In AdS3 gravity with double-trace scalar boundary conditions, zero-frequency boson stars are the true ground state below the instability threshold, and hairy black holes carry higher entropy than BTZ at fixed mass and angular momentum.
New stability results for Einstein scalar gravity
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We consider asymptotically anti de Sitter gravity coupled to a scalar field with mass slightly above the Breitenlohner-Freedman bound. This theory admits a large class of consistent boundary conditions characterized by an arbitrary function $W$. An important open question is to determine which $W$ admit stable ground states. It has previously been shown that the total energy is bounded from below if $W$ is bounded from below and the bulk scalar potential $V(\phi)$ admits a suitable superpotential. We extend this result and show that the energy remains bounded even in some cases where $W$ can become arbitrarily negative. As one application, this leads to the possibility that in gauge/gravity duality, one can add a double trace operator with negative coefficient to the dual field theory and still have a stable vacuum.
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For m²L²=-2 in AdS black holes with integrable mixed boundary conditions, the cubic coefficient in the near-boundary expansion of the solution-dependent W(φ) is fixed by the boundary deformation to ensure a well-posed variational principle and finite renormalized action.
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When AdS$_3$ Grows Hair: Boson Stars, Black Holes, and Double-Trace Deformations
In AdS3 gravity with double-trace scalar boundary conditions, zero-frequency boson stars are the true ground state below the instability threshold, and hairy black holes carry higher entropy than BTZ at fixed mass and angular momentum.
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Holographic renormalization and the variational problem for mixed boundary conditions via a solution-dependent superpotential-like function
For m²L²=-2 in AdS black holes with integrable mixed boundary conditions, the cubic coefficient in the near-boundary expansion of the solution-dependent W(φ) is fixed by the boundary deformation to ensure a well-posed variational principle and finite renormalized action.