Quasi-local mass in the covariant Newtonian space-time

Details Quasi-local mass in the covariant Newtonian space-time Quasi-local mass in the covariant Newtonian space-time

2008-03-14

arxiv.org/abs/0803.2194v1

Class.Quant.Grav.25:135007,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Submit to Class. Quantum Grav

Scientific paper

10.1088/0264-9381/25/13/135007

In general relativity, quasi-local energy-momentum expressions have been constructed from various formulae. However, Newtonian theory of gravity gives a well known and an unique quasi-local mass expression (surface integration). Since geometrical formulation of Newtonian gravity has been established in the covariant Newtonian space-time, it provides a covariant approximation from relativistic to Newtonian theories. By using this approximation, we calculate Komar integral, Brown-York quasi-local energy and Dougan-Mason quasi-local mass in the covariant Newtonian space-time. It turns out that Komar integral naturally gives the Newtonian quasi-local mass expression, however, further conditions (spherical symmetry) need to be made for Brown-York and Dougan-Mason expressions.

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