Negative temperature for negative lapse function
G. E. Volovik
Low Temperature Laboratory, Aalto University, School of Science and Technology, FI-00076 AALTO, Finland
Landau Institute for Theoretical Physics RAS, 119334 Moscow, Russia
Fermion dynamics distinguishes spacetimes having the same metric gμν,
tetrads eμ a, and in particular, it distinguishes a lapse with negative
sign, N<0 (M. Christodoulou, A. Riello, and C. Rovelli, Int. J. Mod. Phys. D
21, 1242014 (2012)).
Here we show that the quasiequilibrium thermodynamic state may exist, in which
the region with N<0 has negative local temperature T( r)<0, while the
global Tolman temperature T0 remains positive. For bosons, only N2
matters. However, if bosons are composite, they may inherit the negative
T( r) from the fermions, and thus they may distinguish the spacetimes
with positive and negative lapse functions via thermodynamics.