# Superradiant instabilities of asymptotically AdS black holes

### APA

Green, S. (2016). Superradiant instabilities of asymptotically AdS black holes. Perimeter Institute. https://pirsa.org/16020103

### MLA

Green, Stephen. Superradiant instabilities of asymptotically AdS black holes. Perimeter Institute, Feb. 16, 2016, https://pirsa.org/16020103

### BibTex

@misc{ pirsa_PIRSA:16020103, doi = {10.48660/16020103}, url = {https://pirsa.org/16020103}, author = {Green, Stephen}, keywords = {Particle Physics}, language = {en}, title = {Superradiant instabilities of asymptotically AdS black holes}, publisher = {Perimeter Institute}, year = {2016}, month = {feb}, note = {PIRSA:16020103 see, \url{https://pirsa.org}} }

Stephen Green Max Planck Institute for Gravitational Physics - Albert Einstein Institute (AEI)

## Abstract

Asymptotically AdS spacetimes with reflecting boundary conditions represent a natural setting for studying superradiant instabilities of rotating or charged black holes. In the first part of this talk, I prove that all asymptotically AdS black holes with ergoregions in dimension d ≥ 4 are linearly unstable to gravitational perturbations. This proof uses the canonical energy method of Hollands and Wald in a WKB limit. In the second part of the talk, I consider a charged Reissner-Nordstrom-AdS black hole---which is superradiantly unstable to charged scalar field perturbations at the linear level---and study the full *nonlinear* evolution of the instability. In this special case, the instability occurs even for spherically symmetric perturbations, which simplifies the analysis and allows for the use of numerical general relativity simulations. Our results show that nonlinear backreaction causes the black hole to lose charge and mass to the scalar field as the instability proceeds. Eventually, higher scalar field harmonics become nonsuperradiant, and they are reabsorbed into the black hole. The final state is described by a “hairy” black hole, surrounded by a scalar condensate in the fundamental (lowest) mode. I discuss implications of this work on the original problem of the rotating black hole superradiant instability.