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## Main Question or Discussion Point

Is the following correct? In Newton's theory, gravity is a force (described in terms of a scalar potential field and its gradient), and the source of gravity is mass. In Einstein's theory, gravity is curvature of spacetime (described by the Riemann curvature tensor), [itex]R_{\alpha\beta\gamma\delta}[/itex], and the sources of gravity are (1) the stress-energy tensor, [itex]T_{\mu\nu}[/itex] (comprising energy density, momentum density and stress), representing the contribution to gravity of every physical thing except for gravity itself, and (2)

In

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?

*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?