TY - JOUR

T1 - Superradiant instability of the Kerr brane

AU - Ishibashi, Akihiro

AU - Pani, Paolo

AU - Gualtieri, Leonardo

AU - Cardoso, Vitor

PY - 2015/9/29

Y1 - 2015/9/29

N2 - We consider linear gravitational perturbations of the Kerr brane, an exact solution of vacuum Einstein's equations in dimensions higher than four and a low-energy solution of string theory. Decomposing the perturbations in tensor harmonics of the trans-verse Ricci-flat space, we show that tensor- and vector-type metric perturbations of the Kerr brane satisfy respectively a massive Klein-Gordon equation and a Proca equation on the four-dimensional Kerr space, where the mass term is proportional to the eigenvalue of the harmonics. Massive bosonic fields trigger a well-known superradiant instability on a Kerr black hole. We thus establish that Kerr branes in dimensions D a parts per thousand yen 6 are gravi-tationally unstable due to superradiance. These solutions are also unstable against the Gregory-Laflamme instability and we discuss the conditions for either instability to occur and their rather different nature. When the transverse dimensions are compactified and much smaller than the Kerr horizon, only the superradiant instability is present, with a time scale much longer than the dynamical time scale. Our formalism can be also used to discuss other types of higher-dimensional black objects, taking advantage of recent progress in studying linear perturbations of four-dimensional black holes.

AB - We consider linear gravitational perturbations of the Kerr brane, an exact solution of vacuum Einstein's equations in dimensions higher than four and a low-energy solution of string theory. Decomposing the perturbations in tensor harmonics of the trans-verse Ricci-flat space, we show that tensor- and vector-type metric perturbations of the Kerr brane satisfy respectively a massive Klein-Gordon equation and a Proca equation on the four-dimensional Kerr space, where the mass term is proportional to the eigenvalue of the harmonics. Massive bosonic fields trigger a well-known superradiant instability on a Kerr black hole. We thus establish that Kerr branes in dimensions D a parts per thousand yen 6 are gravi-tationally unstable due to superradiance. These solutions are also unstable against the Gregory-Laflamme instability and we discuss the conditions for either instability to occur and their rather different nature. When the transverse dimensions are compactified and much smaller than the Kerr horizon, only the superradiant instability is present, with a time scale much longer than the dynamical time scale. Our formalism can be also used to discuss other types of higher-dimensional black objects, taking advantage of recent progress in studying linear perturbations of four-dimensional black holes.

KW - Classical Theories of Gravity

KW - Black Holes

KW - Black Holes in String Theory

KW - BLACK-HOLE

KW - PERTURBATIONS

KW - STRINGS

KW - DIMENSIONS

KW - EQUATION

U2 - 10.1007/JHEP09(2015)209

DO - 10.1007/JHEP09(2015)209

M3 - Journal article

VL - 2015

JO - Journal of High Energy Physics (Online)

JF - Journal of High Energy Physics (Online)

SN - 1126-6708

IS - 9

M1 - 209

ER -