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.     

Neutrino—antineutrino asymmetry around rotating black holes

Propagation of fermion in curved space-time generates gravitational interaction due to the coupling between spin of the fermion and space-time curvature. This gravitational interaction appears as a CPT violating term in the Lagrangian. It is seen that this space-time interaction can generate neutrino asymmetry in the Universe. If the background metric is spherically asymmetric, say, of a rotating black hole, this interaction is non-zero, thus the net difference to the number density of the neutrino and anti-neutrino is non-zero.     

Optimal escape from circular orbits around black holes

An obvious strategy to escape from a stable circular orbit in the Schwarzschild spacetime is to employ a tangential instantaneous acceleration. Using the theory of optimal rocket trajectories in general relativity, recently developed in Henriques and Natário (J Optim Theory Appl 154:500–552; 2011), we show that this manoeuvre satisfies the optimality conditions for maximizing the rocket’s final energy (given a fixed amount of fuel) if and only if the magnitude of the acceleration is smaller than a certain bound. This is the general relativistic version of a result by Lawden (J Brit Interplan Soc 12:68–71; 1953).     

Stationary scalar configurations around extremal charged black holes

We consider the minimally coupled Klein-Gordon equation for a charged, massive scalar field in the non-extremal Reissner-Nordström background. Performing a frequency domain analysis, using a continued fraction method, we compute the frequencies $\omega $ for quasi-bound states. We observe that, as the extremal limit for both the background and the field is approached, the real part of the quasi-bound states frequencies $\mathcal{R }(\omega )$ tends to the mass of the field and the imaginary part $\mathcal{I }(\omega )$ tends to zero, for any angular momentum quantum number $\ell $ . The limiting frequencies in this double extremal limit are shown to correspond to a distribution of extremal scalar particles, at stationary positions, in no-force equilibrium configurations with the background. Thus, generically, these stationary scalar configurations are regular at the event horizon. If, on the other hand, the distribution contains scalar particles at the horizon, the configuration becomes irregular therein, in agreement with no hair theorems for the corresponding Einstein-Maxwell-scalar field system.     

Chaos bound in Kerr-Newman-Taub-NUT black holes via circular motions

In this study, we investigate the influence of the angular momentum of a charged particle around Kerr-Newman-Taub-NUT black holes on the Lyapunov exponent and find spatial regions where the chaos bound is violated. The exponent is obtained by solving the determination of the eigenvalues of a Jacobian matrix in the phase space. Equilibrium positions are obtained by fixing the charge-to-mass ratio of the particle and changing its angular momentum. For certain values of the black holes' electric charge, the NUT charge and rotational parameter, a small angular momentum of the particle, even with zero angular momentum, causes violation of the bound. This violation disappears at a certain distance from the event horizon of the non-extremal Kerr-Newman-Taub-NUT black hole when the angular momentum increases to a certain value. When the black hole is extremal, the violation always exists no matter how the angular momentum changes. The ranges of the angular momentum and spatial regions for the violation are found. The black holes and particle rotating in the same and opposite directions are discussed.     

Near-horizon states of black holes and Calogero models

We find self-adjoint extensions of the rational Calogero model in the presence of the harmonic interaction. The corresponding eigenfunctions may describe the near-horizon quantum states of certain types of black holes.     

Quantum bound states with zero binding energy

After reviewing the general properties of zero-energy quantum states, we give the explicit solutions of the Schrödinger equation with E = 0 for the class of potentials V = −|γ|/r^ν, where −∞ < ν < ∞. For ν > 2, these solutions are normalizable and correspond to bound states, if the angular momentum quantum number l > 0. (These states are normalizable, even for l = 0, if we increase the space dimension, D, beyond 4; i.e for D > 4.) For ν < −2 the above solutions, although unbound, are normalizable. This is true even though the corresponding potentials are repulsive for all r. We discuss the physics of these unusual effects.     

Orbital resonances in discs around braneworld Kerr black holes

Rotating black holes in the brany universe of the Randall–Sundrum type with infinite additional dimension are described by the Kerr geometry with a tidal charge b representing the interaction of the brany black hole and the bulk spacetime. For b < 0 rotating black holes with dimensionless spin a > 1 are allowed. We investigate the role of the tidal charge in the orbital resonance model of quasiperiodic oscillations (QPOs) in black hole systems. The orbital Keplerian frequency v _K and the radial and vertical epicyclic frequencies v _r, v _θ of the equatorial, quasicircular geodetical motion are given. Their radial profiles related to Keplerian accretion discs are discussed, assuming the inner edge of the disc located at the innermost stable circular geodesic. For completeness, naked singularity spacetimes are considered too. The resonant conditions are given in three astrophysically relevant situations: for direct (parametric) resonances of the oscillations with the radial and vertical epicyclic frequencies, for the relativistic precession model, and for some trapped oscillations of the warped discs, with resonant combinational frequencies involving the Keplerian and radial epicyclic frequencies. It is shown, how the tidal charge could influence matching of the observational data indicating the 3 : 2 frequency ratio observed in GRS 1915 + 105 microquasar with prediction of the orbital resonance model; limits on allowed range of the black hole parameters a and b are established. The “magic” dimensionless black hole spin enabling presence of strong resonant phenomena at the radius, where v _K: v _θ : v _r = 3 : 2 : 1, is determined in dependence on the tidal charge. Such strong resonances could be relevant even in sources with highly scattered resonant frequencies, as those expected in Sgr A*. The specific values of the spin and tidal charge are given also for existence of specific radius where v _K : v _θ : v _r = s : t : u with 5≥s >t >u being small natural numbers. It is shown that for some ratios such situation is impossible in the field of black holes. We can conclude that analysing the microquasars high-frequency QPOs in the framework of orbital resonance models, we can put relevant limits on the tidal charge of brany Kerr black holes.