1,390 research outputs found
The Relativistic Generalization of the Gravitational Force for Arbitrary Spacetimes
It has been suggested that re-expressing relativity in terms of forces could
provide fresh insights. The formalism developed for this purpose only applied
to static, or conformally static, space-times. Here we extend it to arbitrary
space-times. It is hoped that this formalism may lead to a workable definition
of mass and energy in relativity.Comment: 16 page
Weyl collineations that are not curvature collineations
Though the Weyl tensor is a linear combination of the curvature tensor, Ricci
tensor and Ricci scalar, it does not have all and only the Lie symmetries of
these tensors since it is possible, in principle, that "asymmetries cancel".
Here we investigate if, when and how the symmetries can be different. It is
found that we can obtain a metric with a finite dimensional Lie algebra of Weyl
symmetries that properly contains the Lie algebra of curvature symmetries.
There is no example found for the converse requirement. It is speculated that
there may be a fundamental reason for this lack of "duality".Comment: 9 page
Uniqueness of Flat Spherically Symmetric Spacelike Hypersurfaces Admitted by Spherically Symmetric Static Spactimes
It is known that spherically symmetric static spacetimes admit a foliation by
{\deg}at hypersurfaces. Such foliations have explicitly been constructed for
some spacetimes, using different approaches, but none of them have proved or
even discussed the uniqueness of these foliations. The issue of uniqueness
becomes more important due to suitability of {\deg}at foliations for studying
black hole physics. Here {\deg}at spherically symmetric spacelike hy-
persurfaces are obtained by a direct method. It is found that spherically
symmetric static spacetimes admit {\deg}at spherically symmetric hypersurfaces,
and that these hypersurfaces are unique up to translation under the time- like
Killing vector. This result guarantees the uniqueness of {\deg}at spherically
symmetric foliations for such spacetimes.Comment: 10 page
Conformal Ricci collineations of static spherically symmetric spacetimes
Conformal Ricci collineations of static spherically symmetric spacetimes are
studied. The general form of the vector fields generating conformal Ricci
collineations is found when the Ricci tensor is non-degenerate, in which case
the number of independent conformal Ricci collineations is \emph{fifteen}; the
maximum number for 4-dimensional manifolds. In the degenerate case it is found
that the static spherically symmetric spacetimes always have an infinite number
of conformal Ricci collineations. Some examples are provided which admit
non-trivial conformal Ricci collineations, and perfect fluid source of the
matter
Foliation of the Kottler-Schwarzschild-De Sitter Spacetime by Flat Spacelike Hypersurfaces
There exist Kruskal like coordinates for the Reissner-Nordstrom (RN) black
hole spacetime which are regular at coordinate singularities. Non existence of
such coordinates for the extreme RN black hole spacetime has already been
shown. Also the Carter coordinates available for the extreme case are not
manifestly regular at the coordinate singularity, therefore, a numerical
procedure was developed to obtain free fall geodesics and flat foliation for
the extreme RN black hole spacetime. The Kottler-Schwarzschild-de Sitter
(KSSdS) spacetime geometry is similar to the RN geometry in the sense that,
like the RN case, there exist non-singular coordinates when there are two
distinct coordinate singularities. There are no manifestly regular coordinates
for the extreme KSSdS case. In this paper foliation of all the cases of the
KSSdS spacetime by flat spacelike hypersurfaces is obtained by introducing a
non-singular time coordinate.Comment: 12 pages, 4 figure
Constructing a Space from the System of Geodesic Equations
Given a space it is easy to obtain the system of geodesic equations on it. In
this paper the inverse problem of reconstructing the space from the geodesic
equations is addressed. A procedure is developed for obtaining the metric
tensor from the Christoffel symbols. The procedure is extended for determining
if a second order quadratically semi-linear system can be expressed as a system
of geodesic equations, provided it has terms only quadratic in the first
derivative apart from the second derivative term. A computer code has been
developed for dealing with larger systems of geodesic equations
Similarities Between Classical Timelike Geodesics in a Naked Reissner-Nordstrom Singularity Background and the Behaviour of Electrons in Quantum Theory
It is generally assumed that naked singularities must be physically excluded,
as they could otherwise introduce unpredictable influences in their future null
cones. Considering geodesics for a naked Reissner-Nordstrom singularity, it is
found that the singularity is effectively clothed by its repulsive nature.
Regarding electron as naked singularity, the size of the clothed singularity
(electron) turns out to be classical electro-magnetic radius of the electron,
to an observer falling freely from infinity, initially at rest. The size
shrinks for an observer falling freely from infinity, with a positive initial
velocity. For geodetic parameters corresponding to negative energy there are
trapped geodesics. The similarity of this picture with that arising in the
Quantum Theory is discussed.Comment: 8 pages, 6 figure
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