The Israel Theorem: What is Nature Trying to Tell Us?

TL;DR

This paper investigates the physical implications of the Israel theorem, suggesting that small deviations from the Schwarzschild metric in compact objects could lead to significant phenomena during the radiation of multipole moments.

Contribution

It analyzes the consequences of the Israel theorem using exact solutions to Einstein's equations, highlighting potential physical phenomena in near-Schwarzschild configurations.

Findings

Small deviations from Schwarzschild can cause notable physical effects.

Radiation of multipole moments influences the behavior of compact objects.

Exact solutions reveal possible phenomena beyond classical expectations.

Abstract

We explore the possible physical consequences derived from the fact that the only static and asymptotically-flat vacuum space-time possessing a regular horizon is the Schwarzschild solution (Israel theorem). If small deviations from the Schwarzschild metric are described by means of exact solutions to Einstein equations (as it should be), then for very compact configurations, at the time scale at which radiatable multipole moments are radiated away, important physical phenomena should occur, as illustrated by some results on different solutions beloging to the Weyl class of static axially--symmetric solutions to the Einstein equations.