Alikram N. Aliev

Rotating black holes in higher dimensional Einstein-Maxwell gravity

The strategy of obtaining the familiar Kerr-Newman solution in general relativity is based on either using the metric ansatz in the Kerr-Schild form, or applying the method of complex coordinate transformation to a non-rotating charged black hole. In practice, this amounts to an appropriate re-scaling of the mass parameter in the metric of uncharged black holes. Using a similar approach, we assume a special metric ansatz in N+1 dimensions and present a new analytic solution to the Einstein-Maxwell system of equations. It describes rotating charged black holes with a single angular momentum in the limit of slow rotation. We also give the metric for a slowly rotating charged black hole with two independent angular momenta in five dimensions. We compute the gyromagnetic ratio of these black holes which corresponds to the value g=N-1.

Five-dimensional rotating black hole in a uniform magnetic field: The gyromagnetic ratio

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 behavior 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 biazimuthal 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 five-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

Superradiant Instability of Five-Dimensional Rotating Charged AdS Black Holes

g=3.

The general type N solution of new massive gravity

We study the instability of small AdS black holes with two independent rotation parameters in minimal five-dimensional gauged supergravity to massless scalar perturbations. We analytically solve the Klein-Gordon equation for low-frequency perturbations in two regions of the spacetime of these black holes: namely, in the region close to the horizon and in the far-region. By matching the solutions in an intermediate region, we calculate the frequency spectrum of quasinormal modes. We show that in the regime of superradiance only the modes of even orbital quantum number undergo negative damping, resulting in exponential growth of the amplitude. That is, the black holes become unstable to these modes. Meanwhile, the modes of odd orbital quantum number do not undergo any damping, oscillating with frequency-shifts. This is in contrast with the case of four-dimensional small Kerr-AdS black holes which exhibit the instability to all modes of scalar perturbations in the regime of superradiance.

Gravitational Effects of Rotating Braneworld Black Holes

We study the effects of an external magnetic field, which is assumed to be uniform at infinity, on the marginally stable circular motion of charged particles in the equatorial plane of a rotating black hole. We show that the magnetic field has its greatest effect in enlarging the region of stability towards the event horizon of the black hole. Using the Hamilton-Jacobi formalism we obtain the basic equations governing the marginal stability of the circular orbits and their associated energies and angular momenta. As instructive examples, we review the case of the marginal stability of the circular orbits in the Kerr metric, as well as around a Schwarzschild black hole in a magnetic field. For large enough values of the magnetic field around a maximally rotating black hole we find the limiting analytical solutions to the equations governing the radii of marginal stability. We also show that the presence of a strong magnetic field provides the possibility of relativistic motions in both direct and retrograde innermost stable circular orbits around a Kerr black hole.

Note on rotating charged black holes in Einstein-Maxwell-Chern-Simons theory

Abstract We find the most general algebraic type N solution with non-vanishing scalar curvature, which comprises all type N solutions of new massive gravity in three dimensions. We also give the special forms of this solution, which correspond to certain critical values of the topological mass. Finally, we show that at the special limit, the null Killing isometry of the spacetime is restored and the solution describes AdS pp-waves.

Type D solutions of 3D new massive gravity

We study the light deflection effect and the relativistic periastron and frame-dragging precessions for a rotating black hole localized on the brane in the Randall-Sundrum braneworld scenario. Focusing on a light ray, which passes through the field of the black hole in its equatorial plane, we first calculate the deflection angle in the weak field limit. We obtain an analytical formula, involving the related perturbative parameters of the field up to the second order. We then proceed with the numerical calculation of the deflection angle in the strong field limit when the light ray passes at the closest distance of approach to the limiting photon orbit. We show that the deflection angles for the light ray, winding maximally rotating Kerr and braneworld black holes in the same direction as their rotation, become essentially indistinguishable from each other for a specific value of the negative tidal charge. The same feature occurs in the relativistic precession frequencies at characteristic radii, for which the radial epicyclic frequency of the test particle motion attains its highest value. These results show that to distinguish between these two types of black holes one also needs to know the precise value of the angular momentum from independent observations, which for a maximally rotating braneworld black hole must exceed the Kerr bound in general relativity.

Slowly rotating black hole solutions to Horava-Lifshitz gravity

We show that the general solution of Chong, Cvetic, Lu and Pope for nonextremal rotating charged black holes in five-dimensional minimal gauged supergravity, or equivalently in the Einstein-Maxwell-Chern-Simons theory with a negative cosmological constant and with the Chern-Simons coefficient {nu}=1, admits a simple description in a Kerr-Schild type framework with two scalar functions. Next, assuming this framework as an ansatz, we obtain new analytic solutions for slowly rotating charged black holes in the Einstein-Maxwell-Chern-Simons theory with {nu}{ne}1. Using a covariant superpotential derived from Noether identities within the Katz-Bicak-Lynden-Bell approach, we calculate the mass and angular momenta for the general supergravity solution as well as for the slowly rotating solution with two independent rotation parameters. For the latter case, we also calculate the gyromagnetic ratios and obtain simple analytic formulas, involving both the parameters of the black holes and the Chern-Simons coefficient.

Gravitational instantons from minimal surfaces

In a recent reformulation of three-dimensional new massive gravity, the field equations of the theory consist of a massive (tensorial) Klein-Gordon type equation with a curvature-squared source term and a constraint equation. Using this framework, we present all algebraic type D solutions of new massive gravity with constant and nonconstant scalar curvatures. For constant scalar curvature, they include homogeneous anisotropic solutions which encompass both solutions originating from topologically massive gravity, Bianchi types II, VIII, IX, and those of non-topologically massive gravity origin, Bianchi types VI{sub 0} and VII{sub 0}. For a special relation between the cosmological and mass parameters, {lambda}=m{sup 2}, they also include conformally flat solutions, and, in particular, those being locally isometric to the previously-known Kaluza-Klein type AdS{sub 2}xS{sup 1} or dS{sub 2}xS{sup 1} solutions. For nonconstant scalar curvature, all the solutions are conformally flat and exist only for {lambda}=m{sup 2}. We find two general metrics which possess at least one Killing vector and comprise all such solutions. We also discuss some properties of these solutions, delineating among them black hole type solutions.