Bar-mode instability of rapidly spinning black hole in higher dimensions: Numerical simulation in general relativity

摘要

Numerical-relativity simulation is performed for rapidly spinning black holes(BHs) in a higher-dimensional spacetime of special symmetries for thedimensionality $6 \leq d \leq 8$. We find that higher-dimensional BHs, spinningrapidly enough, are dynamically unstable against nonaxisymmetric bar-modedeformation and spontaneously emit gravitational waves, irrespective of $d$ asin the case $d=5$ \cite{SY09}. The critical values of a nondimensional spinparameter for the onset of the instability are $q:=a/\mu^{1/(d-3)} \approx0.74$ for $d=6$, $\approx 0.73$ for $d=7$, and $\approx 0.77$ for $d=8$ where$\mu$ and $a$ are mass and spin parameters. Black holes with a spin smallerthan these critical values ($q_{\rm crit}$) appear to be dynamically stable forany perturbation. Longterm simulations for the unstable BHs are also performedfor $d=6$ and 7. We find that they spin down as a result of gravitational-waveemission and subsequently settle to a stable stationary BH of a spin smallerthan $q_{\rm crit}$. For more rapidly spinning unstable BHs, the timescale, forwhich the new state is reached, is shorter and fraction of the spin-down islarger. Our findings imply that a highly rapidly spinning BH with $q > q_{\rmcrit}$ cannot be a stationary product in the particle accelerators, even if itwould be formed as a consequence of a TeV-gravity hypothesis. Its implicationsfor the phenomenology of a mini BH are discussed.