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arXiv · 0803.2194

Quasi-local mass in the covariant Newtonian space-time

Yu-Huei Wu·Chih-Hung Wang
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Abstract

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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Yu-Huei Wu, Chih-Hung Wang. 2008-03-14. Quasi-local mass in the covariant Newtonian space-time. https://doi.org/10.1088/0264-9381%2F25%2F13%2F135007

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