Black hole mergers show GR is finite

While the physics media, popular opinion and generally accepted lecturers says things like ‘GR is wrong because singularities’, the physical and theoretical facts suggest very strongly the opposite.

In a black hole merger we have a well defined, simple to describe, and definitely calculable scenario. To summarize: a black hole – black hole merger releases a few percent of the total mass energy into gravitational waves, the aspects of which have been calculated to high precision.

Consider the electromagnetic equivalent. If two macroscopic (well any mass) charged, massive point particles do the same thing – orbit each other, the equations of Maxwell break down – infinite energy is predicted to be emitted in an ultraviolet catastrophe (Raleigh-Jeans). OK says everyone – that’s why we need quantum mechanics! But QED – which covers orbiting massive particles (say positronium, H atom) has huge renormalization problems and is ‘dippy‘.

GR handles this ultraviolet catastrophe – indeed it does not have one – much better than Maxwell or QED. Standard ‘simple’ QED is a mess (according to its authors). Of course QCD and canonical quantum gravity have much more immediate problems with complexity and are harder/impossible to get working, even with the normal merely dippy renormalization. Indeed if one were to quantize gravity then one might presumably end up with a quantum gravitational ultraviolet catastrophe!

First, the above arguments only hold for black holes (but they can be of any mass, even the mass of a proton). Since most physicists think that naked singularities can’t exist, it only makes the above argument stronger. Let’s also not forget that merging black holes will end up with merged singularities. Gravity is fine when you only consider gravity.

Black hole mergers are well behaved and calculable, while the ‘best theory in the world’ – QED struggles with renormalization and more. QCD is incalculably worse and let’s not get started on quantum theories of gravity.

Tom Andersen, 2021

What about naked singularities?

So how about back to the original question? Are singularities a problem for Einstein’s gravity?

I’ll talk to a few things here: Naked Singularities ( EG Kerr solution with a > m) and also how these overextreme Kerr solutions would interact.

Overextreme Kerr Solutions

The Kerr solution to the Einstein equations contains a parameter, ‘a’ that is a measure of the angular energy in the black hole (or naked) Kerr object. If this parameter is over the mass of the hole (m) then (supposedly) all hell will break loose as a naked singularity will be visible. Having a > m is of more than dry theoretical concern, as for instance a wheel spinning on your car when driving at even 20km/hr has a > m (but it’s not the size of a molecule so the Kerr solution does not apply). More to the point, basically every black hole discovered has a spin > 0.1m, so we know astrophysical real Kerr solutions are already dangerously close to being naked. A little scandalous!

What’s the problem with a > m ?

• Naked singularities could cause a quantum explosion of particles.
• Naked singularities will cause General Relativity to be wrong, as predictions break down.
• See this Wikipedia Naked Singularity article.
• Roger Penrose said they are impossible.

Why I don’t think naked singularities are a problem

• General Relativity on its own does just fine with them. The Kerr solution with a > m is not ‘weird’ math.
• We don’t have a quantum theory of gravity (so arguments invoking QM are moot).
• The Cosmic Censorship Hypothesis is likely wrong: As the same Wiki article points out.
• My own theory is that both QM and EM are built from GR, but that is not needed for this article.
• “Evaporating black holes are naked singularities since they are not fully concealed by their event horizon.” 
• Even Roger Penrose can make a mistake.

Why it’s OK to talk about naked singuarities (almost no one seriously spends time on them).

Instead of finding reasons to avoid naked singularities, we should cherish the opportunity to find them as a path for exploring new physics. Of course, the crucial unknown in this regard is: “What do naked singularities look like?” Owing to the extreme curvature of spacetime in their vicinity, naked singularities might produce high-energy particles in a powerful fireball of energy. Do we observe such fireballs on the sky? Is it possible that we have already detected naked singularities but misinterpreted their nature?

By Avi Loeb on May 3, 2020

https://blogs.scientificamerican.com/observations/in-search-of-naked-singularities/

So what happens when two naked Kerr singularities collide? (Will they merge?)

One can do the orbiting spinning black hole calculation for Kerr solutions with a ~ m. See the references below etc.

The only reason that it has not been done for a > m is in my opinion that a > m is taboo in numerical relativity circles.

Horizons are a global – not local phenomena – so why would things change from a = 0.9999m to a = 1.0001m? In other words how is the other black hole to ‘know’ that a > m? In order to measure a > m requires being well outside the black hole. On merge, it’s not the horizons that merge, but rather the singularity structures, even in a normal a < m black hole merger. Think of a (planar spins +z) collision of two black holes, each with a = 0.9999m. Also imagine them to be huge – two light hours across. There is no feasible way that the black holes can tell a=0.9999m from a = 1.0001m – the bits that hit each other first will be barely concealed singularities (the horizon is very close to the singularity at a ~m).

Play with a single Kerr here!

An interesting circumstance not discussed in O’Neill’s book is that the ergosphere remains for a fast Kerr black hole.

“fast == overextreme (a > m)” Note that in the Visualizing Aspects of the Kerr Metric you can get a to 2 (where m is assumed m=1). Also see the entire https://analyticphysics.com/ – a really great site.

References – how close have numerical relativists come to simulating overextreme mergers?

Note that a > m is not usually specifically talked about, mostly due to technical (numerical code and excise regions need changes) and (according to my reading of the physics community) taboo reasons. Looking at the papers – one can see that there is nothing special at a = m. For instance empirically developed formulas in some of the papers have no dependence on (a – m), etc.

See it on Twitter at https://twitter.com/knobsturner/status/1434586301119012864

General Relativity rules!

While we often hear about how GR must succumb to the quantum overlords, we don't hear about just how neatly GR covers collisions, when compared to the QED equivalent. https://t.co/6V3DVtOHxG

— Tom Andersen (@knobsturner) September 5, 2021