Excuse me for noting that in the general theory of relativity (GTR) time stops at the event horizon of a black hole. So in theory we can never in our "proper" time watch the two black holes merging
Andrew, thanks for your question! It is really the paradox of BH merging and the concept of BH itself - it is impossible for distant observer to see formation of BH and also to see coalescence of newly formed BH. This is because in general relativity there is no clear understanding of the physical sense of the system of coordinates.
There are many paradoxes of the BH concept. For example in the paper by Chowdhury&Krawss http://arxiv.org/abs/1409.0187 they emphasized that BH cannot form because it evaporates (Hawking radiation) before the horizon formation.
Another paradox is the infinite binding energy of BH - due to infinite force of gravity - nothing can escape from BH. However before BH formation the binding energy of a collapsing star or merging binary system was finite. So there is no energy conservation during the formation of BH.
Yes good answer. But herein the solution to those problems.
Fact is that the infinite time dilation at the event horizon does not in reality exist.
Its just a quirky paradox of the maths of GTR
These along with other paradoxes can be lifted by reformulating the maths
Einstein did not predict the existence of black holes, in fact he denied their existence in a paper published in 1936, Simply because that would imply the existence of singularities, with infinite density and zero time passage at the event horizon.
The force of gravity in General relativity (GTR) is thought to come form the curvature of space-time.
Unfortunately the maths of GTR implies infinite curvature and zero time passage at the black hole event horizon and the black hole becomes a singularity- and yet the black hole has a radius.
The Misner Wheeler Thorne interpretation partially resolved this in that the singularity rests inside the event horizon.
But yet another paradox arises if time stops at the event horizon (frozen star) no matter would fall in hence black hole could not accumulate matter, and all the in-falling matter would be situated at or near the event horizon, hence the firewall.
The solution is to alter the maths of GR.
Additionally GR falls down in a number of areas, so any new maths should also resolve these problems
Yes GR works in the weak fields of the the solar system, and Intermediate
fields of neutron stars.
1). It produces infinite density singularities in the very strong fields
such as in black holes.
2).It does not necessarily explain dark matter in galaxy cores where we
know super-massive black holes exist and the galactic dark matter
therein,
3). It does not explain dark mater present in galactic halo's,and galactic
clusters such as the bullet cluster,
4).It does not explain the presence of cosmological dark matter as a whole.
5). It has not yet been fully corroborated by the studies of neutron stars
and in black holes.
6). It does not easily explain the presence of dark energy and cannot be
translated in quantum gravity.
7). It predicts that time stops at the event horizon
Here I enclose a number of publications which explain all of these
phenomena, whilst agreeing with the results of GR where it has been
thoroughly tested.
1).First to obviate the infinite density singularities.
Dear Andrew, unfortunately your "solution" of BH paradoxes looks very naïve. It has no serious physical foundation, just ad hoc assumptions, which cannot convince any professional gravity physicists.
A serious idea is to conserve the concept of force in relativistic gravity theory. In modern theoretical physics it is known as Feynman's Field Gravity approach. FG has very general foundation, based on Lagrangian formalism, conserves the concept of force, exclude BH and horizons and predicts new testable experiments and observations. See e.g. http://arxiv.org/abs/0809.2323 and the book