AT1 - Extended Theories of Gravity and Quantum Cosmology |
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Speaker |
Kothawala, Dawood |
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| Talk Title |
Euclidean Quantum Gravity redux |
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Abstract |
I present a new framework for euclidean quantum gravity that replaces the conventional procedure of Wick rotation by a covariant, observer dependent class of metrics. Given a Lorentzian spacetime (M,g) and a non-vanishing −1 −1 timelike vector field u(λ) with level surfaces Σ, one can construct on M a class of metrics q = g − Θ(λ) u ⊗ u with an arbitrary function Θ that interpolates between the Euclidean (Θ = −2) and Lorentzian (Θ = 0) regimes, separated by the codimension one hypersurface Θ = −1. I will show that the curvature tensor and Einstein-Hilbert action associated with q and show that these have a rich mathematical structure: (i) The curvature acquires additional terms arise in the Euclidean regime Θ → −2 of q, thereby yielding a euclideanisation that is distinct from Wick rotation t → it. (ii) For the simplest choice of a step-profile for Θ, the Ricci scalar Ric[q] of q reduces to the complete Einstein-Hilbert lagrangian with the correct Gibbons-Hawking-York boundary term; the latter arises as a delta-function of strength 2K supported on Θ = −1. I discuss the several implications of the results for Euclidean quantum gravity, quantum cosmology, and small scale structure of spacetime. The talk will be essentially based on results presented in: arXiv: 1705.02504. |
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