# Can a gravitational wave kill you?

1. Feb 23, 2016

### Idunno

Specifically, I am wondering if the stretching that a gravitational wave does to you as it passes through you, if the stretching was big enough (say half a meter), could it rip you apart, or does it not work that way?

I know that gravitational waves that go through Earth do not get this big, they only increase the distance between your head and your feet by a very small amount, but supposing that the amount was much much larger, would it separate your head from your feet, tearing you apart in your midsection? Or would you not even notice, as perhaps the bonds between atoms stay intact, even though spacetime is doing weird stuff?

I suppose that if you die from spaghettification by falling into a black hole, then extreme gravitaiton waves will tear you apart too... ??

Further, I read this black hole merger that LIGO detected released the equivalent of three solar masses worth of energy as gravitational waves in about half a second? Assuming someone was close by, in a nearby spaceship, when that happened - what would happen to the person? Is there much radiation emitted that would fry them? When you're that close to three suns worth of matter becoming energy as gravitational waves, what happens to you in terms of the gravitation waves passing through you? Would a nearby planet be torn apart?

2. Feb 23, 2016

### Hornbein

Look at the so-called sticky bead argument. I'm no expert, but gravitational waves can transfer energy to material things. I think you would get very very hot anywhere near that event.

3. Feb 23, 2016

### pervect

Staff Emeritus
To expand on this with a wiki reference: https://en.wikipedia.org/w/index.php?title=Sticky_bead_argument&oldid=704781521
So gravitational waves can have physical effects that transfer energy, the remaining issue (that's not terribly clear) is what sort of strain level (probably dependent on the frequency as well) would be required to injure or kill somoene.

Probably a good first step would be to take the gravitational plane wave metric and convert it to Fermi normal coordinates to aid in its physical interpretation. The biomechanical aspects of what sort of stretching would be needed to be fatal and the resonance effects of the body if any are a bit more involved.

Probably a better way is just to compute the Riemann tensor, and interpret it as a tidal force. I might do that if I have some time.

Last edited: Feb 23, 2016
4. Feb 23, 2016

### bcrowell

Staff Emeritus
If you were close enough to a black hole merger to feel any physical sensation at all from gravitational waves, you'd probably already have been annihilated by other radiation such as gamma rays, long before the final Chirp of Doom.

5. Feb 23, 2016

### PAllen

Well, you can posit isolated perfectly neutral BH, no matter around. Then no EM radiation. Simply using 1/r scaling, and that the strain observed on earth was one part in 10-21, one gets (in the vicinity of the BH one billion light years away), a strain factor of 104, e.g. a body would be tend to be stretched and compressed by a factor of 10,000. Seems pretty fatal to me. [Trying to emulate Fermi here, with order of magnitude calculations devoid of the details. Of course, his knowledge base was just a little larger than mine ...]

[edit: More important: in the vicinity of the merger, near field effects would be dominant, and they would be many orders of magnitude larger. However, there might be distance such that the GW kill you while the 1/r2 near field effects are not fatal. I would need a little more calculation to determine that, and specifically would need to compute an order of magnitude formula for near field effect. Not difficult, but I am lazy.]

6. Feb 23, 2016

### PAllen

Note, at even one light year away from the merger, GW would already be completely harmless, undetectable without instruments (though pretty crude instruments would suffice).

7. Feb 23, 2016

### pervect

Staff Emeritus
WIthout stumbling through the calculations, I'm basically convinced that one can regard the two force-free test masses as keeping constant coordinates and the metric fluctuationg - which is how the calculations is usually presented, or alternatively as being the result of tidal forces. For something like the response of the human body, though, it's more convenient to use the tidal force approach - which is just the Riemann tensor. If we regard the strain - the change in separation divided by the separation - as being some function h(t) which we can assume for envelope purposes as $h(t) = a \sin \omega t$, then we can (I believe) regard the tidal force (force per meter per kilogram) as the second derivative of h(t), i.e. $\ddot{h}(t) = a \omega^2 \sin \, \omega t$.

How much tidal force is needed to kill someone - say to yank their head off their shoulders - is something I'm not sure of. It probably depends on the duration and frequency of the force.

Being a bound system, the head won't move as much as a free test body does, obviously. The neck tends to keep the head in place, the head only comes off when the "force" is high enough that the neck can't keep it on, unlike the test body which is free to move without anything restraining it.

8. Feb 23, 2016

### Fervent Freyja

Wouldn't the head explode before decapitation could happen in this event?

Now, I need try to go and try to shake off this disturbing imagery this post brought forth...

9. Feb 24, 2016

### bcrowell

Staff Emeritus
Sure. I was talking about an actual astrophysical black hole merger. We have a claim that gamma rays were detected coincident in time with the LIGO event, and if that's not a random coincidence, then clearly the gamma rays were very intense. Maybe intense enough to sterilize a big neighborhood of the host galaxy...? It would be interesting to see an order of magnitude estimate.

10. Feb 24, 2016

### Haelfix

I don't see why you would necessarily 'feel' anything at all, its not clear you can seperate the part coming from the emission of the gravitational wave and the regular gravitational field. Surely, you would feel what could be interpreted as tidal forces in the usual way, however I don't really know what one means anymore when one talks about a 'gravitational wave' in the near field regime. As you say, it is not valid to extrapolate the strain all the way back to the horizon, where the linearization breaks down. Moreover, the scale of a human body is absolutely tiny relative to the size of the wavelengths of the purported effect, so I don't know how to interpret or seperate things anymore without access to the linearization approximation.

11. Feb 24, 2016

### RobtO

Not sure how you got 104. If I take the "near" distance to be 1000 km (pretty much right on top of them, if I did the Schwarschild radius correctly), then I get a strain of 10-2. I don't think that would kill you. At the Earth-Sun distance from the merger, you wouldn't even feel it. Am I doing something wrong?

12. Feb 24, 2016

### PAllen

No, I was. I took 1 meter; then realized that was silly, you can't even talk about GW until near field effects are weaker.