Related papers: Entropy Bound and a Geometrically Nonsingular Univ…
Both classical and quantum arguments suggest that if Barrow entropy is correct, its index $\delta$ must be energy dependent, which would affect the very early universe. Based on thermodynamic stability that sufficiently large black holes…
In order to find out whether empty singular boundaries can arise in higher dimensional Gravity, we study the solution of Einstein's equations consisting in a ($N+2$)-dimensional static and hyperplane symmetric perfect fluid satisfying the…
A geometrical framework for the definition of entropy in General Relativity via Noether theorem is briefly recalled and the entropy of Taub-Bolt Euclidean solutions of Einstein equations is then obtained as an application. The computed…
An explicit calculation is given of the entropy/energy ratio for the TM modes of the electromagnetic field in the half Einstein universe. This geometry provides a mathematically convenient and physically instructive example of how the…
We find obstructions to the existence of Einstein metrics of non-negative sectional curvature on a smooth closed simply connected manifold of any dimension. The results are achieved by combining the classical Morse theory of the loop space…
This contribution inquires into Clausius' proposal that "the entropy of the world tends to a maximum.'" The question is raised whether the entropy of "the world" actually does have a maximum; and if the answer is "Yes!," what such states of…
The entropy for two-dimensional black holes is obtained through the entropy function with the condition that the geometry approaches an $AdS_2$ spacetime in the near horizon limit. It is shown that the entropy is universal and proportional…
Recently, we derived an improved universal upper bound to the entropy of a charged system $S \leq \pi (2E b-q^2)/ \hbar$. There was, however, some uncertainty in the value of the numerical factor which multiplies the $q^2$ term. In this…
We explore the consequences of assuming that the bounded space-time subsets contain a finite number of degrees of freedom. A physically natural hypothesis is that this number is additive for spatially separated subsets. We show that this…
Penrose [1] has emphasized how the initial big bang singularity requires a special low entropy state. We address how recent brane cosmological schemes address this problem and whether they offer any apparent resolution. Pushing the start…
We present a number of explicit calculations of Renyi and entanglement entropies in situations where the entangling surface intersects the boundary in $d$-dimensional Minkowski spacetime. When the boundary is a single plane we compute the…
Based on properties of n-subharmonic functions we show that a complete, noncompact, properly embedded hypersurface with nonnegative Ricci curvature in hyperbolic space has an asymptotic boundary at infinity of at most two points. Moreover,…
Bounds for the area of general closed marginally trapped surfaces (MTSs) are presented. They do not require any stability condition, and are determined by a constant that depends on a particular component of the Einstein tensor on the…
The holographic bound asserts that the entropy $S$ of a system is bounded from above by a quarter of the area ${\cal A}$ of a circumscribing surface measured in Planck areas: $S\leq {\cal A}/4{\ell^2_P}$. This bound is widely regarded a…
Bounds of total curvature and entropy are two common conditions placed on mean curvature flows. We show that these two hypotheses are equivalent for the class of ancient complete embedded smooth planar curve shortening flows, which are…
In this note a notion of generalized topological entropy for arbitrary subsets of the space of all sequences in a compact topological space is introduced. It is shown that for a continuous map on a compact space the generalized topological…
We apply the full set of most update dynamical and geometrical data in cosmology to the nonextensive Barrow entropic holographic dark energy. We show that the data point towards an extensive Gibbs-like entropic behaviour for the…
Considering the isentropic Euler equations of compressible fluid dynamics with geometric effects included, we establish the existence of entropy solutions for a large class of initial data. We cover fluid flows in a nozzle or in spherical…
We derive a universal upper bound to the entropy of a charged system. The entropy bound follows from application of the generalized second law of thermodynamics to a gedanken experiment in which an entropy-bearing charged system falls into…
Clausius inequality has deep implications for reversibility and the arrow of time. Quantum theory is able to extend this result for closed systems by inspecting the trajectory of the density matrix on its manifold. Here we show that this…