# What is the most massive symmetric black hole pair that can pair produce during their collision?

Gravitational waves produced by inspiraling black holes have a similar inverse dependence on mass that the strength of the gravitational field outside of the event horizon has. For example, look at how mass decreases with increasing frequency in this graph. Presumably, if the mass of the black-holes is sufficiently small the peak frequency will become high enough for the gravitons to pair produce, with each-other or off of CMB photons. What is the largest mass at which identical colliding black holes could pair produce, in principle, two particles of identical mass?

Granted, in a real situation there will be difficulties in establishing the energy threshold based on circumstances (graviton + CMB photon will require a really high energy graviton), geometry (graviton + graviton will likely be colliding at an acute angle instead of head on), and factors about which I am unaware. So let's just assume that the highest frequency gravitons produced by the collision can meet head on in finding this mass limit, to keep things simple.

Also, assume this is for electron/positron pairs or neutrino/anti-neutrino pairs, since if this can happen it should produce some interesting neutrino flashes.

• Gravitons are hypothetical particles outside the standard model of particle physics. We don't have a widely accepted theory for what you're asking. I have a sense you're somehow confusing gravitational waves with gravitons. – StephenG Aug 7 '18 at 22:37
• @StephenG If gravity quantizes in anything remotely resembling a standard fashion, this can be translated into, "What is the peak frequency of gravity wave produced as a function of mass?" – Sean E. Lake Aug 8 '18 at 1:11
• I'm not even sure we could define a definite pair production mechanism for gravitons in the absence of a decent theory. We don't know if a quantum theory of gravity is even possible or we need something more radical. We don't know what additional particles would be required by such a theory apart from gravitons (and we don't even really know if gravitons would be the particle taking that role). It's a big leap from "don't know" to what you're asking and I feel it's going to be either opinion based or non-mainstream. – StephenG Aug 8 '18 at 2:10

## 1 Answer

It seems that the maximum frequency of the LIGO black hole is of order 150 Herz. Look at the table on the right . This is pico electron volts , very far away from any pair production energy.

If gravitons follow standard interactions as in the particle model, graviton graviton interaction will be very improbable, due to the smallness of the coupling constant. Even with photon photon one needs gamma ray energies to expect measurable photon photon interactions with pair creation.( There is talk of gamma gamma colliders). The gravitational coupling (assuming quantization of gravity) is orders of magnitude smaller.

There have been a way out proposal that elementary particles are black holes . My impression is that to get to the level of elementary particle pair production by gravitational waves from small black holes, some similar non main stream hypothesis will be needed.

Fig 14 here may interest you , still in the kiloherz range.