Abstract
We propose a covariant entropy bound in gravitational theories beyond general relativity (GR), using Wald-Jacobson-Myers entropy instead of Bekenstein-Hawking entropy. We first extend the proof of the bound known in 4-dimensional GR to D-dimensional GR, f(R) gravity and canonical scalar-tensor theory. We then consider Einstein-Gauss-Bonnet (EGB) gravity as a more non-trivial example and, under a set of reasonable assumptions, prove the bound in the GR branch of spherically symmetric configurations. As a corollary, it is shown that under the null and dominant energy conditions, the generalized second law holds in the GR branch of spherically symmetric configurations of EGB gravity at the fully nonlinear level.
Highlights
Holography is a universal property of gravity that is expected to hold in a wide class of theories
IV, we prove the generalized covariant entropy bound in fðRÞ gravity and canonical scalar-tensor theory in a thermodynamic limit, using Wald entropy
We have extended the covariant entropy bound that was originally formulated in general relativity to gravitational theories beyond GR, as prescribed in Sec
Summary
Holography is a universal property of gravity that is expected to hold in a wide class of theories. It is conjecture that SL for a light sheet will not exceed a quarter of AðBÞ in the Planck unit: SL Bousso conjectured that this inequality holds for thermodynamic systems sufficiently smaller than the curvature radius and for large regions of the spacetime. This entropy bound can be interpreted as a formulation of the holographic principle in general spacetime. Flanagan et al [14] showed two proofs of the Bousso bound, supposing that matter is approximated by fluids, under two different sets of assumptions They extended the setup so that the light sheet can be terminated at another connected (D − 2)-dimensional spatial surface B0 and suggested the stronger bound, AðBÞ.
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