationship between the bulk and surface terms in a general class of action functionals and provides a deeper insight into several aspects of classical gravity which have no explanation in the conventional approach. After highlighting a series of unresolved issues in the conventional approach to gravity, I show that (i) principle of equivalence, (ii) general covariance and (iii)a reasonable condition on the variation of the action functional, suggest a generic Lagrangian for semiclassical gravity of the form $L=Q_a^{bcd}R^a_{bcd}$ with $\nabla_b Q_a^{bcd}=0$. The expansion of $Q_a^{bcd}$ in terms of the derivatives of the metric tensor determines the structure of the theory uniquely. The zeroth order term gives the Einstein-Hilbert action and the first order correction is given by the Gauss-Bonnet action. Any such Lagrangian can be decomposed into a surface and bulk terms which are related holographically. The equations of motion can be obtained purely from a surface term in the gravity sector. Hence the field equations are invariant under the transformation $T_{ab} \to T_{ab} + \lambda g_{ab}$ and gravity does not respond to the changes in the bulk vacuum energy density. The cosmological constant arises as an integration constant in this approach. The implications are discussed.