
VOLUME 118 (2023)  ISSUE 1 
PAGE

On the global temperature of the Schwarzschildde Sitter spacetime
G. E. Volovik
Low Temperature Laboratory, Aalto University, P.O. Box 15100, FI00076 Aalto, Finland Landau Institute for Theoretical Physics, 142432 Chernogolovka, Russia
Abstract
It is shown that the Schwarzschildde Sitter spacetime has the
universal temperature. This temperature describes the thermal processes
of decay of the composite particles and the other processes, which are
energetically forbidden in the Minkowski spacetime, but are allowed in
the de Sitter and in Schwarzschildde Sitter backgrounds. In particular, this temperature
describes the probability of ionization of the atom in the Schwarzschildde Sitter, which is
observed by the stationary observer at the point where the shift function
(velocity) in the ArnowittDeserMisner formalism changes sign. This
activation temperature does not depend on the black hole mass and is
fully determined by the Hubble parameter, .
This temperature is twice the BoussoHawking temperature T_{ BH},
which characterizes the limit of degenerate Lorentzian Schwarzschildde
Sitter universe, when the cosmological and black hole horizons are close
to each other, T_{ SdS}=2T_{ BH}.
The similar doubling of the temperature of Hawking radiation is known in
the pure de Sitter spacetime, where the corresponding local temperature
describing the ionization of atoms is twice the GibbonsHawking
temperature, T_{ dS}=2T_{ GH}=H/π. We suggest that the
activation temperature T_{ dS} can be considered as the
thermodynamic temperature of the de Sitter state, which determines the
local entropy in this state, s=3H/4G.

