Gravity: a new holographic perspective

Abstract

A general paradigm for describing classical (and semiclassical) gravity is presented. This approach brings to the center-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, we 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^bcdR^a_bcd with ∃ _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 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 → T_ab + λg_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.