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We formulate an initial boundary value problem (IBVP) for the vacuum Einstein equations by describing the boundary conditions of a spacetime metric in its associated gauge.
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Alberto Enciso and Niky Kamran, Lorentzian Einstein metrics with prescribed conformal infinity , J. Differential Geom. 112
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Luis Aké, José L. Flores, and Miguel Sánchez, Structure of globally hyperbolic spacetimes-with-timelike-boundary , Rev. Mat. Iberoam. 37
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Zhongshan An and Michael T. Anderson, The initial boundary value problem and quasi-local Hamiltonians in general relativity , Classical Quantum Gravity 38
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Olivier Sarbach and Manuel Tiglio, Continuum and discrete initial-boundary value problems and einstein’s field equations , Living Rev. Relativ. 15
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by same author, On the topology and future stability of the universe , Oxford Mathematical Monographs, Oxford University Press, Oxford, 2013. MR 3186493
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Grigorios Fournodavlos and Jacques Smulevici, The initial boundary value problem for the Einstein equations with totally geodesic timelike boundary , Comm. Math. Phys. 385
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by same author, The initial boundary value problem in general relativity: the umbilic case , Int. Math. Res. Not. (2023), no. 5, 3790–3807
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Michael T. Anderson, On boundary value problems for Einstein metrics , Geom. Topol. 12
2045
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