Related papers: Kerr metric, static observers and Fermi coordinate…
In general relativity, astrophysical black holes are uniquely described by the Kerr metric. Observational tests of the Kerr nature of these compact objects and, hence, of general relativity, require a metric that encompasses a broader class…
Employing a relativistic rotational transformation to study and analyze rotational phenomena, instead of the rotational transformations based on consecutive Lorentz transformations and Fermi coordinates, leads to different predictions. In…
We analytically derive the secular changes of the orbital parameters, i.e., energy, angular momentum, and Carter constant, for general bound orbits in Kerr spacetime, at leading order in the mass ratio, through the 6th post-Newtonian (6PN)…
The dynamical parameters conventionally used to specify the orbit of a test particle in Kerr spacetime are the energy $E$, the axial component of the angular momentum, $L_{z}$, and Carter's constant $Q$. These parameters are obtained by…
Physicists have been interested in accelerated observers for quite some time. Since the advent of special relativity, many authors have tried to understand these observers in the framework of Minkowski spacetime. One of the most important…
We obtain the integral formulae for computing the tetrads and metric components in Riemann normal coordinates and Fermi coordinate system of an observer in arbitrary motion. Our approach admits essential enlarging the range of validity of…
As an extension of our previous paper, instead of the total deflection angle $\alpha$, we will mainly focus on discussing the measurable angle of the light ray $\psi$ at the position of the observer in Kerr--de Sitter spacetime which…
We develop a unified, analytic framework for gravitational lensing by Kerr black holes. In this first paper we present a new, general lens equation and magnification formula governing lensing by a compact object. Our lens equation assumes…
While a physical theory should be independent of the coordinate frame chosen by any observer, the observations themselves in fact depend on the choice of coordinates. In particular, different coordinate frames reflect different symmetries…
We consider the general form of the linear transformation for point rotation coordinate frames. The frames have the rotation axis at every point. In the transformation the frequency of one frame relative to another is not equivalent to the…
We present the whole class of Gaussian coordinate systems for the Kerr metric. This is achieved through the uses of the relationship between Gaussian observers and the relativistic Hamilton-Jacobi equation. We analyze the completeness of…
A spherically symmetric and static metric that describes physical coordinates is introduced. It is defined to be a metric that gives coordinate independent results for physically observable quantities without a further coordinate…
From general relativity we have learned the principles of general covariance and local Lorentz invariance, which follow from the fact that we consider observables as tensors on a spacetime manifold whose geometry is modeled by a Lorentzian…
A physical metric is constructed as one that gives a coordinate independent result for the time delay in infinite order in the perturbation expansion in the gravitational constant. A compact form for the metric is obtained. One result is…
The Kerr-Newman metric describes a very special rotating, charged mass and is the most general of the asymptotically flat stationary 'black hole' solutions to the Einstein-Maxwell equations of general relativity. We review the derivation of…
It is shown that in 2+1 dimensions the Fermi-Walker gauge allows the general solution of the problem of determining the metric from the sources in terms of simple quadratures. This technique is used to solve the problem of the occurrence of…
General orbits of a particle of small mass $\mu$ around a Kerr black hole of mass $M$ are characterized by three parameters: the energy, the angular momentum and the Carter constant. The time-averaged rates of change of the energy and the…
We use the formalism of Fermi coordinates to describe the interaction of a plane gravitational wave in the proper detector frame. In doing so, we emphasize that in this frame the action of the gravitational wave can be explained in terms of…
The Kerr metric is known to present issues when trying to find an interior solution. In this work we continue in our efforts to construct a more realistic exterior metric for astrophysical objects. A new approximate metric representing the…
Suppose that there is a quantum operator that describes the horizon area of a black hole. Then what would be the form of the ensuing quantum spectrum? In this regard, it has been conjectured that the characteristic frequencies of the black…