reply to post by S.J.Crothers
Your so-called proof that General Relativity (GR) forbids infinite density is conceptually flawed. Firstly, your inference from the fact that GR is a
generalisation of Special Relativity (SR) that, by definition, GR cannot violate SR is illogical. SR cannot violate GR because SR is a
special
case of the latter in which space-time is Minkowski. But GR can certainly violate SR because it applies to the general case of 4-d Riemann
manifolds with non-zero curvature, in which observers are non-inertial and light geodesics are curved lines, rather than the straight lines of
Minkowski space-time.
Your fundamental error of logic, on which your conclusion depends, is therefore to say that GR cannot violate SR. The latter certainly holds
approximately in a gravitational field if the latter is weak enough (or over sufficiently small distances). But not exactly. In particular, the
Lorentz transformation equations are exactly valid only in the absence of a gravitational field, where all observers move at constant relative speed.
Secondly, whilst it is certainly true that SR forbids objects reaching the speed of light, it does not hold in the physical situation of a collapsing
black hole. It is therefore incorrect to deduce from the fact that the inertial mass and density of an object approaches infinity as its speed
approaches the velocity of light that SR forbids an object acquiring infinite density in
any space-time (e.g., that of a collapsing black
hole). The Lorentz transformation equations do not apply in a gravitational field and no legitimate deductions about the nature of black holes can be
made from them. Your inference is therefore invalid because it is an elementary error of logic to claim that what can be deduced from a special case
of a theory applies to the general theory itself.
According to the Hawking-Penrose singularity theorems:
en.academic.ru...
singularities must inevitable arise in spacetimes containing matter that obeys certain conditions (e.g., positive energy).
Singularities can be avoided in Riemann-Cartan manifolds containing torsion as well as curvature, i.e., by considering matter with spin angular
momentum, the gravitational effect of which is a repulsive force that counteracts the attractive, gravitational force. This has been known for over 50
years. They violate the Hawking-Penrose theorems because the conditions assumed to hold for these theorems to be valid no longer pertain when
space-times have non-zero torsion.