Necessity and Extensions of Gibbons--Hawking--York Boundary Terms: Variational Well-Posedness, Corners and Null Boundaries, and Closure to Quasilocal Energy and Thermodynamics
Necessity and Extensions of Gibbons--Hawking--York Boundary Terms: Variational Well-Posedness, Corners and Null Boundaries, and Closure to Quasilocal Energy and Thermodynamics
On pseudo-Riemannian manifolds with (possibly non-smooth) boundaries, the variation of the Einstein--Hilbert bulk action contains normal derivative-type boundary fluxes; fixing only Dirichlet data for the induced metric h_{ab} does not suffice for well-posedness. In the framework of Levi--Civita connection and extrinsic curvature, this paper rigorously proves that adding the Gibbons--Hawking--York (GHY) term with orientation factor \varepsilon:=n^\mu n_\mu\in\{\pm 1\} at non-null boundaries canc
- National University of Singapore Singapore
General Relativity, Modular Flow, Unified Time Scale, Information Theory, Boundary Time Geometry, Wigner-Smith Time Delay, Causal Structure, QNEC, Quantum Scattering, Generalized Entropy, Spectral Shift Function, Time Geometry
General Relativity, Modular Flow, Unified Time Scale, Information Theory, Boundary Time Geometry, Wigner-Smith Time Delay, Causal Structure, QNEC, Quantum Scattering, Generalized Entropy, Spectral Shift Function, Time Geometry
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