# Physical measurements and celerity of black hole mergers?

LIGO detected a black hole merger for bh's of about 30 solar masses, with a schwartzchild radii of about 20km.

Were the gravity waves generated by masses distanced by a few microns or a few kilometers?

A LIGO article states: The Keplerian effective black hole separation in units of Schwarzschild radii (RS ¼ 2GM=c2) and the effective relative velocity given by the post-Newtonian parameter v=c ¼ ðGMπf=c3Þ1=3, where f is the gravitational-wave frequency calculated with numerical relativity and M is the total mass (FIG. 2.).

They state a relative velocity of 0.4 c for 100ms, can't we compare that to electron orbits or something practical? Electrons travel at 0.01 c. Can we say that the merging masses are 40 times smaller than an H atom?

Can we state that the signal does not continue for an entire minute up to 90Khz, perhaps forever, except that the rest is too faint to detect on LIGO For some reason?

• You are trying to derive scale from velocity entirely incorrectly. Before the blackholes merged (and the collision entered the 'ringdown' phase), the centers of mass were separated by the Schwartzchild radius for each: they were at least 40 km apart. Orbiting their common center of gravity with an orbital diameter of about 40 km, so a circumference of ~126 km. Going around that cicumference a thousand times a second gives an orbital velocity of about 0.4c. Nothing about the measured interaction was close to the scale of a hydrogen atom or smaller – antlersoft May 31 '18 at 16:56
• So, the speed of light is 299792 km/s... c*0.4 = 125000 kms... the orbital circumference was, let's say, 1250 km, so that's about 100 periods every second, a frequency of around 100 Hz for the signal sounds about right. Ok, I had a hunch that an orbit of 1250km in one hudredth of a second was way faster that the speed of light So I tried image a collision involving the singularities rather than the actual schwartzchild radius. – aliential May 31 '18 at 17:59

A singularity is not a object. it is a time and position at which infinities appear in the solution of general relativity. When you speak of a "non-zero size singularity" I assume you mean a physical object inside a black hole (as could be predicted by some forms of string theory) Such objects are not part of General relativity, which models black holes as a region of spacetime including a point singularity (for a simple black hole) or a ring singularity (for a rotating black hole)

These results are consistent with General Relativity and two merging Kerr black holes (which have a ring singularity in GR).

They would also be consistent with other models of gravity, including models in which a physical singularity doesn't form. But there is no positive evidence here for there being an object that is a millionth of an angstrom behind the event horizon.

I'm not sure what you mean by "binary singularities distanced by a few microns" The amplitude of the gravitational waves detected was much smaller than that, and there is nothing about microns in the linked video.

We would not expect the signal to continue to increase in frequency up to 90KHz. A new single event horizon forms at some point, in this case when the gravitational waves have reached about 200Hz. A short "ring down" period follows the merger as a single black hole settles into a new stable state.

The objects measured by LIGO are black holes, with an event horizon about 20km in diameter. The measurements at LIGO don't suggest that any object exists inside the black hole. Nothing in these data suggest the objects were the size of electrons.

The mass estimates have quite large error bars, for the first Gravitational wave detected, the masses were about 30 solar masses +- 4solar masses, with similar uncertainties in the Schwartzchild radii

See the orginal LIGO article https://physics.aps.org/featured-article-pdf/10.1103/PhysRevLett.116.061102

• Cheers. I changed the misnomers and quoted the spacial distance and velocity equations given by the article. You say it's smaller than microns, there must be a known range for Rs? Is the gravity wave shorter than UV's? The relative velocity of the pair is known: 0.3 to 0.6 c according to that article, and the distance of the discs/the masses must be billionths of a micron? – aliential May 31 '18 at 8:59