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arXiv · 1812.11742

Study of Semiclassical Instability of the Schwarzschild AdS Black Hole in the Large $D$ Limit

Amruta Sadhu·Vardarajan Suneeta
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Abstract

We analyze the semiclassical stability of the Schwarzschild AdS black hole in the Euclidean partition function approach. We perform this computation in the large $D$ limit and focus on scalar perturbations. We obtain the equations for non-spherically symmetric scalar perturbations in a simple form. For a class of perturbations stability is demonstrated by the S-deformation method. For some other classes we rule out unstable modes of $\mathcal{O}(D^2)$. We also analyze the spherically symmetric perturbations and demonstrate the appearance of an unstable mode for small black holes in the large $D$ limit. We obtain an expression for the eigenvalue corresponding to the unstable mode to next to leading order in a $1/D$ expansion. This result agrees with a previously obtained numerical bound on this eigenvalue. For cosmological constant zero, our answer matches a previous result obtained for the corresponding eigenvalue for the $D$ dimensional Schwarzschild-Tangherlini black hole to next to leading order in a $1/D$ expansion.

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Amruta Sadhu, Vardarajan Suneeta. 2018-12-31. Study of Semiclassical Instability of the Schwarzschild AdS Black Hole in the Large $D$ Limit. https://doi.org/10.1088/1361-6382%2Fab1d69

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