On the apparent loss of predictability inside the de-Rham-Gabadadze-Tolley non-linear formulation of massive gravity: The Hawking radiation effect

TL;DR

This paper clarifies the origin of the perceived loss of predictability in the dRGT massive gravity theory, showing that apparent non-conservation issues are resolved when using the correct conserved quantities, with implications for phenomena like Hawking radiation.

Contribution

It demonstrates that the loss of predictability in dRGT is an apparent effect and provides a framework to compare black hole physics in dRGT with general relativity.

Findings

Conserved energy in dRGT involves velocity-dependent terms.

Motion in dRGT matches GR when using the correct conserved quantity.

Differences between GR and dRGT emerge in dynamical situations like Hawking radiation.

Abstract

I explain in a simple and compact form the origin of the apparent loss of predictability inside the dRGT non-linear formulation of massive gravity. This apparent pathology was first reported by Kodama and the author when the stability of the Schwarzschild de-Sitter (S-dS) black-hole in dRGT was analyzed. If we study the motion of a massive test particle around the S-dS solution, we find that the total energy is not conserved in the usual sense. The conserved quantity associated with time appears as a combination of the total energy and a velocity-dependent term. If the equations of motion are written in terms of this conserved quantity, then the three-dimensional motion in dRGT will not differ with respect to the same situation of Einstein gravity (GR). The differences with respect to GR will appear whenever we have a dynamical situation. I explore the Hawking radiation as an example where we can find differences between GR and dRGT.