Quantum radiation from a 5-dimensional rotating black hole (original) (raw)
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Particle and light motion in a space-time of a five-dimensional rotating black hole
Physical Review D, 2003
We study motion of particles and light in a space-time of a 5-dimensional rotating black hole. We demonstrate that the Myers-Perry metric describing such a black hole in addition to three Killing vectors possesses also a Killing tensor. As a result, the Hamilton-Jacobi equations of motion allow a separation of variables. Using first integrals we present the equations of motion in the first-order form. We describe different types of motion of particles and light and study some interesting special cases. We proved that there are no stable circular orbits in equatorial planes in the background of this metric.
Five-dimensional rotating black hole in a uniform magnetic field: The gyromagnetic ratio
Physical Review D, 2004
In four dimensional general relativity, the fact that a Killing vector in a vacuum spacetime serves as a vector potential for a test Maxwell field provides one with an elegant way of describing the behaviour of electromagnetic fields near a rotating Kerr black hole immersed in a uniform magnetic field. We use a similar approach to examine the case of a five dimensional rotating black hole placed in a uniform magnetic field of configuration with bi-azimuthal symmetry, that is aligned with the angular momenta of the Myers-Perry spacetime. Assuming that the black hole may also possess a small electric charge we construct the 5-vector potential of the electromagnetic field in the Myers-Perry metric using its three commuting Killing vector fields. We show that, like its four dimensional counterparts, the five dimensional Myers-Perry black hole rotating in a uniform magnetic field produces an inductive potential difference between the event horizon and an infinitely distant surface. This potential difference is determined by a superposition of two independent Coulomb fields consistent with the two angular momenta of the black hole and two nonvanishing components of the magnetic field. We also show that a weakly charged rotating black hole in five dimensions possesses two independent magnetic dipole moments specified in terms of its electric charge, mass, and angular momentum parameters. We prove that a five dimensional weakly charged Myers-Perry black hole must have the value of the gyromagnetic ratio g = 3.
The Fate of a Five-Dimensional Rotating Black Hole via Hawking Radiation
Progress of Theoretical Physics, 2005
We study the evolution of a five-dimensional rotating black hole emitting scalar field radiation via the Hawking process for arbitrary initial values of the two rotation parameters a and b. It is found that any such black hole whose initial rotation parameters are both nonzero evolves toward an asymptotic state a/M 1/2 = b/M 1/2 = const( = 0), where this constant is independent of the initial values of a and b. * )
A Rigorous Treatment of Energy Extraction from a Rotating Black Hole
Communications in Mathematical Physics, 2009
The Cauchy problem is considered for the scalar wave equation in the Kerr geometry. We prove that by choosing a suitable wave packet as initial data, one can extract energy from the black hole, thereby putting supperradiance, the wave analogue of the Penrose process, into a rigorous mathematical framework. We quantify the maximal energy gain. We also compute the infinitesimal change of mass and angular momentum of the black hole, in agreement with Christodoulou's result for the Penrose process. The main mathematical tool is our previously derived integral representation of the wave propagator.
General Relativity and Gravitation, 2007
We study the effect of an external magnetic field on the stability of circular motion around a five dimensional Myers-Perry metric. Using the Hamilton-Jacobi formalism we derive the effective potential for the radial motion of charged particles around a five dimensional rotating black hole in a uniform magnetic field. We show that there are stable circular orbits around a five dimensional rotating black hole immersed in a uniform magnetic field.
Angular profile of emission of non-zero spin fields from a higher-dimensional black hole
Physics Letters B, 2009
Recent works have included the effect of rotation on simulations of black hole events at the LHC, showing that the angular momentum of the black hole cannot be ignored and it makes a non-trivial contribution for most of the lifetime of the black hole. A key consequence of the rotation of the black hole is that the Hawking radiation is no longer isotropic, making it more difficult to infer space–time parameters from measurements of the emitted particles. In this Letter we study the angular distribution of the Hawking emission of non-zero spin particles with specific helicity on the brane. We argue that the shape of the distribution could be used as a measure of the angular momentum of the black hole.
Scalar radiation emitted from a source rotating around a black hole
Classical and Quantum Gravity, 2000
We analyze the scalar radiation emitted from a source rotating around a Schwarzschild black hole using the framework of quantum field theory at the tree level. We show that for relativistic circular orbits the emitted power is about 20% to 30% smaller than what would be obtained in Minkowski spacetime. We also show that most of the emitted energy escapes to infinity. Our formalism can readily be adapted to investigate similar processes.
Physical Review D
In the context of the dynamics and stability of black holes in modified theories of gravity, we derive the Teukolsky equations for massless fields of all spins in general spherically symmetric and static metrics. We then compute the short-ranged potentials associated with the radial dynamics of spin 1 and spin 1=2 fields, thereby completing the existing literature on spin 0 and 2. These potentials are crucial for the computation of Hawking radiation and quasinormal modes emitted by black holes. In addition to the Schwarzschild metric, we apply these results and give the explicit formulas for the radial potentials in the case of charged (Reissner-Nordström) black holes, higher-dimensional black holes, and polymerized black holes arising from loop quantum gravity. These results are, in particular, relevant and applicable to a large class of regular black hole metrics. The phenomenological applications of these formulas will be the subject of a companion paper.
Emission of massive scalar fields by a higher-dimensional rotating black hole
Physical Review D, 2010
We perform a comprehensive study of the emission of massive scalar fields by a higher-dimensional, simply rotating black hole both in the bulk and on the brane. We derive approximate, analytic results as well as exact numerical ones for the absorption probability, and demonstrate that the two sets agree very well in the low and intermediate-energy regime for scalar fields with mass m_\Phi < 1 TeV in the bulk and m_\Phi < 0.5 TeV on the brane. The numerical values of the absorption probability are then used to derive the Hawking radiation power emission spectra in terms of the number of extra dimensions, angular-momentum of the black hole and mass of the emitted field. We compute the total emissivities in the bulk and on the brane, and demonstrate that, although the brane channel remains the dominant one, the bulk-over-brane energy ratio is considerably increased (up to 33%) when the mass of the emitted field is taken into account.
Black Hole as a Quantum Field Configuration
Universe, 2020
We describe 4D evaporating black holes as quantum field configurations by solving the semi-classical Einstein equation G μ ν = 8 π G ⟨ ψ | T μ ν | ψ ⟩ and quantum matter fields in a self-consistent manner. As the matter fields, we consider N massless free scalar fields (N is large). We find a spherically symmetric self-consistent solution of the metric g μ ν and the state | ψ ⟩ . Here, g μ ν is locally A d S 2 × S 2 geometry, and | ψ ⟩ provides ⟨ ψ | T μ ν | ψ ⟩ = ⟨ 0 | T μ ν | 0 ⟩ + T μ ν ( ψ ) , where | 0 ⟩ is the ground state of the matter fields in the metric and T μ ν ( ψ ) consists of the excitation of s-waves that describe the collapsing matter and Hawking radiation with the ingoing negative energy flow. This object is supported by a large tangential pressure ⟨ 0 | T θ θ | 0 ⟩ due to the vacuum fluctuation of the bound modes with large angular momenta l ≫ 1 . This describes the interior of the black hole when the back reaction of the evaporation is taken into account. In this...