340 research outputs found
The averaged tensors of the relative energy-momentum and angular momentum in general relativity and some their applications
There exist at least a few different kind of averaging of the differences of
the energy-momentum and angular momentum in normal coordinates {\bf NC(P)}
which give tensorial quantities. The obtained averaged quantities are
equivalent mathematically because they differ only by constant scalar
dimensional factors. One of these averaging was used in our papers [1-8] giving
the {\it canonical superenergy and angular supermomentum tensors}.
In this paper we present another averaging of the differences of the
energy-momentum and angular momentum which gives tensorial quantities with
proper dimensions of the energy-momentum and angular momentum densities. But
these averaged relative energy-momentum and angular momentum tensors, closely
related to the canonical superenergy and angular supermomentum tensors, {\it
depend on some fundamental length }.
The averaged relative energy-momentum and angular momentum tensors of the
gravitational field obtained in the paper can be applied, like the canonical
superenergy and angular supermomentum tensors, to {\it coordinate independent}
analysis (local and in special cases also global) of this field.
We have applied the averaged relative energy-momentum tensors to analyze
vacuum gravitational energy and momentum and to analyze energy and momentum of
the Friedman (and also more general) universes. The obtained results are very
interesting, e.g., the averaged relative energy density is {\it positive
definite} for the all Friedman universes.Comment: 30 pages, minor changes referring to Kasner universe
Deep Projective 3D Semantic Segmentation
Semantic segmentation of 3D point clouds is a challenging problem with
numerous real-world applications. While deep learning has revolutionized the
field of image semantic segmentation, its impact on point cloud data has been
limited so far. Recent attempts, based on 3D deep learning approaches
(3D-CNNs), have achieved below-expected results. Such methods require
voxelizations of the underlying point cloud data, leading to decreased spatial
resolution and increased memory consumption. Additionally, 3D-CNNs greatly
suffer from the limited availability of annotated datasets.
In this paper, we propose an alternative framework that avoids the
limitations of 3D-CNNs. Instead of directly solving the problem in 3D, we first
project the point cloud onto a set of synthetic 2D-images. These images are
then used as input to a 2D-CNN, designed for semantic segmentation. Finally,
the obtained prediction scores are re-projected to the point cloud to obtain
the segmentation results. We further investigate the impact of multiple
modalities, such as color, depth and surface normals, in a multi-stream network
architecture. Experiments are performed on the recent Semantic3D dataset. Our
approach sets a new state-of-the-art by achieving a relative gain of 7.9 %,
compared to the previous best approach.Comment: Submitted to CAIP 201
Bergmann-Thomson energy-momentum complex for solutions more general than the Kerr-Schild class
In a very well-known paper, Virbhadra's research group proved that the
Weinberg, Papapetrou, Landau and Lifshitz, and Einstein energy-momentum
complexes ``coincide'' for all metrics of Kerr-Schild class. A few years later,
Virbhadra clarified that this ``coincidence'' in fact holds for metrics more
general than the Kerr-Schild class. In the present paper, this study is
extended for the Bergmann-Thomson complex and it is proved that this complex
also ``coincides'' with those complexes for a more general than the Kerr-Schild
class metric.Comment: RevTex, 12 page
Teleparallel Energy-Momentum Distribution of Spatially Homogeneous Rotating Spacetimes
The energy-momentum distribution of spatially homogeneous rotating spacetimes
in the context of teleparallel theory of gravity is investigated. For this
purpose, we use the teleparallel version of Moller prescription. It is found
that the components of energy-momentum density are finite and well-defined but
are different from General Relativity. However, the energy-momentum density
components become the same in both theories under certain assumptions. We also
analyse these quantities for some special solutions of the spatially
homogeneous rotating spacetimes.Comment: 12 pages, accepted for publication in Int. J. Theor. Phy
Energy and Momentum Distributions of Kantowski and Sachs Space-time
We use the Einstein, Bergmann-Thomson, Landau-Lifshitz and Papapetrou
energy-momentum complexes to calculate the energy and momentum distributions of
Kantowski and Sachs space-time. We show that the Einstein and Bergmann-Thomson
definitions furnish a consistent result for the energy distribution, but the
definition of Landau-Lifshitz do not agree with them. We show that a signature
switch should affect about everything including energy distribution in the case
of Einstein and Papapetrou prescriptions but not in Bergmann-Thomson and
Landau-Lifshitz prescriptions.Comment: 12 page
Teleparallel Energy-Momentum Distribution of Static Axially Symmetric Spacetimes
This paper is devoted to discuss the energy-momentum for static axially
symmetric spacetimes in the framework of teleparallel theory of gravity. For
this purpose, we use the teleparallel versions of Einstein, Landau-Lifshitz,
Bergmann and Mller prescriptions. A comparison of the results shows
that the energy density is different but the momentum turns out to be constant
in each prescription. This is exactly similar to the results available in
literature using the framework of General Relativity. It is mentioned here that
Mller energy-momentum distribution is independent of the coupling
constant . Finally, we calculate energy-momentum distribution for the
Curzon metric, a special case of the above mentioned spacetime.Comment: 14 pages, accepted for publication in Mod. Phys. Lett.
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