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

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.

Minor corrections, maiden derivation of proper GR virial theorem, shows there is no strict adiabatic collapse

References in corpus (2)

• Radiation Pressure Supported Stars in Einstein Gravity: Eternally Collapsing Objects
• A generic relation between baryonic and radiative energy densities of stars

Cited by in corpus (14)

• Nonadiabatic charged spherical gravitational collapse
• Dynamics of viscous dissipative gravitational collapse: A full causal approach
• Some analytical models of radiating collapsing spheres
• Equilibrium, radial stability and non-adiabatic gravitational collapse of anisotropic neutron stars
• Likely formation of general relativistic radiation pressure supported stars or "eternally collapsing objects"
• Stability and gravitational collapse of neutron stars with realistic equations of state
• Study of Charged Cylindrical Collapse in $f(\mathcal{R},\mathcal{T},\mathcal{Q})$ Gravity
• Charged Anisotropic Spherical Collapse in $f(\mathcal{R},\mathcal{T},\mathcal{Q})$ Gravity
• The fallacy of Oppenheimer Snyder Collapse: no general relativistic Collapse at all, no black hole, no physical singularity
• Dynamics of Charged Viscous Dissipative Cylindrical Collapse With Full Causal Approach
• On the Maximum Energy Release from Formation of Static Compact Objects
• Thermal Radiation from Compact Objects in Curved Space-Time
• A Model of Dustlike Spherically Symmetric Gravitational Collapse without Event Horizon Formation
• Masses of radiation pressure supported stars in extreme relativistic realm