# Would we feel the effects of a strong gravitational wave?

1. Mar 15, 2014

### DPRK

So I created an account here just so I could ask this burning question. I keep looking online and through other resources but can't really find any details on this. Apologize if I didn't post on the right forum.

So I know gravitational waves are still being studied and as far as I know any ones that reach us would be exceedingly benign and hard to detect.

But let's say that 2 black holes or 2 neutron stars collided just close enough to the earth to allow some fresh, massive gravitational waves to each us.

Would I be able to feel those gravitational waves? If so, would it be strong enough to kill me? Or would I feel anything weird as they propagate through me? Or would I not even "notice" it? And would everything I see in front of me ripple back and forth as space/time is being rippled?

2. Mar 15, 2014

### WannabeNewton

3. Mar 15, 2014

### bcrowell

Staff Emeritus
I think the OP is asking whether, in theory, there would be an effect, supposing (counterfactually) that it were possible for a wave to arrive with an arbitrarily great strength. The answer is yes. Generically, gravitational waves do interact with matter, and in so doing they can cause vibration and heating.

If the effect was strong enough for you to notice locally, then it would affect your body as well as your surroundings, but in this situation it would also be dissipating energy throughout the entire earth, and I think it would probably make the planet uninhabitable. Whether my guess is right depends on things like the frequency of the wave and the response of various objects to waves of that frequency. These waves typically have extremely low frequencies and therefore extremely long wavelengths, so it may be that the amplitude that would be sufficient to destroy the biosphere would still not cause any immediate, locally observable effects.

For waves produced by the kind of collision you're talking about, I think we'd also be killed by the gamma rays, maybe so quickly that we wouldn't have time to perceive the gravitational effects.

4. Mar 16, 2014

### DPRK

Thanks for the answers so far, folks! Although I forgot to mention in my original post - Let's assume it's a magical black hole or neutron star collision and no gamma rays or other undesirable effects would be created - only gravitational waves, for the sake of my question.

Anyone else has any input on this???

5. Mar 16, 2014

### pervect

Staff Emeritus
I vaguely recall hearing that gravitational waves could kill a person near a binary inspiral. But I don't have much solid information.

http://relativity.livingreviews.org/open?pubNo=lrr-2009-2&amp;page=articlesu8.html [Broken]
goes through some formulae, which I haven' worked out. But it's clearly possible for gravitational waves to carry enormous emounts of energy.

The following equations might be useful:

Last edited by a moderator: May 6, 2017
6. Mar 17, 2014

### Staff: Mentor

Shouldn't we expect shearing stress? Tidal forces?

Strong wave means strong gradient, that in turn means accelerating different parts of a body in different directions at the same time. If these forces are stronger than the mechanical resistance of the body, the only result I can think of is a bloody mess.

Or am I wrong?

7. Mar 17, 2014

### HomogenousCow

i thinkit would depend on the size of the body and the wavelength of the wave.
An object much smaller than the wavelength would probably not feel much, however an object spanning several wave lengths would probably be pulled apart.

8. Mar 17, 2014

### Staff: Mentor

That's already covered by what I wrote - IF the stresses produced (and they are a function of the wavelength/amplitude) are stronger than the body can sustain, it will get broken.

Unless there is more to it.

9. Mar 17, 2014

### pervect

Staff Emeritus
The textbook analysis covers cases where the wavelength is much longer than the object (not the high frequency case). Apparently this is the case of interest (not really a surprise).

Some of the approximations used may need to be checked for the case under consideration, but for a first go-around we can assume the test particle follows geodesic motion in the proper reference frame. (If the wave is too strong, we may need to use the TT gauge - but at the moment I'm looking for the easiest possible reasonable approximation). The results for the proper reference frame approach are: (MTW pg 1010)

$$\frac{d^2 x}{dt^2} = -R_{x0x0}\,x - R_{x0y0}\,y = \frac{1}{2} \left( \ddot{A}_{+}x + \ddot{A}_{x}y \right)$$
$$\frac{d^2 y}{dt^2} = -R_{y0x0}\,x - R_{y0y0}\,y = \frac{1}{2} \left( -\ddot{A}_{+}y+ \ddot{A}_{x}x \right)$$

$d^2x / dt^2$ is the x acceleration of a free particle, for a constrained particle its the driving gravitational "force per unit mass" in the x direction due to the gravity wave

$d^2 y/ dt^2$ is the same, but in the y direction

the R's are the components of the Riemann curvature tensor (tidal forces), which we can ignore if unfamilar and focus instead on the A's (and if you're familiar, no more needs be said than they're the components of the Riemann).

