# A Could gamma rays imply GW sources not black holes?

1. Feb 28, 2016

### Jonathan Scott

When I saw the report of a gamma ray burst associated with the LIGO GW event, my immediate thought was that the obvious explanation is that the compact massive objects were not in fact black holes, and the gamma ray burst was from the energy of the final collision and merger.

This would obviously mean that Einstein's Field Equations would have to be inaccurate at this extreme limit of very strong fields, but as far as I know they have not been experimentally confirmed in this regime anyway, so I would expect this to be worth investigating, especially when balanced against theories such as Loeb's idea about the merger occurring inside a star.

(The alternative option that Einstein's Field Equations are correct even in that case but the object somehow manages to resist gravitational collapse is not mathematically viable for masses as large as those involved in the GW event).

There are of course various clues which suggest that there is a threshold mass which distinguishes between neutron stars and something else, which for example doesn't show thermonuclear flashes from a surface or pulsar emissions, and which is assumed to be a stellar-mass black hole. However, there are few cases where all of the parameters can be pinned down, and there are some definite anomalies, such as ULX source M82X-2 which was thought to be well into the black hole range from its luminosity, but was then found to be a pulsar, and is still essentially unexplained by any standard theory as far as I know.

Is there any other direct evidence (apart from the intrinsic neatness of GR theory) for the existence of stellar-mass black holes as opposed to some sort of extremely dense but non-collapsed object? Has anyone spotted any serious scientific discussions of whether the gamma-ray burst might suggest that black holes do not occur (at least at this mass range)?

2. Feb 28, 2016

### Staff: Mentor

How would such an extremely dense but non-collapsed object look like? Without a proper reference (please provide this before discussion can continue) that is just a set of words, impossible to discuss.

I am not aware of alternative to GR which would (a) not lead to black holes and (b) still lead to the correct emission of gravitational waves - in addition to passing all the other tests of course, including binary pulsars, accretion disk spectroscopy and all the weak-field tests.

3. Feb 28, 2016

### Staff: Mentor

4. Feb 29, 2016

### Jonathan Scott

I'm assuming the object to be just the same as it would be in GR (i.e. a neutron star or perhaps quark star), but with a metric that doesn't go singular, and I'm looking for discussions of this possibility.

The most obvious modification to the metric is to incorporate the Mach's Principle concept that the effective value of $G$ decreases near an extremely large mass, in order to maintain the Brans-Dicke-Whitrow-Randall-Sciama relation that the sum of $Gm/rc^2$ for everything in the universe is a constant $k$ of order 1. Dennis Sciama's beautiful article On the Origin of Inertia shows, admittedly via a toy model, how this relation explains inertia as an inductive effect from the gravitational field of the universe. This concept is referred to as the "Sum for inertia" in MTW, section 21.12, equation 21.160. It was part of the original idea behind the Brans-Dicke theory, which however doesn't match weak field experimental results unless the Machian part is turned right down, basically turning it into GR.

I don't think this is the place to speculate about details of alternative theories, but I can at least give a specific example as an illustration of the possibilities. As this is just an example and not the main subject of the thread I'm skipping the details of the maths, but if it's considered important I could expand it in more detail.

If we define a Machian variable $G$ by taking $k = 1/2$ in the above relation, then a little algebra shows that the time factor in the metric changes from something like $\sqrt(1-2Gm/rc^2)$ (for GR in Schwarzschild coordinates) to $1/\sqrt(1+2Gm/rc^2)$, where $G$ in the Machian case is now the value of $G$ due to all masses except the local central mass, so it is constant over a local region. This clearly eliminates any event horizon if $r$ relates to the physical radius and is therefore always positive.

Obviously for an alternative theory to be viable it would have to match GR for weak to medium-strong fields (which basically means having the same PPN parameters). If we express the vacuum Schwarzschild solution in terms of Marcel Brillouin's radial coordinate $r = R + 2Gm/rc^2$ where $R$ is the Schwarzschild radial coordinate (so Brillouin's coordinate is effectively the distance from the event horizon in Schwarzschild radial units), then the time component of the metric is identical to the above example and the radial and tangential spatial metric factors are also powers of the same Machian expression, so there definitely exists a vacuum solution which satisfies this requirement, and which locally still satisfies Einstein's Field Equations.

(The Machian variable $G$ concept has another major obstacle to overcome, which is that solar system experiments suggest that $G$ is effectively constant even on the scale of the age of the universe, and it is difficult to see how a Machian definition of $G$ could appear to be constant in this way).

5. Mar 1, 2016

### Staff: Mentor

The metric for a stable object like a neutron star does not "go singular" in standard GR, so I'm not sure what you're referring to here. As mfb said, we need a specific reference in order to have a discussion, not vague gestures in the direction of some kind of alternative theory.

6. Mar 1, 2016

### Staff: Mentor

Thread closed pending provision of specific references by the OP. Please PM one of the moderators with reference info.