Remo Ruffini

Absorption and defocusing of electromagnetic radiation by a Schwarzschild black hole

Abstract A comparison of electromagnetic radiation absorbed by a black hole and that emitted at infinity is made for selected circular orbits of a charged particle in a Schwarzschild geometry. Radiation intensity and beaming processes for geodesic as well as ultra-relativistic unbound orbits are compared and contrasted with the special relativistic results of classical electrodynamics.

Black holes and gravitational collapse

Lasciate ogni speranza voi chentrate. Dante Alighieri, The Inferno The dimensionless quantity GM / rc 2 may be regarded as a measure of the strength of the gravitational field. This quantity enters into the formulas for light deflection, time delay, gravitational redshift, perihelion precession, and so on. The small magnitude of the relativistic gravitational effects in the Solar System is related to the small magnitude of this quantity; even at the solar surface, GM / rc 2 is only 2 × 10 −6 . Large relativistic effects are found in the gravitational field in the neighborhood of an extremely compact mass, where GM / rc 2 can attain values of the order of magnitude of 1. For example, near such a compact mass, at a radius r = 3 GM / c 2 , the deflection of light in the Schwarzschild field becomes so large that a light signal will move in a closed circular orbit around the central mass. The relativistic effects become spectacular when r = 2 GM / c 2 . The gravitational fields at this radius are so strong that nothing can escape from their grip. Light signals, particles, and even spacecraft with the most powerful engines are inexorably pulled inward.