Related papers: Entanglement entropy and the Ricci flow
We use a mix of field theoretic and holographic techniques to elucidate various properties of quantum entanglement entropy. In (3+1)-dimensional conformal field theory we study the divergent terms in the entropy when the entangling surface…
Based on a recent proposal for the volume inside a black hole, we calculate the entropy associated with this volume and show that such entropy is proportional to the surface area of the black hole. Together with the consideration of black…
The 2D Ricci flow equation in the conformal gauge is studied using the linearization approach. Using a non-linear substitution of logarithmic type, the emergent quadratic equation is split in various ways. New special solutions involving…
Black hole entropy is shown to be a consequence of restricting our description of physics to the exterior of black holes. This precludes the need for a statistical mechanical description of this entropy in terms of microstates.
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 study the behavior of the Ricci flow at infinity for the full flag manifold $SU(3)/T$ using techniques of the qualitative theory of differential equations, in special the Poincar\'e Compactification and Lyapunov exponents.…
We discuss the entropy change due to fragmentation for black hole solutions in various dimensions. We find three different types of behavior. The entropy may decrease, increase or have a mixed behavior, characterized by the presence of a…
Asymptotic symmetry of the Euclidean 3D gravity with torsion is described by two independent Virasoro algebras with different central charges. Elements of this boundary conformal structure are combined with Cardy's formula to calculate the…
The topology change in quantum gravity is modeled by a Ricci flow. In this approach we offer to consider the Ricci flow as a statistical system. The metric in the Ricci flow enumerated by a parameter $\lambda$ is a microscopical statistical…
In this announcement, we exhibit the second variation of Perelman's $\lambda$ and $\nu$ functionals for the Ricci flow, and investigate the linear stability of examples. We also define the "central density" of a shrinking Ricci soliton and…
In this thesis I examine several different concepts of black hole entropy in order to understand whether they describe the same quantity. I look at statistical and entanglement entropies, Wald entropy and Carlip's entropy from conformal…
We present a theoretical study of the relationship between entanglement and entropy in multi-qubit quantum optical systems. Specifically we investigate quantitative relations between the concurrence and linear entropy for a two-qubit mixed…
Standard methods for calculating the black hole entropy beyond general relativity are ambiguous when the horizon is non stationary. We fix these ambiguities in all quadratic curvature gravity theories, by demanding that the entropy be…
We investigate the inclusion of 10-dimensional string loop corrections to the entropy function of two-charge extremal small black holes of the heterotic string theory compactified on S^1 x T^5 and show that the entropy is given by…
We discuss some recent results on black hole thermodynamics within the context of effective gravitational actions including higher-curvature interactions. Wald's derivation of the First Law demonstrates that black hole entropy can always be…
Entanglement entropy has proven to be a powerful tool for probing renormalization group (RG) flows in quantum field theories, with c-functions derived from it serving as candidate measures of the effective number of degrees of freedom.…
The explanation of black hole entropy as statistical entropy is one of the big successes of string theory. In this article we review recent progress in this subject, focussing on understanding quantum effects on black hole entropy.…
The thermodynamic second law in the evaporating black hole space-time is examined in the context of two-dimensional dilaton black hole. The dynamical evolution of entropy is investigated by using the analytical perturbation method and the…
We characterize the conjugate linearized Ricci flow and the associated backward heat kernel on closed three--manifolds of bounded geometry. We discuss their properties, and introduce the notion of Ricci flow conjugated constraint sets which…
Black hole entropy is identified with the counting of the dynamical degrees of freedom of trapped gravitational modes continually sourced by the Hawking-Unruh process. In the context of linear perturbations of Schwarzschild spacetime the…