相关论文: Entropies for negatively curved manifolds

This note introduces a notion of entropy for submanifolds of hyperbolic space analogous to the one introduced by Colding and Minicozzi for submanifolds of Euclidean space. Several properties are proved for this quantity including…

We study the entropy of the black hole with torsion using the covariant form of the partition function. The regularization of infinities appearing in the semiclassical calculation is shown to be consistent with the grand canonical boundary…

This is a survey of topological properties of open, complete nonpositively curved manifolds which may have infinite volume. Topics include topology of ends, restrictions on the fundamental group, as well as a review of known examples.

It is well known that quantum effects can produce negative energy densities, though for limited times. Here we show in the context of two-dimensional CFT that such negative energy densities are present in any non-trivial conformal vacuum…

We review black hole entropy with special reference to euclidean quantum gravity, the brick wall approach and loop quantum gravity.

In previous works, entropic gravity and ungravity have been considered as possible solutions to the dark energy and dark matter problems. To test the viability of these models, modifications to planetary orbits are calculated for ungravity…

Let $M^n(n\geq3)$ be an $n$-dimensional compact Riemannian manifold with harmonic curvature and positive scalar curvature. Assume that $M^n$ satisfies some integral pinching conditions. We give some rigidity theorems on compact manifolds…

In this paper, by modifying the arguments in \cite{WY}, we get some rigidity theorems on compact manifolds with nonempty boundary. The results in this paper are similar with those in \cite{ST} and \cite{WY}. Like \cite{ST} and \cite{WY}, we…

We investigate the entropy of black holes in Gauss-Bonnet and Lovelock gravity using the Noether charge approach, in which the entropy is given as the integral of a suitable (n-2) form charge over the event horizon. We compare the results…

In this paper, we give both positive and negative answers to Gromov's compactness question regarding positive scalar curvature metrics on noncompact manifolds. First we construct examples that give a negative answer to Gromov's compactness…

An analysis of some modified gravity models, based on the study of pure Schwarzschild and of Schwarzschild-de Sitter black holes, and involving the use of the Noether charge method, is carried out. Corrections to the classical Einsteinian…

We construct ergodic probability measures with infinite metric entropy for typical continuous maps and homeomorphisms on compact manifolds. We also construct sequences of such measures that converge to a zero-entropy measure.

We consider the entropy of a black hole which has zero area horizon. The microstates appear as monopole solutions of the effective theory on the corresponding brane configurations.The resulting entropy formula coincides with the one…

We calculate the configurational entropy of hard particles confined in a cavity using Monte Carlo integration. Multiple combinations of particle and cavity shapes are considered. For small numbers of particles $N$, we show that the entropy…

Deformation theory of complex manifolds is a classical subject with recent new advances in the noncompact case using both algebraic and analytic methods. In this note, we recall some concepts of the existing theory and introduce new notions…

The recently discussed notion of geometric entropy is shown to be related to earlier calculations of thermal effects in Rindler space. The evaluation is extended to de Sitter space and to a two-dimensional black hole.

We consider the universal cover of a closed Riemannian manifold of negative sectional curvature. We show that the linear drift and the stochastic entropy are differentiable under any C^3 one-parameter family of C^3 conformal changes of the…

We explore the concept of negative pressure and its relevance in a variety of physical contexts: the expansion of the universe, mixture theory, cavitation, and the capillary effect in plants. Using thermodynamic arguments, we discuss the…

We study the high--energy limit for eigenfunctions of the laplacian, on a compact negatively curved manifold. We review the recent result of Anantharaman-Nonnenmacher giving a lower bound on the Kolmogorov-Sinai entropy of semiclassical…

In the context of geodesic flows of noncompact negatively curved manifolds, we propose three different definitions of entropy and pressure at infinity, through growth of periodic orbits, critical exponents of Poincar\'e series, and entropy…