Related papers: Optical geometry across the horizon
Spatial curvature is one of the fundamental cosmological parameters that is routinely constrained from observations. The forward modelling of observations, in particular of large-scale structure, often relies on large cosmological…
Typical applications of gravitational lensing use the properties of electromagnetic or gravitational waves to infer the geometry through which those waves propagate. Nevertheless, the optical fields themselves - as opposed to their…
A modern re-visitation of the consequences of the lack of an intrinsic notion of instantaneous 3-space in relativistic theories leads to a reformulation of their kinematical basis emphasizing the role of non-inertial frames centered on an…
We consider a space-time of a spherically symmetric black hole with one simple horizon. As a standard coordinate frame fails in its vicinity, this requires continuation across the horizon and constructing frames which are regular there. Up…
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…
New ray-optical elements allow generalized refraction of light rays, but geometry imposes limitations on possible mappings between the positions of an object and its geometric image. Here I study the case of an infinite, planar,…
Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to…
Contemporary relativity theory is restricted in two points: (1) a use of the Riemannian space-time geometry and (2) a use of inadequate (nonrelativistic) concepts. Reasons of these restrictions are analysed in [1]. Eliminating these…
A simple, geometrical construction is given for three-dimensional spacetimes with negative cosmological constant that contain two particles colliding head-on. Depending on parameters like particle masses and distance, the combined geometry…
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.…
In this paper we discuss some mathematical aspects of the horizon wave-function formalism, also known in the literature as horizon quantum mechanics. In particular, first we review the structure of both the global and local formalism for…
Geometrical structures intrinsic to non-expanding, weakly isolated and isolated horizons are analyzed and compared with structures which arise in other contexts within general relativity, e.g., at null infinity. In particular, we address in…
We examine potential deformations of inner black hole and cosmological horizons in Reissner-Nordstr\"om de-Sitter spacetimes. While the rigidity of the outer black hole horizon is guaranteed by theorem, that theorem applies to neither the…
In the framework of non-riemannian geometry, we derive exact static vacuum solutions of the field equations obtained from the full equivalent version of the Einstein-Hilbert action when torsion degrees of freedom are taken into account. By…
Recent advances in our understanding of foundations of quantum mechanics have shown that information can be made objective through quantum states. Such objectification processes, predicted e.g. in a variety of quantum open systems, must…
We introduce the concept of effective geometry by studying several systems in which it arises naturally. As an example of the power and conciseness of the method, it is shown that a flowing dielectric medium with a linear response to an…
We derive universal properties of the near-horizon geometry of spherically symmetric black holes that follow from the observability of a regular apparent horizon. Only two types of solutions are admissible. After reviewing their properties…
Black holes in General Relativity are described by space-time metrics that are simpler in comparison to non-vacuum compact objects. However, given the universality of the gravitational pull, it is expected that dark matter accumulates…
We write explicitly the complete Lorentzian metric of a singularity-free spacetime where a black hole transitions into a white hole located in its same asymptotic region. In particular, the metric interpolates between the black and white…
A generalized definition of a frame of reference in spaces with affine connections and metrics is proposed based on the set of the following differential-geometric objects: (a) a non-null (non-isotropic) vector field, (b) the orthogonal to…