3 ms·

Something to keep in mind is that gravitational waves are linearized solutions to Einstein equations. That is, they can only be meaningfully defined far away fr

by dsqrt 10y ago

Something to keep in mind is that gravitational waves are linearized solutions to Einstein equations. That is, they can only be meaningfully defined far away from those sources. What happens close to the black holes cannot be described in terms of waves. You should not think of the gravitational waves as being emitted directly by the black holes. Instead what happens is that the black holes distort spacetime in complex non-linear ways, which turn into gravitational waves at large distances (hundreds of Schwarzschild radii). As such, the time dilation imprinted in the waves depends on the motion of the "center of mass of the binary" and the cosmological redshift.

bobbles 10y ago
I keep trying to picture how this would work using a 'drain in a bathtub' image in my head where the water rushing down the plug is like a black hole pulling things in with gravity. Is there any way thinking like that I can get an approximate idea of what the gravitational wave would be in that scenario?
- ars 10y ago
  It's not like a bathtub. (And let's ignore time dilation.) Imagine you have a large mass (sun) moving in a straight line, and an object (sensor) 1 light minute from that mass. The gravity from the sun takes 1 light minute to reach the sensor - that would mean that the sensor is attracted to where the sun was 1 minute ago. That can't work - it violates all sorts of conservation laws. Instead what happens is that the gravitational force itself is ALSO moving in a straight line! So when the gravity from the sun reaches the sensor it attracts the sensor to where the sun is now because both the sun, and the gravitational force, are moving together. This works out very nicely. But what happens if the sun is moving in a circle? Otherwise known as accelerating? The gravitational force can't know what the sun will do in the future (that it will move). So as the sun moves it forces the gravitational force to change - before the force was moving in direction a, now it's moving in direction b. This change in the gravitational force is known as a gravitational wave. This wave, because it is accelerating, has the ability to impart change in other objects, otherwise known as imparting energy. So gravitational waves can carry energy! Potentially huge amounts of it. (And since they carry energy, they themself have mass, and therefor gravity, but these second-order effects as they are called, are too confusing, and weak, and everyone ignores them.) Back to the black hole - as it orbits the other black hole (as they orbit each other), they change direction very very rapidly, causing huge gravitational waves - the waves steal energy from the orbit, causing the two black holes to fall into each other with smaller and smaller orbits, i.e. a spiral. My problem is this: Near a black hole time dilation is enormous, huge gravity, plus huge velocity. So to an outside observer the black holes appear basically frozen and don't move. If they don't move they don't make gravitational waves, so we should detect nothing. I have no answer to this question.
  - raattgift 10y ago
    FWIW, for supermassive black holes, the curvature at the horizon can be arbitrarily flat.
huuu 10y ago
Does this work the same as it does with waves on the ocean? The waves on the ocean are also turbulent distortions by the wind which pack together was waves (a group of 14 waves with the 7th as the highest and all waves after the 7th barely noticeable). It seems that the 7th spike measured at LIGO is also the highest. Maybe the grouping of turbulent distortions as waves is something universal?

by dsqrt 10y ago

bobbles 10y ago

I keep trying to picture how this would work using a 'drain in a bathtub' image in my head where the water rushing down the plug is like a black hole pulling things in with gravity. Is there any way thinking like that I can get an approximate idea of what the gravitational wave would be in that scenario?

ars 10y ago
It's not like a bathtub. (And let's ignore time dilation.) Imagine you have a large mass (sun) moving in a straight line, and an object (sensor) 1 light minute from that mass. The gravity from the sun takes 1 light minute to reach the sensor - that would mean that the sensor is attracted to where the sun was 1 minute ago. That can't work - it violates all sorts of conservation laws. Instead what happens is that the gravitational force itself is ALSO moving in a straight line! So when the gravity from the sun reaches the sensor it attracts the sensor to where the sun is now because both the sun, and the gravitational force, are moving together. This works out very nicely. But what happens if the sun is moving in a circle? Otherwise known as accelerating? The gravitational force can't know what the sun will do in the future (that it will move). So as the sun moves it forces the gravitational force to change - before the force was moving in direction a, now it's moving in direction b. This change in the gravitational force is known as a gravitational wave. This wave, because it is accelerating, has the ability to impart change in other objects, otherwise known as imparting energy. So gravitational waves can carry energy! Potentially huge amounts of it. (And since they carry energy, they themself have mass, and therefor gravity, but these second-order effects as they are called, are too confusing, and weak, and everyone ignores them.) Back to the black hole - as it orbits the other black hole (as they orbit each other), they change direction very very rapidly, causing huge gravitational waves - the waves steal energy from the orbit, causing the two black holes to fall into each other with smaller and smaller orbits, i.e. a spiral. My problem is this: Near a black hole time dilation is enormous, huge gravity, plus huge velocity. So to an outside observer the black holes appear basically frozen and don't move. If they don't move they don't make gravitational waves, so we should detect nothing. I have no answer to this question.
- raattgift 10y ago
  FWIW, for supermassive black holes, the curvature at the horizon can be arbitrarily flat.

huuu 10y ago

Does this work the same as it does with waves on the ocean? The waves on the ocean are also turbulent distortions by the wind which pack together was waves (a group of 14 waves with the 7th as the highest and all waves after the 7th barely noticeable). It seems that the 7th spike measured at LIGO is also the highest. Maybe the grouping of turbulent distortions as waves is something universal?