Gravity: A New Holographic Perspective

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 bcd a R a bcd with ∇b Q bcd a = 0. The expansion of Q bcd a 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 Tab → Tab +λgab 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. 1 Why fix it when it works? Any attempt to provide a radically new perspective on gravity requires strong and clear motivation, since standard general relativity has been a very successful theory. So I will begin by providing the motivation for the alternative approach and identifying the ingredients it should have. The elegance of general relativistic description of gravity rests on the geometric structure, which — in turn — is based on the Principle of Equivalence. I will interpret the Principle of Equivalence as allowing the description of gravity in terms of a metric tensor and a compatible, torsion-free, connection leading to the existence of local inertial frames around each event. This determines the kinematics of gravity (‘how gravity tells matter to move’) through the use of special relativity in the local inertial frames. 1Invited plenary talk delivered at the International Conference on Einstein’s Legacy in the New Millennium, December 15 22, 2005, Puri, India.