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*something else*, representing gravity's effect on itself. The stress-energy tensor is defined at each event except in a vacuum. The something else is in some sense nonlocal. (What sense?) Its influence is present at all events, even those in a vacuum.

In

*The Road to Reality*Penrose appears to call the something else "gravitational field energy". I've also seen the term gravitational binding energy used; is that a synonym in the context of GR, or is it a purely Newtonian concept? In

*Essential Relativity*(2nd ed., 1977), in the section on the Schwarzschild solution, Rindler makes use of a quantity he calls mass (which, setting

*c*= 1, corresponds to what Taylor & Wheeler, in

*Spacetime Physics*call energy). Is the mass that appears in Rindler's "Schwarzschild metric" (§ 8.3, p. 138) the same thing as Penrose's gravitational field energy (still taking

*c*= 1), since it determines curvature in a vacuum. If so, is this the

*only*other source of gravity in GR besides the stress-energy tensor (and thus the only source of gravity in a vacuum)? Is there no gravitational field momentum or force (nonlocal analogues to the momentum density and stress of the stress-energy tensor)?

Looking at what can be deduced from what...

g --> connection --> Riemann --> Ricci

g --> connection --> Riemann --> Weyl

g --> connection --> geodesic equation

g & T --> Ricci

g & Ricci --> T

...it seems that the metric tensor field, [itex]g_{\mu\nu}[/itex], can get us just about anywhere, but how does [itex]g_{\mu\nu}[/itex] depend on the sources of gravity?