Myers-Perry Black Holes Research Articles

New construction of a vacuum doubly rotating black ring by the Ehlers transformation

Using the Ehlers transformation, we derive an exact solution for a doubly rotating black ring in five-dimensional vacuum Einstein theory. It is well known that the vacuum Einstein theory with three commuting Killing vector fields can be reduced to a nonlinear sigma model with SL(3,R) target space symmetry. As shown previously by Giusto and Saxena, the SO(2,1) subgroup in the SL(3,R) can generate a rotating solution from a static solution while preserving asymptotic flatness. This so-called Ehlers transformation actually transforms the five-dimensional Schwarzschild black hole into the five-dimensional Myers-Perry black hole. However, unlike the case with the black hole, applying this method directly to the static black ring or the Emparan-Reall black ring, does not yield a regular rotating black ring due to the emergence of a Dirac-Misner string singularity. To solve this undesirable issue, we use a singular vacuum solution of a rotating black ring/lens that already possesses a Dirac-Misner string singularity as the seed solution for the Ehlers transformation. The resulting solution is regular, indicating the absence of curvature singularities, conical singularities, orbifold singularities, Dirac-Misner string singularities, and closed timelike curves both on and outside the horizon. We show that this solution obtained by the Ehlers transformation coincides precisely with the Pomeransky-Sen’kov solution. We expect that applying this method to other theories may lead to the finding of new exact solutions, such as solutions for black lenses and capped black holes, as well as black ring configurations. Published by the American Physical Society 2024

Efficiency of magnetic Penrose process in higher dimensional Myers-Perry black hole spacetimes

In this paper, we consider a well-established magnetic Penrose process (MPP) and bring out its impact on the efficiency of energy extraction from higher dimensional (i.e., D>4) black holes. We derive the field equations of motion and determine the expressions for the energy efficiency of energy extraction for the case of higher dimensional black holes. We also examine the efficiency of energy extraction from black holes with (n−1) and n rotations. We demonstrate that black holes with (n−1) rotations has only one horizon, resulting in infinitely large energy efficiency even without MPP. On the other hand, for black holes with n rotations in D>4, the energy efficiency is not infinitely large, but the efficiency can be significantly enhanced by MPP. This enhancement allows for arbitrarily large energy efficiency. We find that the efficiency of energy extraction can exceed 100% for D=5, 6 and D=7, 8 dimensions. Interestingly, for rotation parameters near the extremal value, the energy efficiency remains above 100% in D=7, 8 compared to D=5, 6. MPP can eventually make higher dimensional black holes more efficient even with n rotations. Published by the American Physical Society 2024

Five-dimensional Myers-Perry black holes under massive scalar perturbation: bound states and quasinormal modes

The stability of five-dimensional singly rotating Myers-Perry Black Holes against massive scalar perturbations is studied. Both the quasibound states and quasinormal modes of the massive scalar field are considered. For the quasibound states, we use an analytical method to discuss the effective potential felt by the scalar field, and found that there is no potential well outside the event horizon. Thus, singly rotating Myers-Perry Black Holes are stable against the perturbation of quasibound states of massive scalar fields. Then, we use continued fraction method based on solving a seven-term recurrence relations to compute the spectra of the quasinormal modes. For different values of the black hole rotation parameter a, scalar mass parameter μ and angular quantum numbers, all found quasinormal modes are damped. Besides, when the scalar mass μ becomes relatively large, the long-living quasiresonances are also found as in other rotating black hole models. Our results complement previous arguments on the stability of five-dimensional singly rotating Myers-Perry black holes against massive scalar perturbations.

