The Energy-Momentum Pseudo-tensor Of The Cylindrical Gravitational Waves And Gravitational Solitons

It is very difficult to express or to calculate the energy-momentum of the gravitational waves field, not only in Einstein's General Relativity, but also in other relativity theories. At present, the energy-momentum of the single polarized states cylindrical gravitational waves has been calculated in different coordinates, and the rationality of it has also been discussed in detail. From these discussions, we can see that the Cartesian coordinate is better than the cylindrical coordinates in describing the single polarized states cylindrical gravitational waves. But as we know, there is not so much study about the both polarized states cylindrical gravitational waves.In this paper, we study the energy-momentum of the both polarized states cylindrical gravitational waves using Rosen-virbhadra,s(R-V) expression. At last, we get the concrete form of the expression of energy-momentum of the both polarized states cylindrical gravitational waves, then we discussed the positive nationality, We found that compare to the Cylindrical coordinates, the Cartesian coordinate is much better in describing the both polarized states cylindrical gravitational waves. The calculation told us in the Cylindrical coordinates; the energy-momentum density of the both polarized states cylindrical gravitational waves is equal to zero. That's because energy-momentum pseudo-tensor is not a real tensor, and the cylindrical coordinates is not a proper coordinates (coordinates which are significative in physics.) either; But the Cartesian coordinate is a more rational coordinate to describe the both polarized states cylindrical gravitational waves.For the energy-momentum pseudo-tensor of the both polarized states cylindrical gravitational waves we got by using the R-V expression, the positive nationality of the energy and the energy current can be guaranteed very well in a great range in the whole space-time. To sum up, we think that the Cartesian coordinate is much more rational to describe the energy-momentum pseudo-tensor of cylindrical gravitational waves...