Universal temperature corrections to the free energy for the gravitational field

TL;DR

This paper derives a universal temperature correction to the gravitational free energy that is independent of Planck scale physics, applicable across different systems and not reliant on Einstein gravity, useful for quantum condensed matter systems.

Contribution

It introduces a universal temperature correction to the gravitational free energy that applies broadly, regardless of the underlying gravitational theory or energy scale.

Findings

The correction is valid for all T << E_{Planck}

It depends only on the number of low-mass fields

It is applicable to quantum liquids like superfluid helium

Abstract

The temperature correction to the free energy of the gravitational field is considered which does not depend on the Planck energy physics. The leading correction may be interpreted in terms of the temperature dependent effective gravitational constant G_{eff}. The temperature correction to G_{eff}^{-1} appears to be valid for all temperatures T<< E_{Planck}. It is universal since it is determined only by the number of fermionic and bosonic fields with masses m<< T, does not contain the Planck energy scale E_{Planck} which determines the gravitational constant at T=0, and does not depend on whether or not the gravitational field obeys the Einstein equations. That is why this universal modification of the free energy for gravitational field can be used to study thermodynamics of quantum systems in condensed matter (such as quantum liquids superfluid 3He and 4He), where the effective gravity emerging for fermionic and/or bosonic quasiparticles in the low-energy corner is quite different from the Einstein gravity.