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Astronomers Discover 33 Pairs of Waltzing Black Holes
Astronomers from UC Berkeley have identified 33 pairs of waltzing black holes, closing the gap somewhat between the observed population of super-massive black hole pairs and what had been predicted by theory. "Astronomical observations have shown that 1) nearly every galaxy has a central super-massive black hole (with a mass of a million to a billion times the mass of the Sun), and 2) galaxies commonly collide and merge to form new, more massive galaxies. As a consequence of these two observations, a merger between two galaxies should bring two super-massive black holes to the new, more massive galaxy formed from the merger. The two black holes gradually in-spiral toward the center of this galaxy, engaging in a gravitational tug-of-war with the surrounding stars. The result is a black hole dance, choreographed by Newton himself. Such a dance is expected to occur in our own Milky Way Galaxy in about 3 billion years, when it collides with the Andromeda Galaxy."
choreographed by Newton himself.
He might try, but the accurate calculation of black hole orbits requires the complete infrastructure of General Relativity, so Einstein is calling this tune.
Other similarities are that in a waltz, the dancers usually remain in closed position and that the pair makes circular motions. You know, like waltzing black holes.
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That's incorrect. The paper gives the orbital velocities as being ~100 km/s. If the black holes were close enough to one another for their orbits around their mutual center of mass to be significantly affected by relativity, their distance from one another would have to be comparable to the radii of their event horizons. But at a distance that's comparable to the radius of the event horizon, orbital velocities are a significant fraction of the speed of light. Since we observe that their orbital velocities are very small compared to the speed of light, it follows that their orbits are Newtonian to a good approximation.
I assume you're referring to something like MOND, in which case this is also incorrect. MOND gives significant corrections for objects with very small accelerations. These black holes actually have very big accelerations compared to the accelerations of ordinary disk stars, which are what MOND was invented to explain. Therefore even if MOND were right (which seems increasingly unlikely), it wouldn't be relevant for understanding these binary black holes' orbits.
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No, that's incorrect. Newtonian physics is an excellent approximation to the orbit of Mercury. The famous relativistic effects on Mercury's orbit are tiny. To see them, you have to subtract out a whole bunch of other effects, some of them a hundred times bigger than the relativistic one.
No, because the adjustable parameter in MOND is specifically tuned up so that you only get significant anomalous effects for stars farther out in the disks of galaxies. Comerford's paper says they expect the black-hole pairs to be separated by ~1 kpc, which is small compared to the size of a galaxy. If you estimate the acceleration from their numbers, you get a=v^2/r=(100 km/s)^2/(0.5 kpc)=6x10^-10 m/s2, which is about 5 times bigger than the a0 parameter in MOND, so you won't see any significant effect. This isn't a coincidence, because supermassive black holes are observed at the *centers* of galaxies, not out in the disks, whereas the MOND parameter is chosen so as to have an effect on the disk while leaving things at smaller radii alone.
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Absolutely. But the relativistic effects are extremely small at those speeds. For instance, the relativistic time dilation aboard a GPS satellite is about 1 part in 10^10.
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Sure. The error in locating yourself on the earth's surface equals the time error multiplied by the speed of light. Since the speed of light is big, the technique is extremely sensitive to tiny time errors.
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No, I pointed out that you'd misunderstood those alternative theories of gravity.
Both in your original post and in this one, you seem to be displaying a misconception that the mass of the object is what matters. That's incorrect. What makes a black hole a black hole isn't its mass, it's the fact that the mass is compressed into such a small space. When an ordinary, main-sequence star collapses into a black hole, it actually loses mass in the process. Likewise the mass of Mercury is completely irrelevant to the discussion. You seem to think that Mercury's small mass reduces the relativistic effect on its orbit. That's incorrect. The relativistic precession of Mercury's perihelion is 43 seconds of arc. If Mercury's mass was half what it is, or double what it is, the precession would still be 43 seconds of arc.
Similarly, you could analyze the motion of two human bodies doing a literal waltz, and say that Newton isn't the choreographer. You'd be absolutely right. There would be relativistic effects on the motion of their bodies. That would be absolutely irrelevant, however, because the effects would be too small to measure compared to other effects that you couldn't even quantify, like air currents. Similarly, the relativistic effects on the orbits of these black holes are far too small to measure. The gamma factor for an object moving at 100 km/s is 1.00000006. The difference from 1, which is 5x10^-8, quantifies the size of the relativistic effects. If you take a look at the paper, they weren't even able to resolve the black holes well enough to determine their distances from one another. That means that their orbits are not known at all, much less to a precision of parts per billion. Also, if we assume that their order-of-magnitude estimate of 1 kpc for the orbital separation is roughly correct, each one is swimming in the gravitational field of a whole bunch of other densely packed stars near the galactic core. That effect, which is impossible to measure or calculate with any precision, is going to completely swamp the relativistic effect.
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