Stationary electromagnetic fields around black holes

In the framework of the Newman-Penrose formalism the electromagnetic field of a general stationary source occurring in the vicinity of a Schwarzschild black hole is obtained in the test-field approximation. The field is expressed in terms of hypergeometric functions (radial parts) and spin-s spherical harmonics (angular parts) both outside and inside the radius at which the source is, located. As examples, the fields of point charges, charged rings, current loops and magnetic dipoles (generally located in non-axisymmetric positions) are calculated.     

Stationary electromagnetic fields around a rotating black hole

The general stationary solution of Maxwell's equations in the Kerr background geometry is given. Future applications are outlined.     

Stationary axisymmetric solutions of the Jordan-Brans-Dicke equations with electromagnetic sources

Any stationary axisymmetric solution of the coupled JBD-Maxwell field equations such thatF _ab ^* t^ab vanishes, can be determined from a composition of any stationary axisymmetric Einstein-Maxwell spacetime with the Weyl class of metrics.     

A boosted Kerr black hole solution and the structure of a general astrophysical black hole

A solution of Einstein’s vacuum field equations that describes a boosted Kerr black hole relative to an asymptotic Lorentz frame at future null infinity is derived. The solution has three parameters (mass, rotation and boost) and corresponds to the most general configuration that an astrophysical black hole must have; it reduces to the Kerr solution when the boost parameter is zero. In this solution the ergosphere is north-south asymmetric, with dominant lobes in the direction opposite to the boost. However the event horizon, the Cauchy horizon and the ring singularity—which are the core of the black hole structure—do not alter, being independent of the boost parameter. Possible consequences for astrophysical processes connected with Penrose processes in the asymmetric ergosphere are discussed.     

Orbits through the ergosphere of a Kerr black hole

We study the positions of orbits around a Kerr black hole with respect to its ergosphere. Ther– motions of zero-energy (E=0) null geodesies are inside truncated circular sectors, whose outer corners are on the static limit. Timelike geodesies with the same constants of motion are restricted inside a smaller area. For certain parameter values there are also orbits inside the inner horizon not reaching the center. Then we study the various types of orbits on the plane of symmetry for all the values of the angular momentum of the black hole 0aM, and of the angular momentum of the photons, or particles,L, and for all the values of the energyE. In particular we find the possible positions of the turning points with respect to the ergosphere. A restriction imposed by physical considerations is that the coordinate time increases when the proper time increases. This allows us to distinguish between positive and negative energy orbits. All negative energy orbits enter the horizon of the black hole.     

Analytic solutions in the acoustic black hole analogue of the conical Kerr metric

We study the sound perturbation of a rotating acoustic black hole in the presence of a disclination.The radial part of the niassless Klein-Gordon equation is written into a Heun form,and its analytical solution is obtained.These solutions have an explicit dependence on the parameter of the disclination.We obtain the exact Hawking-Unruh radiation spectrum.     

Stationary solutions of the Dirac equation in the gravitational field of a charged black hole

A stationary solution of the Dirac equation in the metric of a Reissner-Nordström black hole has been found. Only one stationary regular state outside the black hole event horizon and only one stationary regular state below the Cauchy horizon are shown to exist. The normalization integral of the wave functions diverges on both horizons if the black hole is non-extremal. This means that the solution found can be only the asymptotic limit of a nonstationary solution. In contrast, in the case of an extremal black hole, the normalization integral is finite and the stationary regular solution is physically self-consistent. The existence of quantum levels below the Cauchy horizon can affect the final stage of Hawking black hole evaporation and opens up the fundamental possibility of investigating the internal structure of black holes using quantum tunneling between external and internal states.     

Back-reaction of the Kerr black hole. A thermodynamical approach

A thermodynamical approach is used to solve the back-reaction problem of the Kerr black hole; the dressed mass, the dressed angular momentum, and the dressed entropy are calculated.     

Point charge in the vicinty of a Kerr black hole

We derive the expression for the electromagnetic field of a point charge at rest on the symmetry axis near a rotating Kerr black hole. This is a generalization of the previously obtained solution for the field of a point charge near a nonrotating Schwarzschild black hole. Unlike the Schwarzschild case the charge is found to give rise to magnetic fields as seen by a stationary or locally nonrotating observer.     

