Why gravitational contraction must be accompanied by emission of radiation in both Newtonian and Einstein gravity

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.