Myers-Perry-AdS-dS black hole exhibits SO(2,1)xU(n) symmetry in the near horizon limit in the special case that all rotation parameters are equal. We consider a massive relativistic particle propagating on such a background and reduce it to superintegrable spherical mechanics with U(n) symmetry. A complete set of functionally independent u(n) generators realized in the model is given.
We demonstrate separability of the dynamical equations for all p-form fluxes in the Myers-Perry-(A)dS geometry, extending the earlier results for electromagnetic field. In the physically important cases of p=(1,2,3,4), we explicitly write the ODEs governing the dynamics of separable solutions.
We demonstrate separability of the Maxwell's equations in the Myers-Perry-(A)dS geometry and derive explicit solutions for various polarizations. Application of our construction to the four-dimensional Kerr black hole leads to a new ansatz for the Maxwell field which has significant advantages over the previously known parameterization.
We apply the new version of gedanken experiment designed recently by Sorce and Wald, to over-spin the 5-dimensional Myers-Perry black holes. As a result, the extremal black holes cannot be over-spun at the linear order. On the other hand, although the nearly extremal black holes could be over-spun at the linear order, this process is shown to be prohibited by the quadratic order correction. Thus no violation of the weak cosmic censorship conjecture occurs around the 5-dimensional Myers-Perry black holes.
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 obtain a new exact solution of the 5D Einstein equations in vacuum describing a distorted Myers-Perry black hole with a single angular momentum. Locally, the solution is interpreted as a black hole distorted by a stationary $U(1)\times U(1)$ symmetric distribution of external matter. Technically, the solution is constructed by applying a 2-fold Bäcklund transformation on a 5D distorted Minkowski spacetime as a seed. The physical quantities of the solution are calculated, and a local Smarr-like relation on the black hole horizon is derived. It possesses the same form as the Smarr-like relati…
In this note we demonstrate the existence of a one-parameter family of initial data for the vacuum Einstein equations in five dimensions representing small deformations of the extreme Myers-Perry black hole. This initial data set has `$t-ϕ^i$' symmetry and preserves the angular momenta and horizon geometry of the extreme solution. Our proof is based upon an earlier result of Dain and Gabach-Clement concerning the existence of $U(1)$-invariant initial data sets which preserve the geometry of extreme Kerr (at least for short times)
We investigate dynamics of probe particles moving in the near-horizon limit of (2N+1)-dimensional extremal Myers-Perry black hole with arbitrary rotation parameters. We observe that in the most general case with nonequal nonvanishing rotational parameters the system admits separation of variables in N-dimensional ellipsoidal coordinates. This allows us to find solution of the corresponding Hamilton-Jacobi equation and write down the explicit expressions of Liouville constants of motion.
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…
In this article we study the geodesic motion of test particles and light in the five-dimensional Myers-Perry-anti de Sitter spacetime. We derive the equations of motion and present their solutions in terms of the Weierstraß $\wp$-, $σ$- and $ζ$-functions. With the help of parametric diagrams and effective potentials we analyze the geodesic motion and give a list of all possible orbit types for timelike, null and spacelike geodesics. We plot examples of the orbits and take a look at the photon region in five dimensions. Furthermore we study spacelike geodesics and their relation to the AdS/CFT …
We study the class of vacuum (Ricci flat) six-dimensional spacetimes admitting a non-degenerate multiple Weyl aligned null direction l, thus being of Weyl type II or more special. Subject to an additional assumption on the asymptotic fall-off of the Weyl tensor, we prove that these spacetimes can be completely classified in terms of the two eigenvalues of the (asymptotic) twist matrix of l and of a discrete parameter $U^0=\pm 1/2, 0$. All solutions turn out to be Kerr-Schild spacetimes of type D and reduce to a family of "generalized" Myers-Perry metrics (which include limits and analytic cont…
We study the null geodesics extending from the near-horizon region out to the far region in the background of the Schwarzschild and the singly-spinning Myers-Perry black holes in the large dimension limit. We find that in this limit the radial integrals of these geodesics can be obtained by using the method of matched asymptotic expansions. If the motion of the photon is confined to the equator plane, then all geodesic equations are solvable analytically. The study in this paper may provide a toy model to analyze the observables relevant to the electromagnetic phenomena occurring near the blac…
We have investigated the upper bound of the radiation energy in the head-on collision of two Myers-Perry black holes. Initially, the two black holes are far away from each other, and they become one black hole after the collision. We have obtained the upper bound of the radiation energy thermodynamically allowed in the process. The upper bound of the radiation energy is obtained in general dimensions. The radiation bound depends on the alignments of rotating axes for a given initial condition due to spin-spin interaction. We have found that the collision may not be occurred for a initially ult…
In the present paper we explore the Hawking radiation as a quantum tunneling effect from a rotating 5 dimensional Myers-Perry black hole (5D-MPBH) with two independent angular momentum components. First, we investigate the Hawking temperature by considering the tunneling of massive scalar particles and spin-1 vector particles from the 5D-MPBH in the Painlevé coordinates and then in the corotating frames. More specifically, we solve the Klein-Gordon and Proca equations by applying the WKB method and Hamilton-Jacobi equation in both cases. Finally, we recover the Hawking temperature and show tha…
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…
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 …
Even though the Myers-Perry five dimensional rotating black hole with two rotations could be overspun by test particle accretion, yet it turns out as we show in this letter that it cannot do so for a single rotation. On the other hand it is known that there exists no extremal limit for a black hole with single rotation in dimensions greater than equal to six. It has been proven that all higher dimensional ($>4$) rotating black holes with only one single rotation can never be overspun under test particle linear accretion and hence would always obey CCC in the weak form.
