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.
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.