Rotating black holes

If you like (?) to think in terms of spherical harmonics then:

monopolar radiation: is out. Conservation of mass/energy means you can't turn the gravity 'light' on and off at a point.

dipolar radiation: also out. Conservation of momentum means you just can't displace a body sideways without a corresponding reacting mass ( Newton's action/reaction law implies conservation of momentum and vice-versa ). So the next highest radiation pattern is ....

quadrupolar radiation: is IN. Non-spherically symmetric mass pattern is the gig here. Think of a barbell say. A spinning neutron star with a mountain/pimple on it. Two body orbiting system ( Taylor-Hulse ), Earth/Sun, NS/NS, NS/BH, BH/BH. Super/hyper novae with asymmetric fireballs, some are posited to eject a neutron star remnant at some speed out of the area. A black hole per se is spherically symmetric, but can be part of a GW radiating system.

Pure GR would imply accounting for effects along all directions of propagation, thus a sort of gravity optics comes into play. This is already recognised as the lensing of distant quasars by more proximal galaxies ( ie. the light paths define the spacetime geodesics for us ). There was that paper we discussed here 12+ months ago - about an eclipsing binary pulsar system altering the timing of received radio signals and the very close correspondence with GR - so you'd have to credit any GW's ( from a more distant source ) following the same paths. Sigh, if only our eyes were GW sensitive ....

Actually we'd discover first off that we are in a really 'dark' part of the universe with all the 'bright' stuff quite distant. So we need some Galileo Gravitie to throw together some 'scope for us - now there's a good sci-fi plot right there!

As for frequency and phase differences at different detector locations ( with same source ): yes indeed you'd get that. Probably even have Doppler'ing. As for whether the magnitudes are measurable ... well these are higher order effects, but then that's why a wide network of detectors is good idea. Essentially you are 'parallax'-ing.

Gravity Probe B is such a great project. If a Nobel doesn't come out of that work for someone then the world's gone awry!

Frame dragging is such a hard one to visualise! It's a 4-D frame getting twisted for starters. I can only liken it to the magnetism resulting from the Lorentz transform of a Coulomb field - the 'test' charge is responding not to where the charge 'is' but where it 'was'. That gives a force component orthogonal to the motion, and also orthogonal to the ( radial ) line between the two. Similiarly the frame ( not geodetic ) effect found would deflect an inward falling body 'to the side' in a tangential and not radial sense. Ah, that's what we need ... 4-D glasses! In an IMAX theatre too .... :-)

Cheers, Mike.

( edit ) 'also orthogonal to the ( radial ) line between the two' - utter tripe, Mike! Parallel or anti-parallel to that axis, depending on the charges : which is why, for instance, transformer coils need to be robust to prevent them rupturing apart when you ramp the current up.

Are there conditions whereby gravity/rotation will push objects apart?

In this news article (Four stars found in amazingly tight bunch), it's mentioned that, “...the spin energy of the rapidly rotating pair, mixed with the gravitational interaction between the two pairs, has pushed the other pair farther away over the years.�

How does that happen?

This is similiar to the assists given to the Voyager and later spacecraft using Earth ( & other planet ) fly-bys. There is momentum transfer and if the paths are right this gives a energy boost to the craft, but at the expense of the planet. It's a bit difficult to come up with a natural language explanation, and you have to be careful which frame you're using, but I'll try. Note that the nett boost to the craft is with respect to it's orbit around the Sun. If only the Earth and the craft are considered then the entire encounter is symmetric, and no overall exchange is possible.

The conditions are, in a rough description :

- approach of the craft is from behind ( w.r.t. direction of planet's travel ). The craft has greater orbital velocity component around the Sun ( tangential to orbit ) than the planet ie. it is 'catching' the Earth up. If we were to look outward from the Sun toward the two we would see a narrowing gap between the leading planet and the trailing spacecraft.

- the craft is already on a net outward course from the Sun. If we were to look down on the situation from a position right out of the Sun/Earth orbital plane ( say well above one of the Sun's poles ), the craft is spiralling outwards. The Earth however is circling, or 'ellipsing' really.

- the craft then enters the gravity well at the 'rear nearside' of the Earth, and is pulled in toward it. This is a kinetic-energy/speed/momentum boost to the craft at the expense of retarding the Earth's motion around the Sun. Given the relative masses of Earth and craft, a large speed change to the craft corresponds to a miniscule change for the Earth.

- the planet is being pulled toward the Sun however, and acts to deflect the Earth inwards ( from where it would have been in the Sun's absence ). If the craft passes by in the direction as specified above the Earth is effectively pulled away from the craft and it thus rises out of Earth's gravity well and proceeds onwards.

Careful spotters will note that the craft also ought be affected by the Sun too, so how can the above be correct?.

Well, when entering the near Earth area initially the craft, while descending into the Earth's well was also ascending the Sun's well. Gravity linearly superposes, so you can think of the Earth's region as a dip in the overall rising well ( going outwards ) of the Sun. Because of the line of approach, that entry into the Earth's well gave an assist to rise out of the Sun's further than otherwise possible compared to the case of the Earth not being there. And on moving past and away from the Earth, after closest approach, the craft is less accelerated toward the Sun than the Earth is, as it is slightly further out in the radial direction. Compare that with the approach phase, when the craft had a greater Sunward acceleration due to the Sun, than the Earth did due to the Sun. So when rising out of the Earth's well on egress it will lose some kinetic energy, but not as much as it gained when going in.

A good visual is the rubber sheet one - the big Sun in the middle weighing the sheet down. But the depression produced by the Earth is a travelling one, and a clever little guy ( spacecraft ) can arrange matters to be pulled along for a short while by coming from the rear. Those of us familiar with arcuate travel on skating rinks ( remember James Caan & 'Rollerball' ? ), or 'drafting' on the banked turns in NASCAR, will see the analogy.

The argument relies on the asymmetry of the entry into vs exit out of the craft's encounter with Earth, because of the craft's differing relations to the Sun and Earth in each phase. This is in turn due to the choice of behind/nearside approach and ahead/farside egress. You could, of course, get other trajectories with different results - indeed a braking effect on the craft's motion around the Sun for that matter.

Now with the quadstar system mentioned, the outer stars are outer because they have had such boost(s) of a like nature. The price is that the inner pair move closer together, as they bleed momentum to the outer pair. Unlike the Earth/spacecraft pair the stars are of similiar mass magnitude and all the participants really alter the other's subsequent courses quite significantly.

This is a general tendency of many planar orbiting systems where the mass moving inward gives momentum to that mass going outward.

Accretion disks for instance. There encounters ( direct collisions in fact ) between material within it give inward flows toward some fate in the centre, and momentum ( angular if you like ) carried outwards.

Jupiter is posited to be the 'vacuum cleaner' of the solar system. Not just by direct collision ( Shoemaker/Levy ) but by gravity assists which flick inwards ( to other future collisions ) or outright ejection from the solar system - if the transferred energy is enough to give escape velocity from the Sun.

Cheers, Mike.

Ah, of course, a kind of natural gravitational slingshot maneuver, that makes sense. I was wondering if it had something to do with rotation, frame dragging, and the energy in the GWs (as with the well known binary system with PSR 1913+16, where orbital energy is converted to gravitational radiation, I was wondering how energy from the more rapidly rotating pair in the quad system might push the other pair farther out, but I see that's not the case, thanks Mike!)