einstein field equations expanded

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Yes you are correct in saying that the principle of equivalence holds good for all frames and is independent of SR or GR and is a universal law without which all our existing scientific understanding about physical laws would break down. This equation describes how black holes warp space around them and helps explain how the Universe evolved. If It is then I can see that the spinning disk thought experiment might imply that mass energy cause the geometry of spacetime to curve(the g_ij( ) to be affected). So thay in the local region the free fall frame IS an inertial frame.

To be more simplistic, say if RHS is about the mass of our Sun, then the LHS would be the space-time curvature caused by this mass. In other words, it is assuming that impact of any other mass-energy is negligible.

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The curvature is nearly flat in space-time far away from any massive body 4. His uncanny intuition about the universe prevailed despite temporary reversals, and his decades-old insights are now at the cutting edge of modern physics and cosmology, helping us shed light on the greatest mysteries of all: the nature of matter, gravity, time, space, and the mysterious dark energy pushing it all outwards.

I think I should start looking at Edwin Taylors and J Wheelers first edition of Exploring Black Holes mwhich is on line at E.F.Taylors web site(eftaylor.com) yours truly Francis. Astronomical knowledge of the time told Einstein that the universe was unchanging in its size.

Starting on November 4, 1915, Einstein gradually expanded the range of the covariance of his field equations. Why? I think he told me that the POE and linear acceleration did go together but that General Relativity was even more general than simply acceleration. The spelling error does hint at the fact that Hubble’s discovery was not yet so strongly established that his name would be well known by all scientists.


yours truly Francis.

So that the ONLY way we can extend the principle of SR to the accelerating frames is to ALSO consider the gravitational field terms AS EQUIVALENT in every way. And it has been widely assumed that he died without ever reconsidering the cosmological constant. A true master designer has created your brain. In other words, field equations relate mass-energy and the space-time curvature at every point in space-time! The twist of GR(it is a background independent theory) is that the very mass-energy that follows the geodesic of the curved spacetime causes the very curvature that determines the motion by var{int[g_ij dx_i dx_j]=0,and so does the mass-energy distributioin all over the cosmos. Finally the curvature is because of the nucleus inside an atom because that is where most of the mass-energy lies.
By an evolving universe I mean, the universe that came into existence after Big Bang.

However I think I would do well to read over your article more closely. There are things in relativity that I don’t understand,and I realize that this always will be with me, But there also are things which I just don’t feel right about and these bother me a lot more(feeling wins hands down against reason all the time,and I think it should)–one of these has to do with gravitational time dilation as opposed to SR “time dilation”. Now from within this spaceship if all its doors and windows are closed, there is no way for one to tell whether the space ship has its rockets fired or is it standing still on earth.

Solutions to the field equations are called metrics. Apple doesn’t knows anything about the earth below.

Dear Mr. Gurudev Is the spatial curvature AT a given point caused by the mass-energy AT that point,and also by all the mass-energy in the universe,that is by its distribution all over the cosmos? So that there are two sources of the non-Euclideanism(curvature) the first being the mass-energy AT the local region of spacetime in question,and the second being the distribution all over the cosmos at other spacetime “POINTS”. The only answer I have been abke to come up with is that the principle of Equivalence is able to have the gravitational field cancell out these accelerationhal terms that otherwise would change the form of the law. When expanded for 4 dimensions, the field equations result in a set of 10 non-linear partial differential equations and have to be solved for the metric tensor!! Finally it comes down to atoms and molecules within the mass and that is the jurisdiction of quantum mechanics. Francis, Yes you are right.

I will, however, have to warn potential readers that this will not be a short answer.

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