Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2006-06-14
Int.J.Mod.Phys. D15 (2006) 1659-1676
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Plenary talk at the International Conference on Einstein's Legacy in the New Millennium, December 15 - 22, 2005, Puri, India;
Scientific paper
10.1142/S0218271806009029
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.
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