Why Gravitational Contraction Must be Accompanied by Emission of Radiation Both in Newtonian and Einstein Gravity

TL;DR

This paper derives the first general relativistic version of the virial theorem and Helmholtz-Kelvin process, demonstrating that gravitational contraction in Einstein gravity must also emit radiation, challenging the notion of purely adiabatic collapse.

Contribution

The paper introduces the first GR derivation of the virial theorem and Helmholtz-Kelvin mechanism, showing gravitational collapse always involves radiation emission in Einstein gravity.

Findings

GR virial theorem derived for static fluid spheres

GR counterparts of internal, gravitational, and binding energies are redefined

Gravitational collapse in GR must emit radiation, not be adiabatic

Abstract

By using virial theorem, Helmholtz and Kelvin showed that the contraction of a bound self-gravitating system must be accompanied by release of radiation energy irrespective of the details of the contraction process. This happens because the total Newtonian energy of the system E_N (and not just the Newtonian gravitational potential energy E_g^N) decreases for such contraction. In the era of General Relativity (GR) too, it is justifiably believed that gravitational contraction must release radiation energy. However no GR version of (Newtonian) Helmholtz- Kelvin (HK) process has ever been derived. Here, for the first time, we derive the GR version of the appropriate virial theorem and Helmholtz Kelvin mechanism by simply equating the well known expressions for the gravitational mass and the Inertial Mass of a spherically symmetric static fluid. Simultaneously, we show that the GR counterparts of global ``internal energy'', ``gravitational potential energy'' and ``binding energy'' are actually different from what have been used so far. Existence of this GR HK process asserts that, in Einstein gravity too, gravitational collapse must be accompanied by emission of radiation irrespective of the details of the collapse process. Consequently, all studies of strictly adibatic gravitational collapse are only of academic interest.