$A_+$ and $A_x$ are the amplitudes of the two components of the gravitational wave. In the frequency domain they would be the amplitude of sine-waves. In the time domain they'd be in general arbitrary functions of time. The double dot over the A's represents taking their second derivative.

We also have the effective gravitational wave energy density expression as:
$$\frac{1}{16 \pi} \left<\dot{A_+}^2 + \dot{A_x}^2 \right>_{time average}$$

I'd guess offhand that if we orient the human body in the y direction, the issue would be what sort of head-foot tidal force the human body could stand for how long before the head comes off (or other similar damage is done) this would be mainly due to $- \frac{1}{2} \ddot{A}_{+}y$ and the time period would be a half-cycle.

What's noticably needed is some idea of the timescales and waveshapes for the amplitudes for the two components of A, given that we could probably find the amplitude for the components from the energy output.

10. Mar 18, 2014

### snorkack

It is possible to be near a source.
Seismic waves can be strong enough to notice locally, they dissipate energy throughout the entire Earth, yet they do not make the planet uninhabitable.
A pair of 1 solar mass black holes at 20 km distance would orbit each other 918 times per second and therefore emit gravity waves at 1836 Hz. Perfectly audible if strong enough.
The bulk of energy is emitted at high frequencies, over a very short period of time.
Not if both are black holes.
They have no hair, and no way of interacting with electromagnetic field. Even if they were heavily charged Nordström or Newman black holes (highly unlikely), they would emit low frequency radio waves (in the same audible range as gravitational ways, up to hectoherzes/hundreds of km wavelength).

11. Mar 20, 2014

### Bill_K

The nearest black hole is 7800 ly away and the nearest neutron star is 250 ly away.

Totally different effect. Seismic waves originate at a point or linear fracture and take some time to propagate, spread out and dissipate, whereas a gravitational wave would affect the entire Earth simultaneously. The tsunamis that can be produced by an earthquake do a pretty good job of devastation over a large area.

The OP asked about a collision, not a decaying orbit. A decaying orbit would emit energy gradually, while a collision releases its entire energy in one millisecond burst.

Black holes are invariably surrounded by matter, such as accretion disks, and the collision of this matter would produce gamma rays.

12. Mar 21, 2014

### snorkack

The nearest we know.
The nearest known neutron dwarfs are Magnificent 7. Yet they are all supposed to be less than a million year old.

Where are all the neutron stars that are 1 milliard or 5 milliard or 13 milliard years old?

Probably they are so cool and dim that we cannot see them.
And they are around... somewhere.
And the decaying orbit also releases most of its energy in one millisecond burst... with frequency in kilohertz region, where ear is most sensitive.
A man can be burned and ripped apart by sound... but there is a huge range of sound intensities where sound is heard without actually hurting the man.

So. Say that a 2 kHz gravity wave hits a man, assuming the man is insulated from propagation of sound waves generated elsewhere.
The millisecond burst of 2 kHz has gravitational wave wavelength in free space of 150 km. But if it deforms the man, it should create sound waves with wavelength, in soft tissues, of about 75 cm. Note that the whole body is deformed effectively simultaneously - it is the later propagation, if any, of the deformation that takes time.

So. After the burst of gravity wave has passed in a few milliseconds, are the flesh and bone returned to their initial position and state of rest, with the only trace being the irritation of inner ear from the few milliseconds of deformed state? Or are flesh and bone left oscillating with respect to each other and propagating the now mechanical waves around the body, including to the ear?
Um, why invariably? Many neutron stars we know do not have accretion discs - pulsars, Magnificent Seven etc.

Just how can you rule out the existence of black holes with very little in the way of accretion disc?

13. Mar 21, 2014

### pervect

Staff Emeritus
Even if there isn't a neutron star or black hole close enough, I think the question is interesting even if the event can't happen.

Though I must admit I would be interested in an inspiral scenario (or an off-center collision which results in an inspiral by having a neutron star and/or black hole pass within the photon sphere of a black hole) because it seems more likely than a direct collision.

I've got almost enough data to attempt to answer the question but not quite. Additionally I'm not sure what sort of tidal G forces the human body can stand on millisecond time scales, I'd say at a rough guess that 100g differential accross the body would be the right order of magnitude for fatality.