I realize that I've never really considered what it would be like to be 'near' (say a few 10's of thousands of light years away) from an event like this. With all that energy, at what level would it pulverize a planetary body?
http://www.businessinsider.com/what-gravitational-wave-feels...
http://www.scottaaronson.com/blog/?p=2651
The alternative take is that LIGO's detectors are unfathomably sensitive, detecting when its ~4km arms stretch by just 10^-19 meters. That's a 10,000th the width of a proton, where the proton is just a 100,000th the width of an atom, and the atom is about a 1,000,000th the width of a hair.
Wow. Hearing the sensitivity described in those terms is absolutely mind-blowing.
"To understand how sensitive the LIGO is, imagine each arm stretched out as far as the sun. Even if we had the resources to build an object this big, we still would not be able to get people to understand this intuitively at all."
So from the article:
> Black holes [merging] produce gravitational waves but not light.
So really, if you were orbiting such a pair of about-to-merge black holes, the gravitational waves produced by the merger would cause just nm-scale fluctuations?
Also, 1 AU seems awfully close to a pair of orbiting ~25 solar-mass black holes. I skimmed the paper, and didn't see anything about how the orbital distance evolved, leading up to the merger. One could probably calculate that from the mass and spin estimates, it's over my head. So maybe, at 1 AU, the about-to-merge black holes would look effectively like a point mass. Anyone want to venture a guess?
https://en.wikipedia.org/wiki/Accretion_disk
A 25 solar-mass BH is about 150km in diameter, and the gravitational waves emitted won't be appreciable until the two BHs had spiraled inward to a separation of a few hundred km. You would need to be roughly 1,000 km away to experience a 1% strain during the merger
https://physics.stackexchange.com/questions/235285/how-stron...
I don't think spin is important at the order-of-magnitude level (for naturally occuring BHs).
To make things dangerous I reckon you'll need to have a strain on the order of 1, and since strain is inversely proportional to distance that would give a distance of 10^-11 ly, or around 100 km. Which is not a 'safe' distance to a black hole in any scenario.
You'll need to simulate the black hole merger to figure out where exactly it would be unsafe, but it looks like it would be distance that's pretty unsafe even without the merger.
In an otherwise expanding vacuum solution, the radiated momentum just propagates to future null infinity. Since we have other matter in our universe, the gravitational radiation can donate some of the original momentum to matter outside our chosen region, causing bits of matter along a lightlike path to move a small amount (or if you want to switch to an energy picture, ordinary matter outside our chosen region will become a tiny bit hotter upon feeling the gravitational radiation).
Although the amount of stress-energy-momentum radiated out of our region comprising the inspirallers is enormous (and at peak is so brief that the power is almost unimaginably enormous), the coupling of gravitational radiation to matter is extremely weak, so there will be very little scattering or absorption by matter outside the region. Consequently, most of the momentum crossing to the outside of our Schwarzschild-like boundary around the merger will still go to future null infinity.
It's this weak coupling that leads to your intuition about a human having to be very close to the merger itself in order to feel anything noticeable from the gravitational radiation.
By comparison one would expect balding to happen so that we recover a no-hair state from the merged BH, and there are decent reasons to expect more than gravitational radiation to be shed during balding. Additionally the individual BHs may have a lot of energetic particles entrained around them, and much of that will be moving on geodesics conducive to extremely high energy interactions (think of a pair of BHs whose rotational axes are parallel but with each BH dragging its accretion disc in the opposite CW/CCW direction, and we can add in extreme inverse Compton scattering just prior to contact as the photon rings around each BH interact relativistically with charged particles around the other). And of course this picture is likely to be much more dramatic in the case of an NS-BH merger.
Another way of thinking about this is that the build-up of momentum due to gravitational interactions is typically slow (and steady) but may have no upper limit, and that's the source of danger rather than a quick (and briefly high amplitude) gravitational interaction that doesn't take away more than a few percent of the built-up momentum of the matter at and near the source of the burst of gravitational radiation.
