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abstract
We consider four-dimensional general relativity with vanishing cosmological constant defined on a manifold with a boundary. In Lorentzian signature, the timelike boundary is of the form $\boldsymbol{\sigma} \times \mathbb{R}$, with $\boldsymbol{\sigma}$ a spatial two-manifold that we take to be either flat or $S^2$. In Euclidean signature, we take the boundary to be $S^2\times S^1$. We consider conformal boundary conditions, whereby the conformal class of the induced metric and trace $K$ of the extrinsic curvature are fixed at the timelike boundary. The problem of linearised gravity is analysed using the Kodama-Ishibashi formalism. It is shown that for a round metric on $S^2$ with constant $K$, there are modes that grow exponentially in time. We discuss a method to control the growing modes by varying $K$. The growing modes are absent for a conformally flat induced metric on the timelike boundary. We provide evidence that the Dirichlet problem for a spherical boundary does not suffer from non-uniqueness issues at the linearised level. We consider the extension of black hole thermodynamics to the case of conformal boundary conditions, and show that the form of the Bekenstein-Hawking entropy is retained.
Forward citations
Cited by 7 Pith papers
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JT gravity on the worldline
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Linearized gravity in a cavity with conformal boundary conditions is ill-posed: a sequence of smooth perturbations with vanishing initial data grows without bound at every positive time.
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Quantum Liouville Cosmology
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Fluid Boundary Conditions from AdS/BCFT
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.
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Quantum stress-energy at timelike boundaries: testing a new beyond-$\Lambda$CDM parameter with cosmological data
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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GGI lectures on boundary and asymptotic symmetries
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