Janusz Garecki

Superenergy and supermomentum of Gödel universes

We review the canonical superenergy tensor and the canonical angular supermomentum tensor in general relativity and calculate them for spacetime homogeneous Godel universes to show that both of these tensors do not, in general, vanish. We consider both an original dust-filled pressureless acausal Godel model of 1949 and a scalar-field-filled causal Godel model of Reboucas and Tiomno. For the acausal model, the nonvanishing components of superenergy of matter are different from those of gravitation. The angular supermomentum tensors of matter and gravitation do not vanish either which simply reflects the fact that the Godel universe rotates. However, the axial (totally antisymmetric) and vectorial parts of supermomentum tensors vanish. It is interesting that superenergetic quantities are sensitive to causality in a way that superenergy density gS00 of gravitation in the acausal model is positive, while superenergy density gS00 in the causal model is negative. That means superenergetic quantities might serve as criteria of causality in cosmology and prove useful.

Energy and superenergy of a closed universe

Abstract In the present paper we show that energy and momentum of a closed Friedmann Universe are undetermined. Moreover, we also show that one can attach to such a Universe definite amount of the superenergy.

Some remarks on the Bel‐Robinson tensor

In this paper we present our point of view on the correct physical interpretation of the Bel-Robinson tensor within the framework of standard General Relativity (GR), i.e., within the framework of GR without supplementary elements like an arbitrary vector field, a distinguished tetrad field or a second metric. We show that this tensor arises as a consequence of the Bianchi identities and, in a natural manner, it is linked to the difference of the canonical gravitational energy-momentum as calculated in normal coordinates in a small vicinity of their origin P and in the origin P.

An interesting property of the isotropic and homogeneous cosmological models

It is shown by using covariant expressions that in the framework of the isotropic and homogeneous cosmology the gravitational energy and matter energy, the gravitational and matter linear and angular momentum, cancel each other out locally, resulting in the corresponding global quantities being zero.

Canonical angular supermomentum tensors in general relativity

We introduce the canonical supermomentum tensors mSikl(P;vt) and gSikl(P;vt) for matter and gravitation, respectively. These tensors give kinds of the quasilocal quantities which have recently been considered in the framework of general relativity though usually constructed in some special cases and for the mass only. Our method to construct the quasilocal quantities (i.e., superenergy and supermomentum tensors) is very general and does not require introducing any supplementary elements into general relativity. It merely extracts covariant data from the suitable canonical objects which exist in the framework of the standard general relativity. Having given a constructive definition of the canonical supermomentum tensors for gravitation and matter, we apply the canonical gravitational supermomentum tensor gSikl(P;vt) for the local analysis of the plane and plane-fronted gravitational waves. Next, we apply the canonical supermomentum tensors gSikl(P;vt) and mSikl(P;vt), gravitation and matter, to local and ...

A superenergetic analysis of the plane and plane-fronted gravitational waves

Abstract In this paper we present the results of calculations of the canonical superenergetic quantities and, also, canonical energetic quantities for the solutions to the vacuum Einstein equations representing gravitational plane wave and plane-fronted gravitational wave. The conclusion is that canonical superenergetic quantities give much better description of these waves than the canonical energetic ones.

Canonical superenergy tensors in general relativity

AbstractWe present the concept of superenergy tensors in the framework of general relativity (GR). These tensors were introduced constructively by the author years ago and they were obtained by a suitable averaging of the energy-momentum tensors or pseudotensors. Because in GR the Einstein canonical energy-momentum pseudotensorE tik of the gravitational field and the canonical energy-momentum complex

Superenergy and angular supermomentum tensors in general relativity

_E K_i^k = \sqrt {|g|} (T_i^k + {}_Et_i^k )