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 ${S}_{{L(B,B}^{\ensuremath{'}})}<~[A(B)\ensuremath{-}{A(B}^{\ensuremath{'}})]/4$ is violated for light sheets ${L(B,B}^{\ensuremath{'}})$ in the neighborhood of the (evolving) apparent horizon. We find no violations of the Bousso bound [for which ${A(B}^{\ensuremath{'}})=0],$ even though certain sufficient conditions for this bound do not hold. This result therefore shows that these conditions are not necessary.
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