# If future measurements of black hole mergers will falsify general relativity, what other theory is there ready to be adopted?

In a recent paper from scientific american:

it's said that general relativity may be wrong at the edge of the black hole. That may be the hint of a new physics in such extreme conditions. What other theory is out there waiting to be tested in such situations?

• This appears rather broad, there's plenty of more-or-less mainstream theories of quantum gravity, or other modifications to general relativity. None is "ready" as I would understand, but many exist. – ACuriousMind Jan 12 '17 at 14:04
• It would be very helpful to possibly write a few lines more about the nature of possible problems, or an abstract. Thanks – user140606 Jan 12 '17 at 14:48
• – John Rennie Jan 12 '17 at 15:35
• – John Rennie Jan 12 '17 at 15:35
• One might suspect that just how GR failed might yield some insight in to what other theory might be 'waiting'. – Jon Custer Jan 12 '17 at 15:38

Fun question! There are two things here:

i) What is the most popular alternative to GR?

ii) What is the best alternative to GR given the detection of these echoes?

I'll address both in turn, but they are interrelated.

What is the most popular alternative to GR?

GR is what's known as a tensor theory. This means that it uses a tensor field to assign a tensor to every point in spacetime. For example at every point around a black hole there is a tensor. The value of these tensors then 'tells' a particle the path to take around a black hole.

The main alternative to this are called tensor-scalar theories. In this case, in addition to the tensor field of classical GR, there is also a scalar field. Analogous to a tensor field, this scalar field assigns a scalar to every point in spacetime. This scalar field is equated to $1/G$, where $G$ is the gravitational constant. Since the scalar field varies from place to place, this is equivalent to $G$ being variable. In classical Einsteinian GR, $G$ is constant. The most well-known tensor scalar theory is Brans-Dicke theory. This theory requires a coupling constant $\omega$ in the field equations, which has a constant value, but that value is unknown and can be altered so as to match experimental observations. Consequently Brans-Dicke theories are hard to falsify which is often the mark of bad explanation and so most physicists stick with Einsteinian GR (for now).

What is the best alternative to GR given the detection of these echoes?

This is where it gets really interesting. The echoes mentioned in the article you linked to arise due to a key priciple of quantum mechanics which is known in fancy language as unitarity, but is better understood as 'information is conserved'.

If we smash together two particles (e.g. at CERN) then gather all the possible information on the particles that result (trajectories, charge, baryon number etc.) we should be able to recreate all the information about the original 2 smashed particles. This is because information is conserved in quantum mechanics. However we run into a problem when we try to apply this principle to black holes.

If the report of these echoes is true (I note they are still far off the required $5 \sigma$ significance), then it would mean that a firewall exists, and consequently the equivalence principle does not hold globally. That is, clearly the equivalence principle is somewhat right - it has been used to form GR which has passed a plethora of tests in the weak field regime - but perhaps it does not apply to every corner of the universe. Perhaps close to the surface of black holes, where we expect quantum effects to play a more significant role, the equivalence principle does not hold.