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.
It has been shown that black holes could be used as particle accelerators to create arbitrarily high center-of-mass (CM) energy if certain critical conditions are satisfied. Most studies so far are confined in four-dimensional spacetimes. In this paper, we present a systematic analysis on five-dimensional Myers-Perry black holes and find some novel properties compared to four-dimensional Kerr black holes. Firstly, we give a rigorous proof that untrhigh energy collisions cannot occur near a five-dimensional nonextremal black hole. Secondly, For extremal black holes, we find a critical condition…
We investigate dynamics of probe particles moving in the near-horizon limit of extremal Myers-Perry black holes in arbitrary dimensions. Employing ellipsoidal coordinates we show that this problem is integrable and separable, extending the results of the odd dimensional case discussed in arXiv:1703.00713. We find the general solution of the Hamilton-Jacobi equations for these systems and present explicit expressions for the Liouville integrals, discuss Killing tensors and the associated constants of motion. We analyze special cases of the background near-horizon geometry were the system posses…
We investigate dynamics of probe particles moving in the near-horizon limit of (2N+1)-dimensional extremal Myers-Perry black hole (in the cases of N=3,4,5) with arbitrary rotation parameters. Very recently it has been shown arXiv:1703.00713v1 [hep-th] that in the most general case with nonequal nonvanishing rotational parameters the system admits separation of variables in N-dimensional ellipsoidal coordinates. We wrote down the explicit expressions of Liouville integrals of motion, given in arXiv:1703.00713v1 [hep-th] in ellipsoidal coordinates, in initial "Cartesian" coordinates in seven, ni…
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 construct a family of asymptotically flat, rotating black holes with scalar hair and a regular horizon, within five dimensional Einstein's gravity minimally coupled to a complex, massive scalar field doublet. These solutions are supported by rotation and have no static limit. They are described by their mass $M$, two equal angular momenta $J_1=J_2\equiv J$ and a conserved Noether charge $Q$, measuring the scalar hair. For vanishing horizon size the solutions reduce to five dimensional boson stars. In the limit of vanishing Noether charge density, the scalar field becomes point-wise arbitrar…
We construct rotating boson stars and Myers-Perry black holes with scalar hair (MPBHsSH) as fully non-linear solutions of five dimensional Einstein gravity minimally coupled to a complex, massive scalar field. The MPBHsSH are, in general, regular on and outside the horizon, asymptotically flat, and possess angular momentum in a single rotation plane. They are supported by rotation and have no static limit. Such hairy BHs may be thought of as bound states of boson stars and singly spinning, vacuum MPBHs and inherit properties of both these building blocks. When the horizon area shrinks to zero,…
We study the geodesic motion of massive and massless test particles in the background of equally spinning Myers-Perry-anti-de Sitter (AdS) black holes in five dimensions. By adopting a coordinate system that makes manifest the cohomogeneity-1 property of these spacetimes, the equations of motion simplify considerably. This allows us to easily separate the radial motion from the angular part and to obtain solutions for angular trajectories in a compact closed form. For the radial motion we focus our attention on spherical orbits. In particular, we determine the timelike innermost stable circula…
We construct dynamical black hole solutions with a helical symmetry in AdS$_5$, called black resonators, as well as their horizonless limits, called geons. We introduce a cohomogeneity-1 metric describing a class of black resonators and geons whose isometry group is $R\times SU(2)$. This allows us to study them in a wide range of parameters. We obtain the phase diagram for the black resonators, geons, and Myers-Perry-AdS$_5$, where the black resonators emerge from the onset of a superradiant instability of the Myers-Perry-AdS$_5$ with equal angular momenta and are connected to the geons in the…
Though under nonlinear accretion, all black holes in four and higher dimensions obey the weak cosmic censorship conjecture (CCC); however, they generally violate it for linear test particle accretion with the exception of five-dimensional rotating black hole with a single rotation. In dimensions greater than five, there exists no extremal condition for black hole with single rotation and hence it can never be overspun. However, the extremal condition does exist for five-dimensional black hole with two rotations and then it could indeed be overspun under linear accretion. In this paper, we stud…
We report on the end state of nonaxisymmetric instabilities of singly spinning asymptotically flat Myers-Perry black holes. Starting from a singly spinning black hole in D=5,6,7 dimensions, we introduce perturbations with angular dependence described by m=2, m=3, or m=4 azimuthal mode numbers about the axis of rotation. In D=5, we find that all singly spinning Myers-Perry black holes are stable, in agreement with the results from perturbation theory. In D=6 and 7, we find that these black holes are nonlinearly stable only for sufficiently low spins. For intermediate spins, although the m=2 bar…
