Black holes and gravitational collapse

Abstract

Lasciate ogni speranza voi ch'entrate. 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.