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General Relativity shows that straight lines do not physically exist. They do however exist in theory

That is a far cry form saying that parallel lines intersect at infinity. There is no reason why two equidistant lines maintaining equidistant separation can not remain perfectly parallel on a curved (warped) surface.

A definition of parallel is that something remains equividstant from another object over extended distance. Parallel lines cannot, by definition, intersect. It doesn't matter that no such entity exists in the real universe (which is only a conjecture!), only convergent lines will intersect.

Please provide your source for the claim that Einstein said there is a “common center to the universe towards all objects will eventually fall.”

That is the only way that he can make a claim that parallel lines intersect at infinity. They must have an infinitissimal angle of convergence in order to meet at infinity. If he didn't make that claim then he is wrong.

As you said: However, you can construct other forms of geometry, so-called non-Euclidean geometries

All man-made models. There is nothing absolute or "ordained" about modern cosmology. Simply new observer definitions and "angles." No matter what geometry you use, two parallel lines cannot have a common point in infinity and remain parallel.

In math, one can add variable to get the desired answer. If the model works, it is not necessarily "true" but working. Like the Ptolemaic navigation system. Ptolemy added epicycles to account for observed behavior. It describes the observed phenomenon, but it does not reflect what we know of plenary motion today empirically.

Your argument doesn’t improve with repetition.

And you are welcome to believe whatever you want to believe.

In math, one can add variable to get the desired answer. If the model works, it is not necessarily "true" but working. Like the Ptolemaic navigation system. Ptolemy added epicycles to account for observed behavior. It describes the observed phenomenon, but it does not reflect what we know of plenary motion today empirically.

Jeepers, there is at least one poster on the forum whose testimony is that, because of coordinate transformation, geocentricity (the earth as the center of the solar system) is just as intellectually acceptable as heliocentricity. Most posters find it amusing, but the scientists and mathematicians cringe.

Likewise, there will always be some who insist that Euclidean geometry is representative of God’s Creation, i.e. space/time. And the mathematicians and physicists will continue to cringe.

me: Please provide your source for the claim that Einstein said there is a “common center to the universe towards all objects will eventually fall.”

kosta50: That is the only way that he can make a claim that parallel lines intersect at infinity. They must have an infinitissimal angle of convergence in order to meet at infinity. If he didn't make that claim then he is wrong.

The Point at Infinity which is defined as the intersection of two parallel lines was first considered by Desargues (1591-1661) and Poncelet (1788-1867) was first to employ it.

Einstein wasn’t even born until 1904.

Since you have no source for it, I shall dismiss your claim at 8447 that Einstein had postulated there is “a common center to the universe towards all object will eventually fall.”

That said, if Lurkers are interested in the relationship between Einstein’s relativity and Poncelet’s math vis-à-vis infinity (quantum theory and space/time) – they might want to check out Penrose’s Twistor Theory.