On S^3, curvature can stabilize R-symmetry charge transport of charged N=4 SYM plasma while thermodynamic instability persists, and volume fluctuations never restore thermodynamic stability.
Instability of charged black holes in anti-de Sitter space
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abstract
We exhibit a tachyonic mode in a linearized analysis of perturbations of large anti-de Sitter Reissner-Nordstrom black holes in four dimensions. In the large black hole limit, and up to a 0.7% discrepancy which is probably round-off error in the numerical analysis, the tachyon appears precisely when the black hole becomes thermodynamically unstable.
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New exact non-SUSY black brane solutions in 10D heterotic supergravity with two gauge charges show a spontaneous symmetry breaking and dynamical instability at low temperature that predicts additional black hole solutions.
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Instability in ${\cal N}=4$ supersymmetric Yang-Mills theory on $S^3$ at finite density
On S^3, curvature can stabilize R-symmetry charge transport of charged N=4 SYM plasma while thermodynamic instability persists, and volume fluctuations never restore thermodynamic stability.
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New analytic solutions of non-SUSY black branes in $10$-D heterotic supergravity and the phase transition
New exact non-SUSY black brane solutions in 10D heterotic supergravity with two gauge charges show a spontaneous symmetry breaking and dynamical instability at low temperature that predicts additional black hole solutions.