Negative temperature for negative lapse function

TL;DR

This paper explores the possibility of negative local temperatures in regions with negative lapse functions in spacetime, showing that fermion dynamics can distinguish such regions thermodynamically, with implications for composite bosons.

Contribution

It demonstrates that quasiequilibrium states with negative local temperature can exist in regions with negative lapse, revealing a new thermodynamic distinction between spacetimes.

Findings

Negative local temperature T(r) can occur with N<0 regions.

Fermion dynamics distinguish spacetimes with negative lapse.

Composite bosons may inherit negative T(r) from fermions.

Abstract

Fermion dynamics distinguishes spacetimes having the same metric $g_{\mu\nu}$, but different tetrads $e_{\mu a}$, and in particular, it distinguishes a lapse with negative sign, $N<0$.[1] Here we show that the quasiequilibrium thermodynamic state may exist, in which the region with $N<0$ has negative local temperature $T({\bf r})<0$, while the global Tolman temperature $T_0$ remains positive. For bosons, only $N^2$ matters. However, if bosons are composite, they may inherit the negative $T({\bf r})$ from the fermions, and thus they may distinguish the spacetimes with positive and negative lapse functions via thermodynamics.