Breaking Black Holes.

[Bear]

In the news I noticed a news story about LIGO (& VIRGO) detecting a very large black hole collision, resulting in an intermediate-mass black hole of 142 solar masses.

The Black Holes that collided were said to have 85 solar masses and 66 solar masses, making their combined mass 151 solar solar masses.  And nine solar masses were converted directly into energy, in the form of gravitational waves, spreading across galaxies to be detected by some smart monkeys seven billion years later.

Now, purely aside from the fact that that's a staggering amount of energy to be released all at once, in any form, it is equally staggering, to me at least, that that energy came directly from inside these colliding black holes.  Nine solar masses worth of matter/energy once contained inside these event horizons, is now outside these event horizons.  The containment of the event horizon somehow failed.

And this failure is something we already know about.  We have documented a lot of cases in which up to 5% of the matter being combined is lost as energy.

The spacetime contingent on a rotating gravitational field is also, to some extent, rotating.  And we have a chaotic situation here because there are three possible rotations to consider.  Each of the BH's individually, and the field generated mutually by their orbit around one another.  There are cases where this can result in 'anisotropic emission of gravitational radiation' which sure as heck sounds like some kind of potentially detectable force.  How much do we imagine there might be?  Do these 'anisotropic emissions' have any large-scale expected statistical effect on the expansion of space or the rotation of galaxies?

We know that the combined area of the event horizons must never decrease in a collision, but surface-area-to-mass ratios being what they are, that doesn't mean the  combined mass can never decrease.  

Here's another thought;  Since black hole mergers release staggering amounts of energy in the form of gravitational radiation, doesn't this energy, like the electromagnetic energy traversing a region, become a form of 'mass' for purposes of measuring the mass density of that region?  IOW, isn't every attempt to account for the mass of a galaxy going to come up short if it doesn't account for the energy (at e=mc^2) of the electromagnetic and gravitational radiation traversing that galaxy?  I've seen models that try to estimate the total electromagnetic energy; I don't think I've ever seen one that tries to estimate the total Gravity-wave energy. 

I don't suppose it accounts for the entirety of "missing matter" that gives rise to the Dark Matter theory; it's just that Dark Matter is a kind of modern phlogiston - implied by our model but never confirmed to exist - and I feel like we really need to account for *EVERYTHING* before we resort to such desperate measures as something we've never directly detected except by the one phenomenon for which we invoke it as explanation, because it may turn out that our model's just wrong.

[stevebowers]

It doesn't matter if the mass-energy of a black hole is inside it or outside (for instance if it is emitted as radiation following a merger). Both forms of mass-energy create the same amount of gravity.

Indeed, if a pair of black holes lose energy by merging, that energy radiates away at or nearly at the speed of light (depending on what form the radiation takes), so relocates to another part of the universe. By radiating away mass-energy, a pair of black holes could cause the local mass-energy of a galaxy to become reduced.

[Bear]

There seems to be a nonlinearity in that the larger the black holes merging, the greater the percentage of their mass released as energy.

Or, if I'm reading correctly - the greater the combined mass, the greater the *maximum* loss ratio, subject to a bound of preserving the area of event horizon. But in any given collision, depending on spins and angles, some smaller proportion is actually lost. So we had detected plenty of mergers in which up to 5% of the mass/energy was radiated away, but in the biggest event we've ever detected, 9/156 or almost 6% was radiated away - a proportion impossible for smaller crashes. But a given collision of identical-size masses might radiate away a little more, or far less.

The idea of gravitational energy as energy which, in and of itself, has gravitational mass, is a new one, and a bit of a mind-bender for me. The mass of a given stretch of "empty" space, aside from the stray hydrogen atoms, dust, etc, must include the mass of the energy traversing that space. Which we can't even see or detect in any other way, until that energy hits something and causes work to be done. So we can look out there at some random region in the Bootes void, or whatever, that completely lacks conventional matter - but if for whatever reason an enormous amount of energy expressed in gravity waves (or photons) completely invisible to us is traversing it, then any mass nearby will be affected as though that region has mass.

And when that happens, the energy it takes to move that gravitationally-attracted mass is somehow subtracted from the radiation that's traversing the region?

At the risk of heresy, doesn't that cause red shift? If light, as energy, causes gravitational effects as though it were mass - and that gravity affects things near its path, however small the effect in total as it zips by at light speed, doesn't the energy exerting a force on those affected things get deducted from the energy of the light? And wouldn't that reduction in energy take the form of redshift? And wouldn't it, in the mean and on very large scales, be proportional to the distance traveled by that light?

So red shift isn't just the doppler effect of relative movement plus the 'stretching' effect of the expansion of spacetime, but also the energy the radiation has lost by gravitationally interacting with, well, everything, as it traverses the universe?

Has that been accounted for in the conflict concerning the hubble constant and the age of the universe? Because if the hubble constant includes a term for energy loss due to gravitational interaction, then finding a conflict when it's interpreted solely as the rate of expansion of the universe is not a huge anomaly. It's the expected result.