Universality in logarithmic temperature corrections to near-extremal rotating black hole thermodynamics in various dimensions

The low-temperature thermodynamics of near-extremal rotating black holes has recently been revisited to incorporate one-loop contributions that are dominant in this regime. We discuss these quantum corrections to the gravitational path integral for asymptotically Anti de-Sitter black holes in four and five dimensions. In four dimensions we explicitly consider Kerr-AdS4, Kerr-Newman-AdS4 and the rotating black hole in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 gauged supergravity with two scalars and two electric charges turned on. In five dimensions we explicitly address the asymptotically flat Myers-Perry black hole and the Kerr-AdS5 black hole. In every case we find that tensor modes contribute 32logTHawking\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{3}{2}\\log {T}_{\ extrm{Hawking}} $$\\end{document} to the low-temperature thermodynamics. We identify the root cause of this universality in two facts: (i) the universal presence of a SL(2, ℝ) subgroup of isometries in the near-horizon geometry and (ii) a set of cancellations in the Lichnerowicz operator. We show that these two conditions hold for near-extremal black holes in asymptotically flat and asymptotically AdS spacetimes of various dimensions.

Negative moment of inertia and rotational instability of gluon plasma

Using first-principle numerical simulations of the lattice SU(3) gauge theory, we calculate the isothermal moment of inertia of the rigidly rotating gluon plasma. We find that the moment of inertia unexpectedly takes a negative value below the “supervortical temperature” Ts=1.50(10)Tc, vanishes at T=Ts, and becomes a positive quantity at higher temperatures. The negative moment of inertia indicates a thermodynamic instability of rigid rotation. We derive the condition of thermodynamic stability of the vortical plasma and show how it relates to the scale anomaly and the magnetic gluon condensate. The rotational instability of gluon plasma shares a striking similarity with the rotational instabilities of spinning Kerr and Myers-Perry black holes.

Dynamics of Myers-Perry black holes with almost equal angular momenta in odd dimensions

We investigate the nonlinear dynamics of D = 2N + 3 Myers-Perry black holes with almost equal angular momenta, which have N equal spins out of possible N + 1 spins. In particular, we study the ultraspinning instability and the fate of its nonlinear evolution using the large D effective theory approach. We find that every stationary phase can be mapped to the counterpart in the singly rotating phase within the leading order effective theory. From the known results of singly rotating solutions, we obtain the phase diagram of almost equally rotating black holes. We also obtain a certain implication for the possible topology changing transition.

Holographic Schwinger effect in spinning black hole backgrounds* *Supported by the National Natural Science Foundation of China (NSFC) (12375140) and the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (G1323523064)

We perform a potential analysis for the holographic Schwinger effect in spinning Myers-Perry black holes. We compute the potential between the produced pair by evaluating the classical action of a string attached on a probe D3-brane at an intermediate position in the AdS bulk. We find that increasing the angular momentum reduces the potential barrier, thus enhancing the Schwinger effect, consistent with previous findings obtained via the local Lorentz transformation. In particular, these effects are more visible for the particle pair lying in the transversal plane compared with that along the longitudinal orientation. In addition, we discuss how the Schwinger effect changes with the shear viscosity to entropy density ratio at strong coupling under the influence of angular momentum.

Black hole horizons from the double copy

We describe a procedure for locating black hole horizons in ‘Kerr–Schild’ spacetimes in the double copy paradigm. Using only single- and zeroth-copy data on flat spacetime, our procedure predicts the existence of trapped surfaces in the double-copy gravitational solution. We show explicitly how this procedure locates the horizon of the Schwarzschild black hole and the general Myers–Perry black hole.

Flows of rotating extremal attractor black holes

We investigate the attractor mechanism of five-dimensional extremal rotating black holes in Einstein gravity minimally coupled with a multiplet complex scalar. By imposing regularity on the horizon, we show that the only possible attractor value of the scalar field is zero in our setup and that the local geometry is determined by the Myers-Perry black hole solution. We numerically obtain the extremal AdS black hole solutions interpolating the near horizon geometry to the asymptotic AdS spacetime under the existence of a bare potential of the scalar field. The black hole energy and the angular momenta are discretized for the usual Dirichlet boundary condition. Under the general boundary condition, we also find hairy extremal AdS black holes in which the energy is smaller than that of the extremal Myers-Perry AdS black hole solution for the same angular momentum.

