Gravitational energy of spherically-symmetric static systems

Astronomy and Astrophysics – Astrophysics

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Gravitation Theory, Gravitational Fields, Space-Time Functions, Schwarzschild Metric, Stellar Gravitation

Scientific paper

Two definitions of gravitational energy, Einstein's pseudo-tensor expression of energy in curved space-time and Lynden-Bell and Katz's (LBK) definition, are shown to give equivalent results, as applied to spherically-symmetric static systems in the presence of arbitrary sources. The conjectured expression for energy density of field plus matter for general static space times, given by Katz, Lynden-Bell, and Israel (KLBI), is applied to a system with internal and external Schwarzschild metric, and also to a vacuum dominated space-time with the De Sitter metric. The physical contents of the KLBI-expression is discussed by analyzing the Newtonian limit in a space filled with matter.

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