Perturbations of near-horizon geometries and instabilities of Myers-Perry black holes
Mark Durkee, Harvey S. Reall
备注：
24 pages (+ 16 pages appendices), 2 figures. v2: Corrected error in CFT operator dimensions (they are all integers). v3: Various improvements and corrections, in particular for electromagnetic perturbations. Accepted by Physical Review D
It is shown that the equations governing linearized gravitational (or electromagnetic) perturbations of the near-horizon geometry of any known extreme vacuum black hole (allowing for a cosmological constant) can be Kaluza-Klein reduced to give the equation of motion of a charged scalar field in AdS_2 with an electric field. One can define an effective Breitenlohner-Freedman bound for such a field. We conjecture that if a perturbation preserves certain symmetries then a violation of this bound should imply an instability of the full black hole solution. Evidence in favour of this conjecture is provided by the extreme Kerr solution and extreme cohomogeneity-1 Myers-Perry solution. In the latter case, we predict an instability in seven or more dimensions and, in 5d, we present results for operator conformal weights assuming the existence of a CFT dual. We sketch a proof of our conjecture for scalar field perturbations.
Inspired by the recent work on the spacetime structure near generic black hole horizons [1], the near horizon charges for an explicit example in higher dimensions than four (d > 4), namely for the five dimensional Myers-Perry metric with two equal rotation parameter are found in Hamiltonian formalism. Finding the supertranslation and the one-form superrotation, it is proved that the Myers-Perry black hole with two equal rotation parameter a = b does not satisfy the gauge flatness condition due to the non-vanishing associated field strength in five dimensional spacetime. It is shown that as the…
We investigate the weak cosmic censorship conjecture in Myers-Perry black holes with arbitrary rotations in general dimensions based on the scattering of a massless scalar field. From the fluxes of the scalar field flowing into the black hole, the changes in mass and angular momenta of the black hole are obtained. However, the extremal and near-extremal black holes with the aforementioned changes are still black holes in the final state. Hence, the conjecture is valid for our investigation. Furthermore, we analyze the changes in the black hole from a thermodynamic perspective to highlight that…
We investigate the separability of Klein-Gordon equation on near horizon of d-dimensional rotating Myers-Perry black hole in two limits : 1) generic extremal case and 2) extremal vanishing horizon case. In the first case , there is a relation between the mass and rotation parameters so that black hole temperature vanishes. In the latter case, one of the rotation parameters is restricted to zero on top of the extremality condition. We show that the Klein-Gordon equation is separable in both cases. Also, we solved the radial part of that equation and discuss its behaviour in small and large r re…
This study investigates the stability of higher-dimensional singly rotating Myers-Perry-de Sitter (MP-dS) black holes against scalar field perturbations. The phase spaces of MP-dS black holes with one spin parameter are discussed. Additionally, the quasinormal modes (QNMs) of MP-dS black holes are calculated via the asymptotic iteration method and sixth-order Wentzel-Kramers-Brillouin approximation. For near-extremal MP-dS black holes, the event horizon may be considerably close to the cosmological horizon. In such cases, the Pöschl-Teller technique yields an accurate analytic formula for the …
In this paper, we will obtain quantum work for a quantum scale five dimensional Myers-Perry black hole. Unlike heat represented by Hawking radiation, the quantum work is represented by a unitary information preserving process, and becomes important for black holes only at small quantum scales. It will be observed that at such short distances, the quantum work will be corrected by non-perturbative quantum gravitational corrections. We will use the Jarzynski equality to obtain this quantum work modified by non-perturbative quantum gravitational corrections. These non-perturbative corrections wil…
Static electromagnetic Love tensors of 5-dimensional Myers-Perry black holes
School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh（爱丁堡大学数学学院与麦克斯韦数学科学研究所）；Center for High Energy Physics, Peking University（北京大学高能物理中心）
We consider the massive Dirac equation in the exterior region of the 5-dimensional Myers-Perry black hole. Using the resulting ODEs obtained from the separation of variables of the Dirac equation, we construct an integral spectral representation for the solution of the Cauchy problem with compactly supported smooth initial data. We then prove that the probability of presence of a Dirac particle to be in any compact region of space decays to zero as $t\to\infty$, in analogy with the case of the Dirac operator in the Kerr-Newman geometry.
