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I would like to understand better about the conservation of energy in GR.

Let us think of infinitesimal vacuum volume [tex]dr\ sin\theta d\theta d\phi[/tex] around the star in center.

Light emitted from the star hit the bottom surface, r, of the volume. Say violet light photons hit the area 1 photon/1 second of the bottom local time.

Ligth escapes the volume at the top surface, r+dr, with red-shifted color with the rate less than 1 photon/1 second of the top local time, I guess.

In coming energy and out going energy should be equal in this stationary case. How can I cofirm it for the case?

Let us think of infinitesimal vacuum volume [tex]dr\ sin\theta d\theta d\phi[/tex] around the star in center.

Light emitted from the star hit the bottom surface, r, of the volume. Say violet light photons hit the area 1 photon/1 second of the bottom local time.

Ligth escapes the volume at the top surface, r+dr, with red-shifted color with the rate less than 1 photon/1 second of the top local time, I guess.

In coming energy and out going energy should be equal in this stationary case. How can I cofirm it for the case?

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