Related papers: Canonical superenergy tensors in general relativit…
Here we present a new method to study stability of the solutions to the Einstein equations. This method uses the canonical superenergy tensors which have been introduced in past in our papers.
We define super-energy tensors for arbitrary physical fields, including the gravitational, electromagnetic and massless scalar fields. We also define super-super-energy tensors, and so on. All these tensors satisfy the so-called "Dominant…
In this contribution I intend to give a summary of the new relevant results obtained by using the general superenergy tensors. After a quick review of the definition and properties of these tensors, several of their mathematical and…
We quantise General Relativity for a class of energy-momentum-stress tensors.
Many years ago we have introduced into general relativity, {\bf GR}, the canonical superenergy tensors, $S_i^{~k}$, and the canonical angular supermomentum tensors, $S^{ikl}=(-)S^{kil}$, matter and gravitation. We have obtained these…
In this paper we investigate a class of basic super-energy tensors, namely those constructed from Killing-Yano tensors, and give a generalization of super-energy tensors for cases when we start not with a single tensor, but with a pair of…
In Lorentzian manifolds of any dimension the concept of causal tensors is introduced. Causal tensors have positivity properties analogous to the so-called ``dominant energy condition''. Further, it is shown how to build, from ANY given…
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…
A purely algebraic construction of super-energy tensors for arbitrary fields is presented in any dimensions. These tensors have good mathematical and physical properties, and they can be used in any theory having as basic arena an…
We report about the state of the art on complex and real generic identifiability of tensors, we describe some of our recent results obtained in [6] and we present perspectives on the subject.
General relativity is the theory with unclear energy momentum tensor. An approach is considered, allowing to construct the energy momentum tensor for relativity with nonsymmetric metric. A consequence of the approach is confirmed in the…
Canonical tensor model is a theory of dynamical fuzzy spaces in arbitrary space-time dimensions. Examining its simplest case, we find a connection to a minisuperspace model of general relativity in arbitrary dimensions. This is a first step…
It is dealt with the question, under which circumstances the canonical Noether stress-energy tensor is equivalent to the gravitational (Hilbert) tensor for general matter fields under the influence of gravity. In the framework of general…
The "positive square" of any tensor is presented in a universal and unified manner, valid in Lorentzian manifolds of arbitrary dimension, and independently of any (anti)-symmetry properties of the tensor. For rank-m tensors, the positive…
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…
We show how to generalize the classical electric-magnetic decomposition of the Maxwell or the Weyl tensors to arbitrary fields described by tensors of any rank in general $n$-dimensional spacetimes of Lorentzian signature. The properties…
The aim of this chapter is to present an introduction and also an overview of some of the most relevant results concerning positivity energy theorems in General Relativity. These theorems provide the answer to a long standing problem that…
We present gravitoelectromagnetism and other decompositions of the Riemann tensor from the differential-geometrical point of view.
Specific definitions of the core and core-EP inverses of complex tensors are introduced. Some characterizations, representations and properties of the core and core-EP inverses are investigated. The results are verified using specific…
We introduce subspace rank as a tool for studying ranks of tensors and X-rank more generally. We derive a new upper bound for the rank of a tensor and determine the ranks of partially symmetric tensors in C^2 \otimes C^b \otimes C^b. We…