I tried to find the "Proper Formula", I'm afraid I don't know tensor math.
The formula looks really simple, but, as you may have discovered, isn't. "Gab = -8πTab" essentially relates local "material" quantities about the universe -- momentum, energy, and rotation (Tab) -- with "geometric" quantities -- curvature (Gab).
What's worse is the site I found tried to explain my time paradox, after do ing a lot of graghing and math it says "What this paradox illustrates is that in Special Relativity simultaneity is relative." http://www.friesian.com/separat.htm So even "Now" has no meaning .
This site seems pretty cryptic. I think I posted a list of recommended reading -- it continues to be recommended. I've just started "An introduction to Einstein's Relativity" by Ray D'Inverno, and it's very good and very comprehensive. Better than the other stuff I've recommended so far.
On "now": yes, simultaneity is relative. Things that appear to happen at the same time to some observers happen at different times to other observers. I'll try to explain this borrowing a figure from the aforementioned reference (p. 23).
The thick lines are the word lines of two observers, A and B. They each observe two events P and Q. As A measures things, P and Q happen the same distance away along a line. A has determined this using the following method: at some point (M) he sent out a flash of light (the thin solid lines) that illuminated P and Q and bounced back, the reflection being received at the same time (N). He knows that light travels at speed c, and he has a clock, so he knows that the events occurred halfway between M and N, at O.
Suppose that observer B flies past A at some speed, meeting A briefly at O. Suppose also that B sends out two flashes of light (the thin dashed lines) -- one at R and one at S -- that illuminate Q and P and whose reflections are received back at U and V. Obviously the light rays emitted by B must be parallel to those emitted by A, since the speed of light is constant.
But now B, using the same method for determining when the events occured as A did, concludes that they happened at different times -- I've marked them as "t(B,P)" and "t(B,Q)"; they are just the midpoints of RU and SV, respectively. Clearly not simultaneous.
You might say, "Well, it just
looks like P and Q happened at different times, but they didn't
really happen that way." For B, however, they
really did happen that way. If, for example, P and Q were two bombs going off, when they
really happened is pretty important, right? But the effects of those explosions can't travel faster than light, so the blasts can't affect B at the same time either.
The whole point of relativity is that we can't have "absolute" knowledge about the universe. We only have what we
measure, and our measurements have certain limitations. To the degree that B can observe P and Q, they really did happen at different times.
Poll