Classical Scalar Fields and the Generalized Second Law

TL;DR

This paper investigates whether classical scalar fields that violate energy conditions can lead to violations of the generalized second law of thermodynamics, finding that such violations are prevented by horizon effects and entropy modifications.

Contribution

It demonstrates that despite large negative energy fluxes from scalar fields, the generalized second law remains valid due to horizon and entropy effects.

Findings

Large negative energy fluxes can be produced in flat spacetime.

Injected fluxes do not violate the GSL even when decreasing horizon area.

Horizon acausality and entropy modifications preserve the GSL.

Abstract

It has been shown that classical non-minimally coupled scalar fields can violate all of the standard energy conditions in general relativity. Violations of the null and averaged null energy conditions obtainable with such fields have been suggested as possible exotic matter candidates required for the maintenance of traversable wormholes. In this paper, we explore the possibility that if such fields exist, they might be used to produce large negative energy fluxes and macroscopic violations of the generalized second law (GSL) of thermodynamics. We find that it appears to be very easy to produce large magnitude negative energy fluxes in flat spacetime. However we also find, somewhat surprisingly, that these same types of fluxes injected into a black hole do {\it not} produce violations of the GSL. This is true even in cases where the flux results in a decrease in the area of the horizon. We demonstrate that two effects are responsible for the rescue of the GSL: the acausal behavior of the horizon and the modification of the usual black hole entropy formula by an additional term which depends on the scalar field.