More from Hawking on the scientific support for the formation of singularities in a pre-universe multiverse Quantum World. It is based on The Penrose-Hawking Singularity Theorem based on Einstein's General Relativity.
Summary from:
Penrose–Hawking singularity theorems - Wikipedia
A singularity in
solutions of the Einstein field equations is one of two things:
- a situation where matter is forced to be compressed to a point (a space-like singularity)
- a situation where certain light rays come from a region with infinite curvature (a time-like singularity)
Space-like singularities are a feature of
non-rotating uncharged black-holes, while time-like singularities are those that occur in charged or rotating black hole exact solutions. Both of them have the property of
geodesic incompleteness, in which either some light-path or some particle-path cannot be extended beyond a certain proper-time or affine-parameter (affine-parameter being the null analog of proper-time).
The
Penrose theorem guarantees that some sort of
geodesic incompleteness occurs inside
any black hole whenever matter satisfies reasonable
energy conditions (It does not hold for matter described by a super-field, i.e., the
Dirac field). The energy condition required for the black-hole singularity theorem is weak: it says that light rays are always focused together by gravity, never drawn apart, and this holds whenever the energy of matter is non-negative.
Hawking's singularity theorem is for the whole universe, and works backwards in time: it guarantees that the (classical)
Big Bang has infinite density.
[1] This theorem is more restricted and only holds when matter obeys a stronger energy condition, called the
dominant energy condition, in which the energy is larger than the pressure. All ordinary matter, with the exception of a vacuum expectation value of a
scalar field, obeys this condition. During
inflation, the universe violates the dominant energy condition, and it was initially argued (e.g. by Starobinsky
[2]) that inflationary cosmologies could avoid the initial big-bang singularity. However, it has since been shown that inflationary cosmologies are still past-incomplete
[3], and thus require physics other than inflation to describe the past boundary of the inflating region of spacetime.
It is still an open question whether (classical) general relativity predicts time-like singularities in the interior of realistic charged or rotating black holes, or whether these are artefacts of high-symmetry solutions and turn into spacelike singularities when perturbations are added.