Black Hole Collision & Gravitational Waves The Gravitational waves detected by LIGO on 14th September 2015 are attributed to a collision of two black holes, which had been rotating near the speed of light around each other just before the actual collision. The collision happened 1.3 billion years ago, approximately 1.3 billion light-years away and apparently, the energy of the collision exceeded the combined energy of all stars in the observable universe.
LIGO was able to detect the deformation in the fabric of space induced by the gravitational wave caused by the collision, even though the deformation was the magnitude of a fraction of an atomic radius. The reason why the deformation was so &quot;small&quot; by the time the wave had reached planet Earth was due to the relatively large distance of the collision from Earth.
Question: could someone qualified give an estimate of the magnitude of the space-time deformation we would experience on planet Earth, had the collision happened closer to us? I.e. how close would the collision have to happen for the space-time deformation to be millimeters? What about meters? At what magnitude of the deformation would the gravitational wave be dangerous or lethal for humans on planet Earth?
Bryan Greene described the gravitational wave deformation of space-time as a temporary &quot;shrinkage&quot; or &quot;compression&quot; of Earth (and everything on it). Am I right to assume that being compressed by even 1 centimeter could potentially be lethal for all live on Earth?
Part of the answer is easy. The strain measured in that event was about $0.25\times 10^{-21}$. That is an object $1m$ long would be squeezed by $0.25\times 10^{-21} m$ in one direction and stretched by the same amount in the orthogonal direction.
The strain drops off linearly with distance from the black hole, so to achieve a distortion of 1mm in something the size of the Earth (ie about $8\times 10^{-11}$ it would need to be about $5\times 10^{10}$ times closer, so about $0.03$ light years away, or about 2000 AU. Two 30 solar mass plus black holes at that distance would have disrupted the solar system quite a bit before they collided.
To achieve a distortion of 1mm in something the size of a human they would need to be another factor of $6\times 10^6$ closer, so about $\mathrm{30000 km}$, closer than geostationary orbit. In this case we would certainly have bigger problems than the gravity waves.
What I don't know how to calculate is the energy absorbed by the Earth, or a human, in one of these scenarios. I suspect it would not be all that much, at least from the wave.
Added later: this answer gives the total energy passing through the Earth (about 34GJ with the black holes at their current distance) but offers no ideas for how much is absorbed. This would increase according to the inverse square law if the black holes were closer.