Space-Time Theorem Of General Relativity
In 1970 Stephen Hawking and Roger Penrose published the first of the space-time theorems.
What it says is this. If the universe contains mass and general relativity is accurate then space and time must have a beginning along with matter and energy. Also, there must exist a cause that brings the universe into existence outside of physical time and space. I would say that the First Cause exists in metaphysical time or eternity. But that is for another time.
The Singularity of the space-time theorem is outside the universe. It’s transcendent. The Singularity of the space-time theorem is a causal singularity.
Stephen Hawking and Roger Penrose “The Singularities of Gravitational Collapse and Cosmology,” Proceedings of the Royal Society of London series A, 314 (1970): 529-548. States:
We are now in a position to state the corollary to our theorem.
COROLLARY. A space-time M cannot satisfy causal geodesic completeness if, together with Einsteins equations, the following four conditions hold:
(3.20) M contains no closed timelike curves
(3.21) the energy condition (3.6) is satisfied at every point,
(3.22) the generality condition
(3.10) is satisfied for every causal geodesic,
(3.23) M contains either
(i) a trapped surface,
(ii) a point p for which the convergence of all the nullgeodesics through p
changes sign somewhere to the past of p,
(iii) a compact spacelike hypersurface
We may interpret failure of the geodesic completeness condition in our corollary as virtually a statement that any space-time satisfying (3.20)-(3.23) ‘possesses a singularity’…..The implication is virtually, that a space-time satisfying (3.20-3.23) must contain a causal geodesic which possesses no pair of conjugate points….Instead, we see that our theorem implies that some causal geodesic ‘enters a singularity’ (i.e. is compelled to be geodesically incomplete) before any repeated focusing has time to take place.
Gravitational Singularity-Wikipedia, The Free Encyclopedia states:
More generally, a spacetime is considered singular, if it is geodesically incomplete……The simplest Big Bang cosmological model contains a causal singularity at (t=0), where all timelike geodesics have no extensions into the past. Extrapolating bakwards to 0 results in a universe of size 0 in all spacial dimensions…So, at the singularity 0 (the lack of space, time, matter, and energy) there’s a CAUSE. This places the CAUSE outside our universe. So, the corollary of the space-time theorem is that if general relativity accurately describes the dynamics of the universe then there is not only a beginning to space, time, matter, and energy but there must also be a transcendent non-physical CAUSAL AGENT that brings the universe into existence. Since General Relativity has been established beyond reasonable doubt the space-time theorem can be trusted.