Probing entropy bounds with scalar field spacetimes

TL;DR

This paper investigates covariant entropy bounds in a scalar field spacetime with naked singularities, demonstrating violations of the generalized bound near horizons while confirming the Bousso bound remains valid.

Contribution

It provides explicit calculations showing the generalized covariant entropy bound can be violated in certain dynamical spacetimes, challenging previously assumed necessary conditions.

Findings

Generalized covariant bound is violated near apparent horizons.

Bousso bound remains valid despite violations of its sufficient conditions.

Certain conditions thought necessary for the bounds are not actually required.

Abstract

We study covariant entropy bounds in dynamical spacetimes with naked singularities. Specifically we study a spherically symmetric massless scalar field solution. The solution is an inhomogeneous cosmology with an initial spacelike singularity, and a naked timelike singularity at the origin. We construct the entropy flux 4-vector for the scalar field, and show by explicit computation that the generalized covariant bound $S_{L(B,B')}\le (A(B)-A(B'))/4 $ is violated for light sheets $L(B,B')$ in the neighbourhood of the (evolving) apparent horizon. We find no violations of the Bousso bound (for which $A(B')=0$), even though certain sufficient conditions for this bound do not hold. This result therefore shows that these conditions are not necessary.