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The initial boundary value problem in General Relativity: the umbilic case

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arxiv 2104.08851 v1 pith:7GF2S55A submitted 2021-04-18 gr-qc math.APmath.DG

classification gr-qcmath.APmath.DG
keywords boundaryumbilicconditioncaseconditionscoordinatesgeneralgeometric
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We give a short proof of local well-posedness for the initial boundary value problem in general relativity with sole boundary condition the requirement that the boundary is umbilic. This includes as a special case the totally geodesic boundary condition that we had previously addressed in [8]. The proof is based on wave coordinates and the key observation that the momentum constraint is always valid for umbilic boundaries. This allows for a greater freedom in the choice of boundary conditions, since imposing the umbilic condition also provides Neumann boundary conditions for three of the four wave coordinates conditions. Moreover, the umbilic condition, being geometric, implies that geometric uniqueness in the sense of Friedrich holds in this specific case.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Fluid Boundary Conditions from AdS/BCFT

    hep-th 2025-07 conditional novelty 6.0 of 10

    In AdS/BCFT, the metric boundary condition on the end-of-the-world brane determines the fluid boundary condition: Neumann gives no-penetration plus Neumann conditions on velocity and temperature, and Dirichlet gives no-slip.

  2. Quantum stress-energy at timelike boundaries: testing a new beyond-$\Lambda$CDM parameter with cosmological data

    astro-ph.CO 2025-06 conditional novelty 6.0 of 10

    Timelike boundaries sourcing negative, 1/a-scaling vacuum energy fit CMB+BAO data slightly better than LCDM and relax the neutrino-mass constraint, though the preference is only about 2 sigma.

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