QG2 - Quantum Gravity Phenomenology |
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Speaker |
Kothawala, Dawood |
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| Talk Title |
Euclidean Action And The Einstein Tensor |
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Abstract |
The conventional formulation of Euclidean Quantum Gravity is based on Wick rotation, a procedure that is ill-defined and ambiguous. I give a local description of the Euclidean regime (M,g,u) of Lorentzian spacetimes (M,g) based on timelike geodesics u passing through an arbitrary event p0 ∈ M. I show that, to leading order, the Euclidean Einstein-Hilbert action S is proportional to the Einstein tensor G[g](u, u). The positivity of S follows if G[g](u,u) > 0 holds. I suggest an interpretation of this result in terms of the amplitude A[Σ0] = exp[−S] for a single space-like hypersurface Σ0 ∈ I+(p0) to emerge at a constant geodesic distance λ0 from p0. Implications for classical and quantum gravity are discussed. I discuss several implications of the results for classical and quantum gravity, as well as for the small scale structure of spacetime. In particular, the relevance of the result for the emergence of Einstein equations in the classical limit, through the euclidean action, is highlighted. The talk will be essentially based on the results presented in: arXiv: 1802.07055. |
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