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arXiv · 2202.08513

On the energy of Schwarzschild spacetime with the post-Newtonian approximation

I-Ching Yang
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Abstract

With the post-Newtonian approxination, the energy of Schwarzschild spacetime in the Weinberg prescription is obtained. The energy for the first post-Newtonian approximation $E^{(1)} = m$ gives the Newtonian treatment of Schwarzschild spacetime. However, for the second post-Newtonian approximation, the erergy is shown that $E^{(1)}$ adds extra terms $E^{(2)}$ which consist of the energy stored in the configuration $E_{\rm config}$, in the gravitational field $E_{\rm field}$. and a term of surface integral. These extra terms gives post-Newtonian corrections to the Newtonian treatment.

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I-Ching Yang. 2022-02-17. On the energy of Schwarzschild spacetime with the post-Newtonian approximation. https://doi.org/10.1142/s0217732322501383

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