Andrea Geralico

Spinning test particles and clock effect in Kerr spacetime

We study the motion of spinning test particles in Kerr spacetime using the Mathisson-Papapetrou equations; we impose different supplementary conditions among the well known Corinaldesi-Papapetrou, Pirani and Tulczyjews and analyze their physical implications in order to decide which is the most natural to use. We find that if the particles center of mass world line, namely the one chosen for the multipole reduction, is a spatially circular orbit (sustained by the tidal forces due to the spin) then the generalized momentum

Emission versus Fermi coordinates: applications to relativistic positioning systems

P

The general relativistic Poynting-Robertson effect: II. A photon flux with nonzero angular momentum

of the test particle is also tangent to a spatially circular orbit intersecting the center of mass line at a point. There exists one such orbit for each point of the center of mass line where they intersect; although fictitious, these orbits are essential to define the properties of the spinning particle along its physical motion. In the small spin limit, the particles orbit is almost a geodesic and the difference of its angular velocity with respect to the geodesic value can be of arbitrary sign, corresponding to the spin-up and spin-down possible alignment along the z-axis. We also find that the choice of the supplementary conditions leads to clock effects of substantially different magnitude. In fact, for co-rotating and counter-rotating particles having the same spin magnitude and orientation, the gravitomagnetic clock effect induced by the background metric can be magnified or inhibited and even suppressed by the contribution of the individual particles spin. Quite surprisingly this contribution can be itself made vanishing leading to a clock effect undistiguishable from that of non spinning particles. The results of our analysis can be observationally tested.

Generalized Kerr spacetime with an arbitrary mass quadrupole moment: geometric properties versus particle motion

A four-dimensional relativistic positioning system for a general spacetime is constructed by using the so-called emission coordinates. The results apply in a small region around the world line of an accelerated observer carrying a Fermi triad, as described by the Fermi metric. In the case of a Schwarzschild spacetime modeling the gravitational field around the Earth and an observer at rest at a fixed spacetime point, these coordinates realize a relativistic positioning system alternative to the current GPS system. The latter is indeed essentially conceived as Newtonian, so that it necessarily needs taking into account at least the most important relativistic effects through post-Newtonian corrections to work properly. Previous results concerning emission coordinates in flat spacetime are thus extended to this more general situation. Furthermore, the mapping between spacetime coordinates and emission coordinates is completely determined by means of the world function, which in the case of a Fermi metric can be explicitly obtained.

Spinning test particles and clock effect in Schwarzschild spacetime

We study the motion of a test particle in a stationary, axially and reflection-symmetric spacetime of a central compact object, as affected by interaction with a test radiation field of the same symmetries. Considering the radiation flux with fixed but arbitrary (nonzero) angular momentum, we extend previous results limited to an equatorial plane motion within a zero angular-momentum photon flux in the Kerr and Schwarzschild backgrounds. While a unique equilibrium circular orbit exists if the photon flux has zero angular momentum, multiples of such orbits appear if the photon angular momentum is sufficiently high.

Confirming and improving post-Newtonian and effective-one-body results from self-force computations along eccentric orbits around a Schwarzschild black hole

An exact solution of Einsteins field equations in empty space first found in 1985 by Quevedo and Mashhoon is analyzed in detail. This solution generalizes Kerr spacetime to include the case of matter with an arbitrary mass quadrupole moment and is specified by three parameters, the mass M, the angular momentum per unit mass a and the quadrupole parameter q. It reduces to the Kerr spacetime in the limiting case q = 0 and to the Erez–Rosen spacetime when the specific angular momentum a vanishes. The geometrical properties of such a solution are investigated. Causality violations, directional singularities and repulsive effects occur in the region close to the source. Geodesic motion and accelerated motion are studied on the equatorial plane which, due to the reflection symmetry property of the solution, also turns out to be a geodesic plane.

New gravitational self-force analytical results for eccentric orbits around a Schwarzschild black hole

We study the behaviour of spinning test particles in the Schwarzschild spacetime. Using Mathisson–Papapetrou equations of motion, we confine our attention to spatially circular orbits and search for observable effects which could eventually discriminate among the standard supplementary conditions, namely the Corinaldesi–Papapetrou, Pirani and Tulczyjew. We find that if the world line chosen for the multipole reduction and whose unit tangent we denote as U is a circular orbit then the generalized momentum P of the spinning test particle is also tangent to a circular orbit even though P and U are not parallel four-vectors. These orbits are shown to exist because the spin-induced tidal forces provide the required acceleration irrespective of the supplementary conditions we select. Of course, in the limit of a small spin, the particles orbit is close to being a circular geodesic and the (small) deviation of the angular velocities from the geodesic values can be of an arbitrary sign, corresponding to the possible spin-up and spin-down alignment to the z-axis. When two spinning particles orbit around a gravitating source in opposite directions, they make one loop with respect to a given static observer with different arrival times. This difference is termed the clock effect. We find that a nonzero gravitomagnetic clock effect appears for oppositely orbiting spin-up or spin-down particles even in the Schwarzschild spacetime. This allows us to establish a formal analogy with the case of (spin-less) geodesics on the equatorial plane of the Kerr spacetime. This result can be verified experimentally.

Frenet–Serret formalism for null world lines

We analytically compute, through the six-and-a-half post-Newtonian order, the second-order-in-eccentricity piece of the Detweiler-Barack-Sago gauge-invariant redshift function for a small mass in eccentric orbit around a Schwarzschild black hole. Using the first law of mechanics for eccentric orbits [A. Le Tiec, Phys. Rev. D {\bf 92}, 084021 (2015)] we transcribe our result into a correspondingly accurate knowledge of the second radial potential of the effective-one-body formalism [A. Buonanno and T. Damour, Phys. Rev. D {\bf 59}, 084006 (1999)]. We compare our newly acquired analytical information to several different numerical self-force data and find good agreement, within estimated error bars. We also obtain, for the first time, independent analytical checks of the recently derived, comparable-mass fourth-post-Newtonian order dynamics [T. Damour, P. Jaranowski and G. Shaefer, Phys. Rev. D {\bf 89}, 064058 (2014)].

Kerr black holes as retro-MACHOs

We raise the analytical knowledge of the eccentricity-expansion of the Detweiler-Barack-Sago redshift invariant in a Schwarzschild spacetime up to the 9.5th post-Newtonian order (included) for the

High post-Newtonian order gravitational self-force analytical results for eccentric equatorial orbits around a Kerr black hole

e^2