Integrate the energy density U of Eq. (5) of Box 13.4 over the interior and surroundings of an isolated gravitating system to obtain the system’s total energy. Show that the gravitational contribution to this total energy 

(i) Is independent of the arbitrariness (parameter α) in the energy’s localization

(ii) Can be written in the following forms:

Interpret each of these expressions physically.

Eq. (5) of Box 13.4.

Transcribed Image Text:

Eg = [ dv²/po = - -G √ [dvg²= = ² / fa dVg2 ² ff dvd v¹ P(x) p(x) 2 |x - x'| 87 G (13.62)