Zero Value of the Schwarzschildian Mass of Asymptotically Euclidian Time-Symmetrical Gravitational Waves

Details Zero Value of the Schwarzschildian Mass of Asymptotically Euclidian Time-Symmetrical Gravitational Waves Zero Value of the Schwarzschildian Mass of Asymptotically Euclidian Time-Symmetrical Gravitational Waves

Aug 1974

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974ijtp...10..145f&link_type=abstract

International Journal of Theoretical Physics, Volume 10, Issue 3, pp.145-151

Physics

2

Scientific paper

It is shown that a coordinate system with simple coordinate conditions can be chosen such that one can explicitly see that the Schwarzschildian mass of an asymptotically Euclidian time-symmetrical system of gravitational waves is equal to zero. It is explicitly seen in the coordinate system with coordinate conditions ∂ i (- gg ik)=0 and in the set of coordinate systems with the coordinate condition ∂ i (- gg 0 i )=0. In this set of coordinate systems one of the field equations can be written in the form - 8π surd ( - g)(T_0^0 - tfrac{1}{2}T) = partial _α L_0^{0α } whereL_i^{kn} = tfrac{1}{2}surd ( - g)(g^{mn} Γ _{im}^k - g^{km} Γ _{im}^k ), α=1, 2, 3. From this equation it follows thatm = 2int (T_0^0 - tfrac{1}{2}T)surd ( - g) dV, and m=0 at T {i/k}=0.

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