Related papers: Schwarzschild spacetime under generalised Gullstra…
The Einstein theories of space-time and gravity as well the stander cosmology are reconstructed thoroughly in this paper based on flat reference frame. The rational parts of the Einstein theories are reserved while the irrational parts…
Non-relativistic quantum particles in the Earth's gravitational field are successfully described by the Schr\"{o}dinger equation with Newton's gravitational potential. Particularly, quantum mechanics is in agreement with such experiments as…
We consider the Schwarzschild black hole and show how, in a theory with limiting curvature, the physical singularity "inside it" is removed. The resulting spacetime is geodesically complete. The internal structure of this nonsingular black…
The physical interpretation and eventual fate of gravitational singularities in a theory surpassing classical general relativity are puzzling questions that have generated a great deal of interest among various quantum gravity approaches.…
We show that the field equations of the Schwarzschild geometry are invariant under passive Lorentz transformations to a freely falling system. We decompose the field equations with respect to the accelerated system and find that the force…
We consider light propagation as a probe of non-metricity in area metric spacetimes, and find a deviation from the standard Etherington relation for linearized area metric Schwarzschild. This is joint work with Frederic P. Schuller…
We motivate and construct a mathematical theory for the separation of space and time in general relativity. The formalism only requires a single observer and an optional choice of reference frame at each instant. As the splitting is done…
Recently, the current authors have formulated and extensively explored a rather novel Painleve-Gullstrand variant of the slow-rotation Lense-Thirring spacetime, a variant which has particularly elegant features -- including unit lapse,…
It is shown that if an asymptotically flat spacetime is asymptotically stationary, in the sense that $\Lie_{\xi} g_{ab}$ vanishes at the rate $\sim t^{-3}$ for asymptotically timelike vector field $\xi^a$, and the energy-momentum tensor…
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…
We have developed a method to study the effects of a perturbation to the motion of a test point--like object in a Schwarzschild spacetime. Such a method is the extension of the Lagrangian planetary equations of classical celestial mechanics…
The concept of a marginally trapped surface is important in the theory of general relativity. In the Schwarzschild black hole spacetime, its event horizon is foliated by marginally trapped surfaces. In a more general black hole spacetime,…
We investigate proper infall times in the Schwarzschild and Kerr spacetimes from a covariant perspective, focusing on the role of black--hole rotation in the focusing properties of timelike geodesic congruences.To perform a geometrically…
For quantum field theory on curved spacetimes, a critical role is played by their foliation into spacelike time-slices at each value $t$ of a coordinate time, with corresponding metric in ADM form. We provide a general construction for the…
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…
The Schwarzschild and Reissner-Nordstrom solutions to Einstein's equations describe space- times which contain spherically symmetric black holes. We consider solutions to the linear wave equation in the exterior of a fixed black hole space-…
In the first course of general relativity, the Schwarzschild spacetime is the most discussed analytic solution to Einstein's field equations. Unfortunately, there is rarely enough time to study the optical consequences of the bending of…
We demonstrate that in the case of Schwarzschild spacetime the Doppler shift is partially factorized into terms representing relativistic, kinematical and the gravitational contributions. The condition for the complete factorization is…
The Lense--Thirring spacetime describes a 4-dimensional slowly rotating approximate solution of vacuum Einstein equations valid to a linear order in rotation parameter. It is fully characterized by a single metric function of the…
As it 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…