Related papers: Kerr metric, static observers and Fermi coordinate…
I provide a prescription to define space, at a given moment, for an arbitrary observer in an arbitrary (sufficiently regular) curved space-time. This prescription, based on synchronicity (simultaneity) arguments, defines a foliation of…
The local Carroll symmetry of a gravitational wave found in Baldwin-Jeffery-Rosen coordinates is extended to a globally defined one by switching to Brinkmann coordinates. Two independent globally defined solutions of a Sturm-Liouville…
One of the fundamental postulates of the special relativity theory is existence of a single system of universal coordinate transforms for inertial reference frames, that is coordinate transforms, which are uniquely determined by space-time…
The usual concepts of topological physics, such as the Berry curvature, cannot be applied directly to non-Hermitian systems. We show that another object, the quantum metric, which often plays a secondary role in Hermitian systems, becomes a…
Spherometer is an instrument widely used for measuring the radius of curvature of a spherical surface. Cylindrometer is a modified spherometer, which can measure the radii of both spherical and cylindrical surfaces. Both of these…
We give a precise theoretical description of initially aligned sets of orthogonal gyroscopes which are transported along different paths from some initial point to the same final point in spacetime. These gyroscope systems can be used to…
We derive an effective Kerr metric from an effective Schwarzschild metric inspired by loop quantum gravity through the Newman-Janis algorithm. The resulting spacetime is free from the classical ring singularity and does not allow the…
Designing Luenberger observers for nonlinear systems involves the challenging task of transforming the state to an alternate coordinate system, possibly of higher dimensions, where the system is asymptotically stable and linear up to output…
We derive an ansatz for the five dimensional equal-rotation Kerr-Newman metric that contains two unknown functions. By solving for these functions through perturbation series, we find that the metric can be cast into the Kerr-Shild form in…
With the aid of a Fermi-Walker chart associated with an orthonormal frame attached to a time-like curve in spacetime, a discussion is given of relativistic balance laws that may be used to construct models of massive particles with spin,…
It is well known that the interior of a constant density spherical star is conformally flat. In this paper we obtain the coordinate system in which the conformal flatness of the metric manifests itself. In a similar way, we also construct…
Nonlinear optical media of Kerr type are described by a particular version of an anharmonic quantum harmonic oscillator. The dynamics of this system can be described using the Moyal equations of motion, which correspond to a quantum phase…
Explicit Fermi coordinates are given for geodesic observers comoving with the Hubble flow in expanding Robertson-Walker spacetimes, along with exact expressions for the metric tensors in Fermi coordinates. For the case of non inflationary…
We construct a new type of Chandrasekhar transformation in Kerr spacetime using the different tortoise coordinate, which is useful for exact analysis to study Teukolsky equation with arbitrary frequency. We also give the interpretation of…
In this review, we collect several results for conformally standard stationary spacetimes (SxR,g) obtained in terms of a Finsler metric of Randers type on the orbit manifold S that we call Fermat metric. This metric is obtained by applying…
The difference in travel time of corotating and counter-rotating light waves in the field of a central massive and spinning body is studied. The corrections to the special relativistic formula are worked out in a Kerr field. Estimation of…
The world lines of null particles admit arbitrary parametrizations. In the presence of a family of observers one may introduce along a null world line an extension of the so-called Cattaneo's relative standard time parameter (valid for…
Bound geodesic orbits around a Kerr black hole can be parametrized by three constants of the motion: the (specific) orbital energy, angular momentum and Carter constant. Generically, each orbit also has associated with it three frequencies,…
We introduce in the explicit form the tetrads of arbitrary observers in spacetimes with spherical and axial symmetries. The observers confined to the equatorial plane are parametrized by the pair of functions. We apply this description in…
A number of scalar invariant characterizations of the Kerr solution are presented. These characterizations come in the form of {\em quality factors} defined in stationary space-times. A quality factor is a scalar quantity varying in the…