Related papers: Optical geometry across the horizon
A general relativistic description of a disk rotating at constant angular velocity is given. It is argued that conceptually this direct approach poses fewer problems than the special relativistic one. For observers on the disk, the geometry…
Geometrical optics provides an instructive insight into Brownian motion, ``pushed" into a large-deviations regime by imposed constraints. Here we extend geometrical optics of Brownian motion by accounting for diffusion inhomogeneity in…
The coupling between the electromagnetic and gravitational fields results in "faster than light" photons and invalids the Lorentz invariance and some laws of physics. A typical example is that the first and third laws of geometric optics…
We discuss black hole spacetimes with a geometrically defined quasi-local horizon on which the curvature tensor is algebraically special relative to the alignment classification. Based on many examples and analytical results, we conjecture…
The geometrical-optics expansion reduces the problem of solving wave equations to one of solving transport equations along rays. Here we consider scalar, electromagnetic and gravitational waves propagating on a curved spacetime in general…
We consider the standard problem of observational astronomy, i.e. the observations of light emission from a distant region of spacetime in general relativity. The goal is to describe the changes between the measurements of the light…
Theorists are often told to express things in the "observational plane". One can do this for space-time geometry, considering "visual" observations of matter in our universe by a single observer over time, with no assumptions about…
We pursue a geometrical approach to gravitational lensing theory. We present a survey of the background theory of General Relativity, including particular properties of the Schwarzschild and Kerr solutions. Next we outline a proof of the…
We present an overall picture of the advances in the description of black hole physics from the perspective of loop quantum gravity. After an introduction that discusses the main conceptual issues we present some details about the classical…
We construct the spacetime in the vicinity of a general isolated, rotating, charged black hole. The black hole is modeled as a weakly isolated horizon, and we use the characteristic initial value formulation of the Einstein equations with…
One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…
In this work, Einstein's view of geometry as physical geometry is taken into account in the analysis of diverse issues related to the notions of inertial motion and inertial reference frame. Einstein's physical geometry enables a…
We consider a class of black holes for which the area of the two-dimensional spatial cross-section has a minimum on the horizon with respect to a quasiglobal (Krusckal-like) coordinate. If the horizon is regular, one can generate a tubelike…
What if physics is just the way we perceive geometry? That is, what if geometry and physics will one day become one and the same discipline? I believe that will mean we will at last really understand physics, without postulates other than…
The paper is based on the recently proposed 4-dimensional optical space theory and draws some of its consequences for gravitation. Starting with the discussion of central movement, the paper proceeds to establish the a metric compatible…
Working in a semi-classical setting, we consider solutions of the Einstein equations that exhibit light trapping in finite time according to distant observers. In spherical symmetry, we construct near-horizon quantities from the assumption…
The geodesic equations for optical media whose refractive indices have a non-vanishing gradient are developed. It is shown that when those media are optically isotropic, the light paths will be mull geodesics of a spatial metric that is…
In this paper, we perform a detailed investigation on the various geometrical properties of trapped surfaces and the boundaries of trapped region in general relativity. This treatment extends earlier work on LRS II spacetimes to a general 4…
A general theory of frames of reference proposed in a preceding publication is considered here in the framework of the post-Newtonian approximation, assuming that the frame of reference is centered on a time-like geodesic. The problem of…
The basic laws of geometrical optics can be deduced from energy-momentum conservation for electromagnetic waves, without other wave concepts. However, the concept of quanta is required; it arises naturally, hence such a hypothesis could…