General Relativity solutions overview

Looking at General Relativity and its use in science, it is found that at least in astronomy there is no single solution with it. It is a source of many resolutions. Even back in the time of Albert Einstein, the solutions to the field equations were not singular. Other workings arose from the same from the minds of de Sitter, Friedmann, LeMaitre, Eddington, Milne and others. This continues to this day, the many makings off of it.

So the field equations do not represent of themselves the singular resolution of astronomy. And they are varied including the postulations that there may not arise a universe to having a ponderous singularity or living in a black hole, among many. It seems the general relativity equations have not solved everything but rather left some open ends  Recall that "general" as in General Relativity means general, not comprehensive or exhaustive.

Consider, earlier, Einstein had promoted a simple relation that should broadly and easily represent the nature of the cosmos, G=T (G is geometry). That held for a while as an easy guide on an overall view of the universe and how it functions. In recent discoveries, the relationship, G=T as applied universally is cast into doubt. Other natures do not give support for that. Among others, some quantum fields which do not demonstrate adhering strictly to G=T. (The rest is details?) By 1918, the equation was modified to G-^=T.

As a consideration perhaps for ratios. It is claimed as an illustration of E=MC2 that there should be found a balance of matter and energy production and that they produce each other. With current data and extrapolations, it is hard to see this activity as remaining mutually contributive. Data indicates that the expansion leaves the quantity of the of those elements as diminishing. Not only that, but how will matter and element forming stars contribute even anything ample when the stars stop burning and creating elements? There seems to be no functioning of that famous equation for the far future in a vastly dissipated, cold cosmos. Nor will there be likely to be found a favorable ratio of matter and energy, matter would be greatly dissipated to be utilized anymore as mutually creative. It would indeed be challenging to find macro elements to cobble in that distant future. No stars and no new matter. With the famous equation, could there be challenges to the 'm' mass? It is said more now that there are massless bodies at least in the microscopic realm. How can that support the equation? And that process may be obviated anyway if quantum entanglement which could proceed faster than light from one end of the universe to the other is substantiated.

 One could be critical that such a fabled equation does not fully anticipate or address those conditions of the cosmos, especially of the distant future where it may not hold, unless "ripped", an essentially atomless cosmos but remains as a universe. Which is almost odd since it is also shown that Einstein did draw concepts of how the universe could end, but did not work in his famous equation directly.

Others of the same time wrangled with general relativity, like those named above. Some found errors in Einstein's work ups, and those allowed somewhat different solutions on the universe like a rebounding or universe with no dark energy and more, like Friedmann, than Einstein's. A letter from Alexander A. Friedmann II to Einstein in early 1920's made a case for a nonstationary universe. He also wrote, "it will follow from the world equations derived by you that the radius of curvature of the world is a quantity independent of time." Further, it was pointed in a Friedmann letter to Einstein, "showed by direct calculations that the necessary condition for the disappearance of the divergence of the  matter tensor, which was pointed out by Einstein in his note, by no means implies that the radius of the curvature of the world is constant in time." An Einstein response, "The conclusion I shall arrive at is that the field equations of gravitation which I have championed hitherto still need a slight modification..."

 Friedmann further computed a solution, "We saw that the Einstein's cosmological equations have solutions describing a world with constant negative curvature of space." He further noted, "from this that non-stationary worlds with constant negative curvature of space and with positive density of matter could exist."

Friedmann concluded that general relativity could not have the capacity to explain the total space volume of the universe in its limitation. He offered that making the calculations based on global orientation would improve congruous outcomes.

Friedmann considered the Einstein possibility of presence of anti-gravity or cosmological term. Much in accordance with his above work on other features, Friedmann's calculations prompted Einstein to write, "we need a generalizing modification of the field equations of gravitation."

Friedmann also made time manageable, "Thus, time is overthrown from its pedestal."

He said the monolith would become instead an assistant in computations.

It should be recalled that Einstein did not favor infinities. They proved cumbersome and awkward for calculations. So he made it easy on himself by banishing infinities which then made things more manageable.

In some cases, many follow the need to express sizes as diminishing even to the point of vanishing that may follow the equations both in General Relativity and Quantum mechanics. Many also will go to great lengths  to retain elements of matter in cosmos equations, no matter how diminutive.  

One curious concept is found that many scientists try to avoid. That is that calculations can be made on subjects reducing them to vanishing. This is really a problem for scientists. Yet, with all the exploratory measuring of things, it now seems unavoidable that the unresolved but ever diminishing measurements that are far smaller than Planck's length can only be typified as vanishing for as far as practical purposes are concerned. But really, to a billionth trillionth?  Not that such calculations might come in handy at times, like to depict something clearing away  for something else. But for a few, they even calculate the universe as subject to a vanishing point.(?) One might wonder, with so many of these vanishing equations coming to the fore, whether these calculations truly represent a viable approach toward resolving some of the issues. 

Note: the material herein is not necessarily a reflection of entropy of current societies.