A human being close enough to the merger to feel the effects of gravitational radiation is thus likely to be feeling an awful lot more from excitations in the non-gravitational fields, or alternatively, the nearby human being is at risk of collision with ultrarelativistic (i.e., ultra-high-momentum) matter.
Unfortunately, for gravitational waves this is trivial, since they are vacuum--so T^{\mu\nu} itself is zero, and its covariant divergence is trivially zero.
There are ways to mathematically compute the "energy carried away by gravitational waves" from an isolated system like a black hole merger, but you have to use global methods to do it. For example, you can compare the ADM mass with the Bondi mass of the system; the latter decreases over time as GWs carry energy away, while the former stays the same.
On that last point, the latter (ADM) always stays the same, doesn't it? In early spacelike slices when the binary system is radiating basically nothing, the quantities you will find in the GWs in later slices are just clustered around the black holes.
Mass in General Relativity will give anyone a headache; I was trying to side-step that without being caught shuffling gravitational radiation off to the source side using pseudotensors. :-)
On spacetimes where it is defined, yes, I believe it does.
100km from the horizon.
"Distance" from the singularity does not actually make sense; the singularity is best thought of as a moment of time, not a place in space.
Sure, if you're a pansy. HOLD MY BEER!
Your buddy could be holding your beer for a very long time though, because gravitational time dilation at a given small distance outside the horizon increases with the mass of the black hole, and it will take you more of your own proper time to move through the region near a very large black hole than through the region near a small one.
I am not an astrophysicist, but was also wondering the same thing.
Gravitational waves move at the speed of light. Here is a graph showing the wavelength of gravitational waves from various sources
http://www.tapir.caltech.edu/~teviet/Waves/gwave_spectrum.ht...
The Ligo sensitivity range is about 10^6 meters. The speed of light is about 3*10^8 m/s. So peak to trough a few hundred per second. Much higher frequency than earthquake.
(Again, assuming an amplitude somewhere between perceptible and lethal, and assuming you're protected from other almost certainly lethal forms of radiation at that distance)
Edit: A sibling comment has a physics exchange link to a proper answer
https://www.youtube.com/watch?v=QyDcTbR-kEA
If you turn it up real loud and press your hand against your speaker maybe it would be some idea of what it would feel like.
The main issue is that the gravitational waves only couple with you (or rather your microscopic bits) very slightly.
If you get close enough (~ 10^2-10^4 GW wavelengths depending on the system) then you have several sensory systems that in principle could -- with some awkward assumptions about signal transduction in the middle of some even more awkward changes of gauge -- produce something noticeable. The principal problem is that while a cell at one end of your body may move noticeably compared to a cell at the other end of your body from the perspective of someone watching a cell in the middle of your body, these three cells don't move around much with respect to their neighbouring cells, and the "guts" of each cell move around even less with respect to the cellular membranes. Some senses rely on groups of cells moving with respect to one another; some rely on intracellular activity alone.
There is the possibility of a small slosh in your inner ears, where there are some structures that are exquisitely responsive to small strains; that might make you nauseous, or it might trigger an episode of tinnitus. It might also go unnoticed.
That close to the merger you're likely to be vaporized by non-gravitational radiation, though. ( https://news.ycombinator.com/item?id=15352994 )
Finally I think intuitions break down before you get to the near field regime, and nobody can really tell you what to expect within a couple of wavelengths of the source of the gravitational radiation even some time before the merger. Certainly linearized gravity fails to produce gravitational waves thanks to an explosion of non-linearities. You can only really say that the dynamical spacetime is even more full of distortions in that regime. Unfortunately if we had a purely linear gravity in reality (i.e., if gravity wasn't itself a source of gravity), it is also the regime where one would expect several human senses would be obviously stimulated.
The fundamental nature of the force that rips you apart during spaghettification is exactly the same. And you would definitely feel that one.
It all boils down to how strong the distortion is at one extreme of your body, versus the opposite extreme. If it's about the same, you won't feel it. If the difference is sizable, you would feel it to some extent. If it's very large, it's a meat grinder.