Spacetime Curvature 2024 (original) (raw)
Related papers
Gravitational collapse: an overview
Austrian Reports on Gravitation, 2022
We investigate classical and newer models that describe a gravitational collapse. In our previous work, we examined well-known models using mathematical methods based on the use of rods and clocks. As a result, we obtained coordinate-invariant equations, which, however, revealed some contradictions. We also discuss in detail the possibility of black holes and singularity formation. Contents
Comments on the use of the Flatness Theorem by Melia
Austrian Reports on Gravitation, 2021
We refer to a recently published paper by Melia concerning the Local Flatness Theorem. We argue that Melia's claim that the timelike metrical coefficient gtt=1 is closely connected with the equation of state mu+3p=0 is based on a mathematical artifact. Melia's model is analyzed using coordinate independent methods and is compared with our Subluminal Model.
The Geometry of Black Hole Singularities
Advances in High Energy Physics, 2014
Recent results show that important singularities in General Relativity can be naturally described in terms of finite and invariant canonical geometric objects. Consequently, one can write field equations which are equivalent to Einstein's at nonsingular points but, in addition remain well-defined and smooth at singularities. The black hole singularities appear to be less undesirable than it was thought, especially after we remove the part of the singularity due to the coordinate system. Black hole singularities are then compatible with global hyperbolicity and do not make the evolution equations break down, when these are expressed in terms of the appropriate variables. The charged black holes turn out to have smooth potential and electromagnetic fields in the new atlas. Classical charged particles can be modeled, in General Relativity, as charged black hole solutions. Since black hole singularities are accompanied by dimensional reduction, this should affect Feynman's path ...
Austrian Reports on Gravitation, 2021
We show that some of the FRW models are hybrid models. In the hybrid case, spatial parts of the line elements occur, which are typical for non-comoving systems, but the time in these models is the universal cosmological time-a comoving coordinate of a freely falling system. We investigate the line elements of models in the Florides metric and models in the Lemaître metric.
Geodesic-invariant equations of gravitation
2008
Einstein's equations of gravitation are not invariant under geodesic mappings, i. e. under a certain class of mappings of the Christoffel symbols and the metric tensor which leave the geodesic equations in a given coordinate system invariant. A theory in which geodesic mappings play the role of gauge transformations is considered.
Cosmological models (Carg\`{e}se lectures 1998)
arXiv: General Relativity and Quantum Cosmology, 1998
The aim of this set of lectures is a systematic presentation of a 1+3 covariant approach to studying the geometry, dynamics, and observational properties of relativistic cosmological models. In giving (i) the basic 1+3 covariant relations for a cosmological fluid, the present lectures cover some of the same ground as a previous set of Carg\`{e}se lectures \cite{ell73}, but they then go on to give (ii) the full set of corresponding tetrad equations, (iii) a classification of cosmological models with exact symmetries, (iv) a brief discussion of some of the most useful exact models and their observational properties, and (v) an introduction to the gauge-invariant and 1+3 covariant perturbation theory of almost-Friedmann-Lema\^{\i}tre-Robertson-Walker universes, with a fluid description for the matter and a kinetic theory description of the radiation.
The twin paradox in a cosmological context
arXiv (Cornell University), 2009
Recently Abramowicz and Bajtlik [ArXiv: 0905.2428 (2009)] have studied the twin paradox in Schwarzschild spacetime. Considering circular motion they showed that the twin with a nonvanishing 4-acceleration is older than his brother at the reunion and argued that in spaces that are asymptotically Minkowskian there exists an absolute standard of rest determining which twin is oldest at the reunion. Here we show that with vertical motion in Schwarzschild spacetime the result is opposite: The twin with a non-vanishing 4-acceleration is younger. We also deduce the existence of a new relativistic time effect, that there is either a time dilation or an increased rate of time associated with a clock moving in a rotating frame. This is in fact a first order effect in the velocity of the clock, and must be taken into account if the situation presented by Abramowicz and Bajtlik is described from the rotating rest frame of one of the twins. Our analysis shows that this effect has a Machian character since the rotating state of a frame depends upon the motion of the cosmic matter due to the inertial dragging it causes. We argue that a consistent formulation and resolution of the twin paradox makes use of the general principle of relativity and requires the introduction of an extended model of the Minkowski spacetime. In the extended model Minkowski spacetime is supplied with a cosmic shell of matter with radius equal to its own Schwarzschild radius, so that there is perfect inertial dragging inside the shell.