If Black Holes are a singularity, and....?

Question

singularities are a breakdown of a mathematical model, usually. Then why is their the Big Bang Theory, which also predicts a singularity?

Answer 1

You are right that ALL black holes have a singularity at their centre.

Singularities arise as solutions of the field equations where the curvature of space time becomes asymptotic.

It is not quite fair to say that mathematics then breaks down. Mathematics has perfectly good mecahnisms for coping with infinity, zero and the other notions involved in a singularity. Indeed Cantor showed an "infinity of infinities" and how to handle them.

However, there are two problems with the singularity in a black hole. The first is that a well defined, zero volume space containing matter conflicts with quantum mechanics, because it violates the uncertainty priciple which says that [x,p] must be greater than zero.

The second is that there is simply no mathematical way to trace the field equations through the singularity. In effect, they are undefinied at the singularity and so you do not know what your starting point is. Indeed it is also implicit that you cannot trace the laws of physics through a singularity - they may or may not be different. Hawking has suggested the introduction of imaginary time to resolve this.

Answer 2

Not all black holes are singularities. Whether there is a singularity concealed within the event horizon depends on the mass forming the black hole. If the mas is large enough, the gravitational forces can exceed all atomic forces and produce a singularity. Any mathematical model of fields outside the singularity is valid (one of the initial solutions of the equations of general relativity is to assume a point mass). The models break down at the point of the singularity, and the big bang theory model "starts out" at a very small time after the initial singularity.

Answer 3

Physically, the mass has been compressed until it has literally zero volume and non-zero mass. The density is infinite. Therefore we have a singularity.

We might presume that the universe arose out of a singularity, but once the volume was non-zero, there was no longer a singularity. I don't see that there is a problem.

As far as I know, all black holes contain singularities. Technically a black hole just has to be something with an escape velocity that is greater than the speed of light, but no form of physical matter can exist under those conditions. A black hole cannot have a neutron star inside it, for example. Before the escape velocity approaches c, gravity will already have crushed the neutron star to a singularity.

Answer 4

A black hole is not a singularity. When singularities appear in a mathematical model of physics, it is generally an indication that the model is defective. Sometimes a model can be renormalized to resolve some singularities. It is exceedingly unlikely that a mathematical singularity is relevant for any physical phenomenon.

Answer 5

Black holes are not a singularity. Black holes are massive. Singularities exist as a tiny point in space - not the same thing.

Answer 6

They break down because gravitational equations do not jive with electromagnetic equations.