Related papers: Approximate Symmetries in General Relativity
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.…
In this paper we propose a general framework to study the quantum geometry of $\sigma$-models when they are effectively localized to small quantum fluctuations around constant maps. Such effective theories have surprising exact descriptions…
In teleparallel geometries, symmetries are represented by affine frame symmetries which constrain both the (co)frame basis and the spin-connection (which are the primary geometric objects). In this paper we shall study teleparallel…
The most general set of static and spherically symmetric solutions for conformal Killing gravity coupled to Maxwell fields is presented in closed form. These solutions, depending on six parameters, include non-asymptotically flat black…
We define the concept of an internal symmetry. This is a symmety within a solution of a constraint satisfaction problem. We compare this to solution symmetry, which is a mapping between different solutions of the same problem. We argue that…
A linear transformation f(S) of configurational entropy with length scale dependent coefficients as a measure of spatial inhomogeneity is considered. When a final pattern is formed with periodically repeated initial arrangement of point…
We investigate (local) automorphisms of parabolic geometries that generalize geodesic symmetries. We show that many types of parabolic geometries admit at most one generalized geodesic symmetry at a point with non-zero harmonic curvature.…
Finding correspondences between 3D shapes is a crucial problem in computer vision and graphics, which is for example relevant for tasks like shape interpolation, pose transfer, or texture transfer. An often neglected but essential property…
We characterize symmetric spaces of non-positive curvature by the equality case of general inequalities between geometric quantities
This note describes a local scheme to characterize and normalize an axial Killing field on a general Riemannian geometry. No global assumptions are necessary, such as that the orbits of the Killing field all have period $2 \pi$. Rather, any…
Let $P$ be a set of at most $n$ points and let $R$ be a set of at most $n$ geometric ranges, such as for example disks or rectangles, where each $p \in P$ has an associated supply $s_{p} > 0$, and each $r \in R$ has an associated demand…
Similarity search is an important problem in information retrieval. This similarity is based on a distance. Symbolic representation of time series has attracted many researchers recently, since it reduces the dimensionality of these high…
Harmonicity of holomorphic maps between various subclasses of almost contact metric manifolds is discussed. Consequently, some new results are obtained. Also some known results are recovered, some of them are generalized and some of them…
This paper is devoted to study the energy problem in general relativity using approximate Lie symmetry methods for differential equations. We evaluate second-order approximate symmetries of the geodesic equations for the stringy charged…
The symmetry of complex networks is a global property that has recently gained attention since MacArthur et al. 2008 showed that many real-world networks contain a considerable number of symmetries. These authors work with a very strict…
We explore the interplay between symmetry and randomness in quantum information. Adopting a geometric approach, we consider states as $H$-equivalent if related by a symmetry transformation characterized by the group $H$. We then introduce…
Consider an asymptotically flat Riemannian manifold $(M,g)$ of dimension $n \geq 3$ with nonempty compact boundary. We recall the harmonic conformal class $[g]_h$ of the metric, which consists of all conformal rescalings given by a harmonic…
Since the development of Relativity theory, a variety of solutions have been found around Einstein field equations, depending on the time-space. For instance, we can find the axially symmetric space which describes a rotanting black hole.…
Symmetry based approaches to the black hole entropy problem have a number of attractive features; in particular they are very general and do not depend on the details of the quantization method. However we point out that, of the two…
A generic method for combinatorial constructions of intrinsic geometrical spaces is presented. It is based on the well known inverse sequences of finite graphs that determine (in the limit) topological spaces. If a pattern of the…