Giovanni Preti

On charged particle orbits in dipole magnetic fields around Schwarzschild black holes

We consider the motion of charges around Schwarzschild black holes when a magnetic field is present; analysis is focused on the exact solution of Maxwell equations in Schwarzschild spacetime describing dipolar fields generated by current loops around the black hole. This solution deserves particular attention, since it is suggestive of a relation with toroidal currents in accretion discs; with reference to applications of this same field solution, we point out and discuss an existing physical incoherence in past studies, and give the necessary emendation. Critical comparison with previous results is made. The circular orbit characteristics are examined in detail; two sets of solutions are found, both allowing stable circular orbits close to the event horizon, well beyond the Schwarzschild static limit at r = 6M. The existence of potential traps for highly relativistic particles within this same limit is also worth noting, since these same trapped particles may represent an effective source of synchrotron radiation.

On the meaning of the separation constant in the Kerr metric

The existence of a fourth constant of motion, beyond rest mass, energy and axial angular momentum, for a free particle in a Kerr spacetime has been shown by Carter through the separability of the Hamilton-Jacobi equation using oblate spheroidal coordinates. This fourth constant of motion is connected to a second-rank Stackel-Killing tensor related to the symmetries of the Kerr solution; while this mathematical aspect is clear, the physical meaning of the separation constant is not. In this note we solve this problem, showing how the separation constant can be interpreted physically.

Light cones and repulsive gravity

Contrary to common belief, gravitation can also be repulsive. Examples of repulsive gravity are provided by the naked singularity solutions of the Einstein equations corresponding to the negative mass Schwarzschild, the Reissner–Nordstrom, and the Kerr spacetimes. We show that their repulsive gravity regions can be identified by a particular behavior of the light cones when use is made of symmetry-adapted coordinate systems.

Ray tracing in relativistic astrometry: the satellite attitude error and the comprehensive error budget

The general relativistic analysis of the astrometric data which will be soon provided by the satellite GAIA?ready to be launched in 2012?should include an accurate estimation of the errors which are due to the uncertainties of the boundary conditions. These uncertainties stem from the errors of the observables which can be intrinsic but also induced by the instabilities of the satellite attitude. Following previous work, we take these additional sources of uncertainties into account and provide semi-analytically, at the requested order of accuracy , the complete error equations for the line of sight and the stellar position at the emission event.

Relativistic satellite astrometry: the stellar radial velocity

We present a general-relativistic analysis that allows the stellar radial velocities to be determined from a suitable implementation of the spectroscopic data with the astrometric ones shortly to be provided by new generations of astrometric satellites at μarcsec levels of accuracy at least. This analysis leads to an enhancement of the c −1 Doppler-shift formula presently planned for the Gaia mission to an all-inclusive, general-relativistic formula at the c −3 level, consistently with the expected accuracy. From this formula, which is shown to provide relevant corrections already at the c −2 level to a previously proposed one, we are then able to derive the explicit expression for the stellar radial velocity in terms of the spectroscopic and astrometric data, thereby accounting for all the necessary relativistic corrections up to and including the c −3 level.

Stäckel potentials and the relevance of the spheroidal coordinates

We study some consequences of the use of spheroidal coordinate frames to describe axisymmetric gravitational fields. In particular, we shall explain the meaning of the third integral of motion, and we shall analyse torque effects measured in a Stackel potential field.

Magnetically induced confinement near a Kerr black hole

We study the orbital behaviour of a magnetized particle in the dipole magnetic field generated by a toroidal current loop around a Kerr black hole. Specifically, the modifications of the orbits in the zone between the hole and the loop are evaluated, and comparison with the pure Kerr case is made. The presence of the magnetic field gives rise to potential wells where the magnetized particle can be trapped; as a result, new stable states are allowed, even very near the hole. Worth remarking on is, in particular, the possibility of obtaining in the ergosphere stable circular orbits with total negative energy, a possibility which is geodesically forbidden.

Coalescing Binary Systems of Compact Objects: Dynamics of Angular Momenta

The end state of a coalescing binary of compact objects depends strongly on the final total mass M and angular momentum J. Since gravitational radiation emission causes a slow evolution of the binary system through quasi-circular orbits down to the innermost stable one, in this paper we examine the corresponding behavior of the ratio J/M^2 which must be less than 1(G/c) or about 0.7(G/c) for the formation of a black hole or a neutron star respectively. The results show cases for which, at the end of the inspiral phase, the conditions for black hole or neutron star formation are not satisfied. The inclusion of spin effects leads us to a study of precession equations valid also for the calculation of gravitational waveforms.