Related papers: Fermi coordinates and static observer in Schwarzsc…
We extend the non-commutative coordinates relationship into other than the Minkowski space-time. We clarify the non-commutativity dependency to the geometrical structure. As well as, we find an inverse map between Riemann's normal and…
We attempt to study three significant tests of general relativity in higher dimensions both in commutative and non-commutative spaces. In the context of non-commutative geometry, we will consider a solution of the Einstein equation in…
A local observer can measure only the values of fields at the point of his own position. By exploring the coordinate transformation between two Fermi frames, it is shown that two observers, having the same instantaneous position and…
The method of simple straightforward calculation of the curvature tensor of the Finsleroid--regular space is indicated. The Schwarzschild metric which underlines the gravitational field produced by static spherical-symmetric body is shown…
The geodesic equations for the general case of diagonal metrics of static, spherically symmetric fields are calculated. The elimination of the proper time variable gives the motion equations for test particles with respect to coordinate…
In this work, we develop a general perturbative procedure to find the off-equatorial plane deflections in the weak deflection limit in general stationary and axisymmetric spacetimes, allowing the existence of the generalized Carter…
The design of navigation observers able to simultaneously estimate the position, linear velocity and orientation of a vehicle in a three-dimensional space is crucial in many robotics and aerospace applications. This problem was mainly dealt…
We discuss solution generating techniques treating stationary and axially symmetric metrics in the presence of a cosmological constant. Using the recently found extended form of Ernst's complex equation, which takes into account the…
The aim of this Letter is rather pedagogical. We considered the static spherically symmetric ensemble of observers, having finite bare mass and trying to measure geometrical and physical properties of the environmental static…
We examine length measurement in curved spacetime, based on the 1+3-splitting of a local observer frame. This situates extended objects within spacetime, in terms of a given coordinate which serves as an external reference. The radar metric…
The Kruskal-Szekeres coordinates construction for the Schwarzschild spacetime could be viewed geometrically as a squeezing of the $t$-line associated with the asymptotic observer into a single point, at the event horizon $r=2M$. Starting…
We construct Schwinger functions as the superposition of Schwinger functions which correspond to those of free fields with sharp masses $ m $. We prove that all axioms of Osterwalder and Schrader are satisfied. This construction works…
Starting from the equations of motion in a 1 + 1 static, diagonal, Lorentzian spacetime, such as the Schwarzschild radial line element, I find another metric, but with Euclidean signature, which produces the same geodesics x(t). This…
We study further a general relativistic mechanism for the acquisition of tidal energy by free test particles near a gravitationally collapsed configuration. Specifically, we investigate the solutions of timelike geodesic equation in a Fermi…
An exact solution for the field of a charge in a uniformly accelerated noninertial frame of reference (NFR) alongside the "Equivalent Situation Postulate" allows one to find space-time structure as well as fields from arbitrarily shaped…
We prove that a generalized Schwarzschild-like ansatz can be consistently employed to construct $d$-dimensional static vacuum black hole solutions in any metric theory of gravity for which the Lagrangian is a scalar invariant constructed…
We discuss geodesic motion in the vacuum C metric using Bondi-like spherical coordinates, with special attention to the role played by the "equatorial plane." We show that the spatial trajectory of photons on such a hypersurface is formally…
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…
We show that mass parameter and radial coordinate values can be indirectly measured in thought experiments performed in Schwarzschild spacetime, without using the Newtonian limit of general relativity or approximations based on Euclidean…
Fermi surfaces are basic objects in solid state physics and in the spectral theory of periodic operators. We define several measures connected to Fermi surfaces and study their measure theoretic properties. From this we get absence of…