Hawking has written about gravitational

singularity theorems in the framework of general relativity.

And the occurrence of singularities is unavoidable, according to the singularity theorems [6-8].

The least radical approach is usually considered the avoidance of singularity, by modifying gravity (i.e., the relation between the stress-energy tensor and the spacetime curvature as expressed by the Einstein equation), so that one or more of the three assumptions of the singularity theorems [6-8] no longer hold.

According to the Penrose-Hawking singularity theorems [22-24], a trapped surface inevitably leads to a geodesically incomplete spacetime manifold, implying the imminent formation of a singularity.

Like the singularity theorems, the principle of topological censorship [14] assumes the presence of a trapped surface.

The highlight was the cosmological

singularity theorems, developing from Roger Penrose's ideas about black holes, showing that (under reasonable assumptions) classical general relativity necessarily implies there was a start to the universe: a space-time singularity that is the boundary to where normal physics applies.

It is considered as a cornerstone for the achievement of the

singularity theorems, the analysis of gravitational collapse, the cosmic censorship hypothesis, the Penrose inequality, etc.

Moreover, the unconditional universal coupling is a crucial assumption (1) for the

singularity theorems of Hawking and Penrose (Hawking and Ellis 1973).

Chandra had a deep appreciation of Penrose's work; in fact he once remarked to me, "The

singularity theorems of Hawking and Penrose are the most important results in general relativity since Einstein!" Certainly Chandra was capable of recognizing genius in his younger colleagues, something that, alas, Eddington was not.

A full answer to this question is beyond the scope of this paper, but let us call attention to one topic whose standard treatment is essentially non-constructive, but which arrives at some of the most striking results in general relativity and cosmology, namely the spacetime

singularity theorems of Hawking, and Hawking and Penrose.

The so-called "

singularity theorems" are not theorems at all, as they are based upon false concepts.

If Friedmann's solutions are supplemented by the Hawking-Penrose

singularity theorems, and the theorems are satisfied, it follows that our Friedmann univers began to exist with a big bang singularity.