Quasinormal modes and stability of higher dimensional rotating black holes under massive scalar perturbations

We consider the stability of six-dimensional singly rotating Myers-Perry black holes under massive scalar perturbations. Using Leaver's continued fraction method, we compute the quasinormal modes of the massive scalar fields. All modes found are damped under the quasinormal boundary conditions. It is also found that long-living modes called quasiresonances exist for large scalar masses as in the four-dimensional Kerr black hole case. Our numerical results provide a direct and complement evidence for the stability of six-dimensional MP black holes under massive scalar perturbation.

Scalar Love numbers and Love symmetries of 5-dimensional Myers-Perry black holes

The near-zone “Love” symmetry resolves the naturalness issue of black hole Love number vanishing with SL (2, ℝ) representation theory. Here, we generalize this proposal to 5-dimensional asymptotically flat and doubly spinning (Myers-Perry) black holes. We consider the scalar response of Myers-Perry black holes and extract its static scalar Love numbers. In agreement with the naturalness arguments, these Love numbers are, in general, non-zero and exhibit logarithmic running unless certain resonant conditions are met; these conditions include new cases with no previously known analogs. We show that there exist two near-zone truncations of the equations of motion that exhibit enhanced SL (2, ℝ) Love symmetries that explain the vanishing of the static scalar Love numbers in the resonant cases. These Love symmetries can be interpreted as local SL (2, ℝ) SL (2, ℝ) near-zone symmetries spontaneously broken down to global SL (2, ℝ) × U (1) symmetries by the periodic identification of the azimuthal angles. We also discover an infinite-dimensional extension of the Love symmetry into SL (2, ℝ) ltimes hat{U}{(1)}_{mathcal{V}}^2 that contains both Love symmetries as particular subalgebras, along with a family of SL (2, ℝ) subalgebras that reduce to the exact near-horizon Myers-Perry black hole isometries in the extremal limit. Finally, we show that the Love symmetries acquire a geometric interpretation as isometries of subtracted (effective) black hole geometries that preserve the internal structure of the black hole and interpret these non-extremal SL (2, ℝ) structures as remnants of the enhanced isometry of the near-horizon extremal geometries.

A Penrose-Type Inequality with Angular Momenta for Black Holes with 3-Sphere Horizon Topology

We establish a Penrose-type inequality with angular momentum for four-dimensional, biaxially symmetric, maximal, asymptotically flat initial datasets (M, g, k) for the Einstein equations with fixed angular momenta and horizon inner boundary associated to a 3-sphere outermost minimal surface. Moreover, equality holds if and only if the initial dataset is isometric to a canonical time slice of a stationary Myers-Perry black hole.

Exotic marginally outer trapped surfaces in rotating spacetimes of any dimension

The recently developed MOTSodesic method for locating marginally outer trapped surfaces (MOTSs) was effectively restricted to non-rotating spacetimes. In this paper we extend the method to include (multi-)axisymmetric time slices of (multi-)axisymmetric spacetimes of any dimension. We then apply this method to study MOTSs in the BTZ, Kerr and Myers–Perry black holes. While there are many similarities between the MOTSs observed in these spacetimes and those seen in Schwarzschild and Reissner-Nordström, details of the more complicated geometries also introduce some new, previously unseen, behaviours.

Phases of Rotating Black Objects in d = 5 Einstein–Gauss–Bonnet Theory

We considered several different classes of asymptotically flat, rotating black objects in d=5 Einstein–Gauss–Bonnet (EGB) theory. These are black holes with two equal-magnitude angular momenta, in which case extremal configurations are studied as well. Numerical evidence is also given for the existence of EGB generalizations of the Myers–Perry black holes with a single plane of rotation and of the Emparan–Reall balanced black rings. All solutions approach asymptotically the Minkowski background and present no singularities outside or on the horizon. The numerical results suggest that, for any mass of the solutions and any topology of the horizon, the rotating configurations exist up to a maximal value of the GB coupling constant, while the solutions with a spherical horizon topology still satisfy the Einstein gravity bound on angular momentum.

