Related papers: Coordinate Independence and a Physical Metric in C…
We introduce the notion of dynamical metric order of a continuous map on a compact metric space, study its basic properties, and compute it for several classes of maps. This concept which is a counterpart of the metric mean dimension with…
A gravitational theory is formulated by considering the physical processes underlying relativistic dilation of time and contraction of space. It is shown that the point mass solution of general relativity's field equation - the…
For generalized coordinate systems, the numerical values of vector and tensor components do not generally equal the physical values, i.e., the values one would measure with standard physical instruments. Hence, calculating physical…
The equations for the second-order gravitational perturbations produced by a compact-object have highly singular source terms at the point particle limit. At this limit the standard retarded solutions to these equations are ill-defined.…
This paper presents a comprehensive perspective of the metric of quantum states with a focus on the background independent metric structures. We also explore the possibilities of geometrical formulations of quantum mechanics beyond the…
It is well-known that the coordinate as a continuous variable, consisting of a set of all points between 0 and $L$ contradicts the observability of measurement. In other words there might exist a fundamental length in nature, such as the…
As is well known, the 0 - 0 component of the Schwarzschild space can be obtained by the requirement that the geodesic of slowly moving particles match the Newtonian equation. Given this result, we show here that the remaining components can…
A geometric theory for spacetimes whose world lines associated with physical particles have an upper bound for the proper acceleration is developed. After some fundamental remarks on the requirements that the classical dynamics for point…
This article aims at comparing gravitational wave memory effect in a Schwarzschild spacetime with that of other compact objects with static and spherically symmetric spacetime, with the purpose of proposing a procedure for differentiating…
The metric perturbation tensor corresponding to a transverse oscillation of spacetime is composed of products of cosines. When averaged over many wavelengths, such a metric may look either Minkowskian or Euclidean at large scales, depending…
The fidelity (Shannon mutual information between measurements and physical quantities) is proposed as a quantitative measure of the quality of physical measurements. The fidelity does not depend on the true value of unknown physical…
We provide a general contractibility criterion for subsets of Riemannian metrics on the disc. For instance, this result applies to the space of metrics that have positive Gauss curvature and make the boundary circle convex (or geodesic).…
Symmetry is one of the most general and useful concepts in physics. A theory or a system that has a symmetry is fundamentally constrained by it. The same constraints do not apply when the symmetry is broken. The quantitative determination…
We consider the problem of gravitational collapse of a fluid under the effect of a Schwarzschild black hole (e.g. a primordial one) that suddenly forms inside the fluid. We assume the fluid initially be a uniform dust. Starting from this…
A phase of massive gravity free from pathologies can be obtained by coupling the metric to an additional spin-two field. We study the gravitational field produced by a static spherically symmetric body, by finding the exact solution that…
Astrophysical observations provide compelling evidence for the existence of dark matter, a non-luminous component dominating the universe's mass-energy budget. Its gravitational influence is well-established on galactic scales; however,…
Recently we have presented a new formulation of the theory of gravity based on an implementation of the Einstein Equivalence Principle distinct from General Relativity. The kinetic part of the theory - that describes how matter is affected…
The second-order gravitational self-force on a small body is an important problem for gravitational-wave astronomy of extreme mass-ratio inspirals. We give a first-principles derivation of a prescription for computing the first and second…
In this work, we compute the metric corresponding to a static and spherically symmetric mass distribution in the general relativistic weak field approximation to quadratic order in Fermi-normal coordinates surrounding a radial geodesic. To…
We use results by Kirilin to show that in general relativity the nonleading terms in the energy-momentum tensor of a particle depends on the parameterization of the gravitational field. While the classical metric that is calculated from…