Motion of the charged particles off the equatorial plane of a Kerr black hole in an electromagnetic field

Charged particle orbits off the equatorial plane of a Kerr black hole in an external electromagnetic field is studied, both for dipole as well as uniform magnetic field. Particles are found to get trapped by the magnetic field if the initial value of the parallel velocity is small. Bending of the field lines in the vicinity of the hole and the consequent trapping of the particles in an otherwise uniform magnetic field indicates the significance of general relativistic effects in such cases.     

Notes on the hidden conformal symmetry in the near horizon geometry of the Kerr black hole

Toward the Kerr/CFT correspondence for the generic non-extremal Kerr black hole, the analysis of scattering amplitudes by near extremal Kerr provides a clue. This pursuit reveals a hidden conformal symmetry in the low frequency wave equation for a scalar field in a certain spacetime region referred to as the near region. For extremal case, the near region is expected to be the near horizon region in which the correspondence via the asymptotic symmetry is studied. We investigate the hidden conformal symmetry in the near horizon limit and consider the relation between the hidden conformal symmetry and the asymptotic symmetry in the near horizon limit. By using an appropriate definition of the quasi-local charge, we obtain the deviation of the entropy from the extremality.     

Counting the microstates of a Kerr black hole in M theory

We show that an extremal Kerr black hole, appropriately lifted to M theory, can be transformed to a Kaluza-Klein black hole in M theory, or a D0-D6 charged black hole in string theory. Since all the microstates of the latter have recently been identified, one can exactly reproduce the entropy of an extremal Kerr black hole. We also show that the topology of the event horizon is not well defined in M theory.     

Globally regular solutions of a schwarzschild black hole and a Reissner-Nordström black hole

A new physical concept about globally regular solutions is suggested. The globally regular solutions corresponding to the Schwarzschild black hole and the Reissner-Nordström black hole are examined.     

A class of exact solutions to the force-free,axisymetric, stationary magnetosphere of a Kerr black hole

We analyze the constraint equation giving allowed solutions describing fields and currents in a force-free magnetosphere around a rotating black hole. Utilizing the divergence properties of the energy and angular-momentum fluxes, for physically allowed solutions with nonzero energy and angular momentum extraction, we conclude that poloidal surfaces are independent of the radial coordinate for large values of r. Imposing this requirement and the Znajek regularity condition, we explicitly derive all possible exact solutions admitted by the constraint equation for r independent poloidal surfaces which are given in terms of the electromagnetic angular velocity function , where a is the angular momentum per unit mass of the black hole. Further, we show that for the class of solutions we have developed there is no electromagnetic extraction of energy. G. M. acknowledges funding through a Troy University sabbatical. The work of C. D. D. is supported by the Office of Naval Research. This research was also supported through NASA GLAST Science Investigation No. DPR-S-1563-Y.     

Wave optics of the spherical gravitational lens. II. Diffraction of a plane electromagnetic wave by a black hole

This paper gives (in a suitable approximation) the Poynting vector of a plane electromagnetic wave diffracted by the gravitational field of a Schwarzschild black hole. The relation between the approximation procedure and the concept of rays is established. The main results are as follows: (1) On the focal line an extreme amplification of intensity takes place. (2) In the whole space off this focal line a double image is to be seen. (3) Rays having revolved around the black hole repeatedly give small corrections only. (4) The phase differences (transit-time differences) along the different rays are computed.     

Exact solutions for spherical gravitational collapse around a black hole:the effect of tangential pressure

Spherical gravitational collapse towards a black hole with non-zero tangential pressure is studied.Exact solutions corresponding to different equations of state are given.We find that when taking the tangential pressure into account,the exact solutions have three qualitatively different outcomes.For positive tangential pressure,the shell around a black hole may eventually collapse onto the black hole,or expand to infinity,or have a static but unstable solution,depending on the combination of black hole mass,mass of the shell and the pressure parameter.For vanishing or negative pressure,the shell will collapse onto the black hole.For all eventually collapsing solutions,the shell will cross the event horizon,instead of accumulating outside theeventhorizon,even if clocked by a distant stationary observer.     

Hawking radiation of scalar and Dirac quanta from a Kerr black hole

Unruh’s technique of replacing collapse by boundary conditions on the past horizon (theξ-quantisation scheme) for the derivation of the well-known Hawking radiation is extended to the Kerr black hole for the scalar and especially for the spin half field. The expectation value of the energy momentum tensor is evaluated asymptotically in theξ-vacuum state yielding explicitly the net Hawking flux of scalar and spin half quanta. The appropriate statistical distribution that emerges naturally for Dirac quanta validates the ξ-scheme for fermions and confirms the association of temperature with a Kerr black hole.