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

Department of Physics, Osaka University - Toyonaka, Osaka 560-0043, Japan

Received: 19 October 2014
Accepted: 15 December 2014

Abstract

I explain in a simple and compact form the origin of the apparent loss of predictability inside the de Rham-Gabadadze-Tolley (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.