Gravity exerted by a fast moving object versus stationary object?

[PeterDonis]

When approaching:
Objects gain momentum towards each other.

When the light has disappeared:

The momentum of the black hole =
The momentum of the black hole at time t + the momentum of the light at time t
(t can be chosen freely)

Once again, you are using a coordinate chart in which you can't assume that conservation of momentum works. Unless you have done the math, you can't just help yourself to the above statements. A coordinate chart in which a black hole is moving does *not* work like a standard inertial frame in SR, nor does it work like standard Schwarzschild coordinates in GR.

Velocity change of the black hole = momentum change / mass

Even if the coordinates you are using did work like standard coordinates, this would not be true; relativistic momentum is not mass times velocity. You really need to do some math on this problem.

 

[Naty1]

Quote by dipole
I think "relativistic mass" is a concept which should be avoided. It's better to think in terms of energy and to understand that energy is a source of gravitation, so an object moving with a lot of kinetic energy is going to have a stronger gravitational field.

ok on the first part, but the rest depends on your definition of gravity; such an increase in KE is not sourced from the Einstein stress energy momentum tensor...the source of gravity as usually defined...which is in the rest frame of the mass.

Hmmm... a faster moving object, with more KE, say going past a large gravitating source such as a planet, would be deflected LESS than a similar object with lower velocity...?

Anyway, if the objects were two space ships, each would measure the planet as having the different KE relative to them...