Fernando de Felice

On the Gravitational field acting as an optical medium

Given a curved space-time with a metric tensorgij, Maxwells equations may be written as if they were valid in a flat space-time in which there is an optical medium with a constitutive equation.When optical phenomena are considered, this medium turns out to be equivalent to the gravitational field. Optical phenomena in various gravitational fields are analysed and we find that the language of classical optics for the ‘equivalent medium’ is as suitable as that of Riemannian geometry.

RELATIVISTIC CHARGED SPHERES : II. REGULARITY AND STABILITY

We present new results concerning the existence of static, electrically charged, perfect fluid spheres that have a regular interior and are arbitrarily close to a maximally charged black-hole state. These configurations are described by exact solutions of Einsteins field equations. A family of these solutions had already been found (de Felice et al 1995 Mon. Not. R. Astron. Soc. 277 L17) but here we generalize that result to cases with different charge distributions within the spheres and show, in an appropriate parameter space, that the set of such physically reasonable solutions has a non-zero measure. We also perform a perturbation analysis and identify the solutions which are stable against adiabatic radial perturbations. We then suggest that the stable configurations can be considered as classic models of charged particles. Finally, our results are used to show that a conjecture of Kristiansson et al (1998 Gen. Rel. Grav. 30 275) is incorrect.

Turning a black hole into a naked singularity

We show that an extremal Reissner-Nordstrom black hole may be turned into a Kerr-Newman naked singularity after capture of a flat and electrically neutral spinning body which is initially gravitationally bound and plunges in radially with its spin aligned to a radial direction. It is argued that backreaction and emission of gravitational radiation would not help to preserve the black hole condition.

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

On El Naschie's complex time, Hawking's imaginary time and special relativity

P

Absolute and relative Frenet-Serret frames and Fermi-Walker transport

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.

On the meaning of the separation constant in the Kerr metric

Abstract The idea of complex time, as first proposed by El Naschie in 1995, not only provided a very important mathematical utility in clarifying the nature of nowness, but also opened a definite possibility for the instantaneous transmission of information through the theoretical prediction of massless particles travelling at velocities larger than the speed of light. Based on a very simple thought experiment, here we show that the complex nature of time arises when two independent inertial observers, in relative uniform motion, communicate via a light signal in order to compare their own proper time measurements for the same event. The observation that the time employed by the signal to go from one observer to the other is calculable, but not measurable, permits to build up a general expression for the complex time, which not only complies with the possibility of time decomposition into two dimensions, but also conciliates with the idea of a complex space. In particular, we find that El Naschie’s complex time can be interpreted as an asymptotic limit when the velocity of the moving observer equals that of light. Within this new formulation, the inverse Lorentz transformations of special relativity follow as a direct consequence of the complex time.

Spinning test particles and clock effect in Schwarzschild spacetime

Relative Frenet-Serret 3-frames are defined along a test particle worldline with respect to a family of observers and a corresponding comoving relative Frenet-Serret 3-frame is introduced in the local rest space of the test particle itself. The latter frame provides the tools to geometrically define a generalized centrifugal force, tied to the rotation of the relative velocity of the test particle with respect to the observers relative to gyro-fixed axes in the test particle local rest space. For circular orbits in a stationary axisymmetric spacetime, all of these relative frames for any circular observers are closely related to the spacetime Frenet-Serret frame, but it is the comoving frame, which reveals the geometric interpretation of the minimal intrinsic rotation observers, which are complementary to the extremely accelerated observers to which they reduce in the equatorial plane of rotating black hole spacetimes.

Orbiting frames and satellite attitudes in relativistic astrometry

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.

Kerr metric: the permitted angular velocity pattern and the pre-horizon regime

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.