Related papers: Simple sufficient conditions for the generalized c…
Starting from the universal entropy bounds suggested by Bekenstein and Susskind and applying them to the black-body radiation situation, we get a cut-off of space $ \Delta x \geq \chi l_{\mathrm{P}}$ with $\chi \geq 0.1$. We go further to…
A new entropy bound, tighter than the standard holographic bound due to Bekenstein, is derived for spacetimes with non-rotating isolated horizons, from the quantum geometry approach in which the horizon is described by the boundary degrees…
We consider quantum algebras of observables associated with subregions in theories of Einstein gravity coupled to matter in the $G_N\rightarrow 0$ limit. When the subregion is spatially compact or encompasses an asymptotic boundary, we…
Assuming the Bousso bound, we prove a singularity theorem: if the light rays entering a hyperentropic region contract, then at least one light ray must be incomplete. "Hyperentropic" means that the entropy of the region exceeds the…
Black hole entropy appears to be ``universal''--many independent calculations, involving models with very different microscopic degrees of freedom, all yield the same density of states. I discuss the proposal that this universality comes…
We explore several extensions of the generalized entropy construction of Lewkowycz and Maldacena, including a formulation that does not rely on preserving replica symmetry in the bulk. We show that an appropriately general ansatz for the…
For models with several time-dependent components generalized entropies can be defined. This is shown for the Bianchi type IX model. We first derive the Cardy-Verlinde formula under the assumption that the first law of thermodynamics is…
Expanding the black hole thermodynamics from the horizon to achronal Cauchy hypersurface, the general relation between the Einstein equation and thermodynamics is established. Starting from trivial entropy that is generalized by…
According to the entropy bound, the entropy of a complete physical system can be universally bounded in terms of its circumscribing radius and total gravitating energy. Page's three recent candidates for counterexamples to the bound are…
We construct the generalized entropy optimized by a given arbitrary statistical distribution with a finite linear expectation value of a random quantity of interest. This offers, via the maximum entropy principle, a unified basis for a…
I argue that black hole entropy counts only those states of a black hole that can influence the outside, and attempt (with only partial success) to defend this claim against various objections, all but one coming from string theory.…
The quantum entropy-typical subspace theory is specified. It is shown that any mixed state with von Neumann entropy less than h can be preserved approximately by the entropy-typical subspace with entropy= h. This result implies an universal…
We present a semi-rigorous justification of Bekenstein's Generalized Second Law of Thermodynamics applicable to a universe with black holes present, based on a generic quantum gravity formulation of a black hole spacetime, where the bulk…
We consider classical Euclidean gravity solutions with a boundary. The boundary contains a non-contractible circle. These solutions can be interpreted as computing the trace of a density matrix in the full quantum gravity theory, in the…
General relativity cannot be formulated as a perturbatively renormalizable quantum field theory. An argument relying on the validity of the Bekenstein-Hawking entropy formula aims at dismissing gravity as non-renormalizable per se, against…
We investigate the covariant Hamiltonian symplectic structure of General Relativity for spatially bounded regions of spacetime with a fixed time-flow vector. For existence of a well-defined Hamiltonian variational principle taking into…
This is a review of my work published in the papers [1-4]. It offers a more detailed discussion of the results than what was given in the published papers and it links my results to some conclusions recently made by other people. It also…
Co-compact entropy is introduced as an invariant of topological conjugation for perfect mappings defined on any Hausdorff space(compactness and metrizability not necessarily required). This is achieved through the consideration of…
It has been recently proposed that the interpretation of gravity as an emergent, entropic force might have nontrivial implications to cosmology. Here two approaches are investigated: in one, the Friedman equation receives entropic…
We prove a lower bound on the relative entropy between two finite-dimensional states in terms of their entropy difference and the dimension of the underlying space. The inequality is tight in the sense that equality can be attained for any…