The gravitation energy for a cylindrically and spherically symmetrical system

TL;DR

This paper proposes a new method to define the energy density of static cylindrically and spherically symmetrical gravitational fields using metric tensor components, addressing limitations of previous pseudotensor approaches.

Contribution

It introduces an approach based on isothermal compression to express gravitational energy density in terms of metric components, improving interpretation over traditional pseudotensor methods.

Findings

Energy density expressed via metric tensor components.

Addresses limitations of t00 pseudotensor component.

Applicable to static cylindrical and spherical systems.

Abstract

It has been shown that t00 component of the energy-momentum pseudotensor in the case of cylindrically symmetrical static gravitational field cannot be interpreted as energy density of the gravitation field. An approach has been suggested allows one to express the energy density of the cylindrically or spherically symmetrical static gravitation field in terms of the metric tensor components. The approach based on the consideration of the process of isothermal compression of a cylinder consisted of incoherent matter.