Gregory-Laflamme encounters Superradiance

We investigate the effect of superradiant scattering of gravitational perturbations on the stability of rotating black strings, focusing on the six dimensional equal-spinning Myers-Perry black string. We find that rapidly rotating black strings are unstable to gravitational superradiant modes within a bounded range of string lengths. The instability occurs because momentum along the string direction creates a potential barrier that allows for the confinement of superradiant modes. Yet, five dimensional Myers-Perry black holes do not have stable particle orbits so, unlike other known superradiant systems, these black strings remain stable to perturbations with sufficiently high azimuthal mode number — this is a ‘finite-m’ superradiant instability. For some parameters, this instability competes with the Gregory-Laflamme instability, but otherwise exists independently. The onset of this instability is degenerate and branches to multiple steady-state solutions. This paper is the first of a trilogy: in the next two, we construct two distinct families of rotating strings emerging from the superradiant onset (the ‘black resonator strings’ and ‘helical black strings’). We argue that similar physics is present in 5-dimensional Kerr black strings, but not in D > 6 equal-spinning Myers-Perry black strings.

From rotating to charged black holes and back again

The mild form of the Weak Gravity Conjecture (WGC) requires higher derivative corrections to extremal charged black holes to increase their charge-to-mass ratio. This allows decay via emission of a smaller extremal black hole. In this paper, we investigate if similar constraints hold for extremal rotating black holes. We do so by considering the leading higher derivative corrections to the four-dimensional Kerr black hole and five-dimensional Myers-Perry black hole. We use a known mapping of these rotating solutions to a four-dimensional non-rotating dyonic Kaluza-Klein black hole and impose the WGC on this charged solution. Going back again to the rotating solutions, this fixes the sign of the corrections to the rotating extremality bounds. The sign of the corrections is non-universal, depending on the black hole under consideration. We argue that this is not at odds with black hole decay, because of the presence of a superradiant instability that persists in the extremal limit. When this instability is present, the WGC is implied for the four-dimensional charged black hole.

Killing tensors of a generalized Lense-Thirring spacetime

We investigate the Hamilton-Jacobi equation of a probe particle moving on d-dimensional generalized Lense-Thirring metric. This space-time is different from the slowly rotating Myers-Perry black hole at second order in rotation parameters. We show that the dynamics of the probe particle along the time-like geodesic of the generalized Lense-Thirring space-time is super-integrable and has more constants of motion with respect to the same dynamics on Myers-Perry black hole. We also discuss the second rank Killing tensors associated with the generalized Lense-Thirring metric.

Local Dirac energy decay in the 5D Myers-Perry geometry using an integral spectral representation for the Dirac propagator

We consider the massive Dirac equation in the exterior region of the five-dimensional Myers-Perry black hole. Using the resulting ordinary differential equations (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 , in analogy with the case of the Dirac operator in the Kerr–Newman geometry (Finster et al 2003 Adv. Theor. Math. Phys. 7 25–52).

Signatures of extra dimensions in black hole jets

One of the leading mechanisms powering relativistic black hole jets is the Blandford-Znajek (BZ) process. Inspired by its success we construct energy extracting models for black holes in five space-time dimensions. Here, we find solutions to the force-free electrodynamic equations representing plasma-magnetospheres for slowly rotating Myers-Perry black holes. Both, energy and angular momentum fluxes are computed for these solutions realizing power extraction from black holes in higher dimensions. Comparisons of the main features of the five-dimensional BZ models with lower four-dimensional counterparts are discussed.

Weak cosmic censorship conjecture in Myers-Perry black hole with separability

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 the laws of thermodynamics support the conjecture.