[stevebowers]

Even Newton realised that the universe must have expanded somehow, for some unknown reason, and that this expansion works against the contraction caused by the gravity in the Universe. So these factors have been part of the equation for a long time. As far as I can recall, the amount of gravity caused by radiated energy in transit is nearly negligible, but it has been accounted for.

[Bear]

I must be expressing this badly...

Newton could not possibly have had the remotest beginnings of this in his model.
First, E=mc2 was not known. So he had no reason to even suspect that energy had mass. He was familiar with light and knew that it transmitted energy - heat for example. But missing the idea that energy has mass means he could not possibly have even attempted to calculate how much mass the universe had in terms that include the mass-energy of the electromagnetic radiation.

As Newton understood gravity it was a simple force. Proportional to the sum of masses and inversely proportional to the separating distance. That is not a formulation that allows energy to be expressed as gravity, thus even if you're wise to E=mc2, Newtonian gravity is massless.

I'm not talking about Newton's gravity. I'm talking about Einstein's.

Specifically, about gravity waves. In the same way you can take a static force like magnetism and make it oscillate, creating electromagnetic energy, black hole mergers take a static force like gravity and make it oscillate creating gravity-wave energy.

A static force doesn't have energy, and therefore the force itself doesn't have mass. Gravity waves are different, because gravity waves do have energy. And since Einstein worked out E=mc2, we know that means they also have mass.

And so the mass of the universe includes the energy expressed as gravity waves, in exactly the same way it includes the energy expressed as light waves.

[stevebowers]

Yes it does, and gravity waves are even more negligible than light waves as a source of mass-energy and gravity.

You can't explain dark matter using either lightwaves or gravity waves, because they both constitute a small fraction of the mass-energy of the universe, and they are not local, because they continually propagate away from their source. Dark matter needs to stay where it is so that it can form halos.

[Drashner1]

Specifically, about gravity waves.  In the same way you can take a static force like magnetism and make it oscillate, creating electromagnetic energy, black hole mergers take a static force like gravity and make it oscillate creating gravity-wave energy.  

A static force doesn't have energy, and therefore the force itself doesn't have mass.  Gravity waves are different, because gravity waves do have energy.  And since Einstein worked out E=mc2, we know that means they also have mass.

And so the mass of the universe includes the energy expressed as gravity waves, in exactly the same way it includes the energy expressed as light waves.

Erm. I don't think it's accurate to say gravity waves have mass in and of themselves any more than it's accurate to say that light has mass. Matter and energy are interchangeable and can be neither truly created or destroyed, just converted. Stars shining convert matter into energy, they don't create energy out of nowhere. Similarly, black hole mergers or other events that generate large amounts of gravity waves are converting the mass of the black holes or some other form of mass-energy into gravity waves, not creating them out of nothing.

As far as the contribution of gravity waves (and light) to the total mass of the universe -

While 9 solar masses of gravity wave energy is impressive by the standards of our current civ, it's really utterly insignificant when compared to the hundreds of billions to a trillion solar masses of a galaxy like the MW or Andromeda. Similarly, while the amount of EM radiation produced by a star (of a galaxy) is huge by the standards of our RL civ, the real question is what it works out to as a percentage of the total mass of all the stars (and possibly nebula and to a tiny degree the planets orbiting the stars - although the last is so insignificant as to likely be something we can ignore at least for a first approximation).

As far as taking even a first shot at figuring out how much mass-energy is tied up in radiation zipping back and forth across the universe since the Big Bang - it should be possible to produce at least a rough initial number and then compare that against the estimated mass of dark matter/energy believed to exist in the universe based on current observations. Let's see...

Per Wikipedia, the estimated annual energy output of the Sun = 1.2e34J
Multiply that by the age of the sun - ~ 5 billion years
Multiply that by the estimated mass of the MW galaxy in solar masses. Assume that each solar mass is a star like the sun (obviously it's not, but this is a rough first approximation).
Multiply by how much older the universe is than the Sun - Maybe x3? or x2.5?
Multiply by the estimated number of galaxies in the universe
Possibly multiply by some value for a fudge factor to allow for additional galaxies we haven't found yet and/or things like gravity waves. Maybe just up the number from everything before by 1-2 orders of magnitude to be 'conservative'.

Take the resulting value and run it backward through E=mc2 to get how much mass that adds up to.

If the result is only a tiny fraction of the estimate mass or mass-energy of the universe, then it seems unlikely that radiant energy - in whatever form - is contributing in any significant way to the missing mass in the universe.

Interestingly enough this Wikipedia page - LINK -also lists the total mass-energy of the MW and the Virgo Supercluster including dark matter and dark energy. Not sure if that might impact anything but it might provide a basis of comparison somewhere along the way.

Just some thoughts,

Todd

[Bear]

I wasn't supposing it accounted for a significant fraction - until you get down to the level of the difference between hubble constant and microwave background energy estimate of the universe's age. They're off by a tiny "insignificant" fraction from each other. And this might be something that affects them unequally.