Gravity & Light: Does Gravitational Field Slow Down?

[Pizer]

Something I've been wondering about with gravity and light:

Assuming the speed of gravity is c, does an objects gravitational field have to slow down as light it emits slows down? i.e. as an extreme example, if an object is falling towards a black hole, any light it emits takes longer and longer to reach an observer as it nears the event horizon, so it's gravitational field should take longer and longer [presumably equally as long] to reach the observer as well.

If that is true, can a black hole's gravitational pull ever increase? Would it be possible to have the object's (delayed) gravitational field exist near the event horizon, and have the black hole's gravity increase?

Or is it possible that an objects gravitational field can exceed its light cone?

 

[cosmik debris]

The speed of light measured in a local intertial frame is c, light does not slow down in the scenario you mentioned it red shifts.

 

[JesseM]

Something I've been wondering about with gravity and light:

Assuming the speed of gravity is c, does an objects gravitational field have to slow down as light it emits slows down? i.e. as an extreme example, if an object is falling towards a black hole, any light it emits takes longer and longer to reach an observer as it nears the event horizon, so it's gravitational field should take longer and longer [presumably equally as long] to reach the observer as well.

Yes, this is basically addressed in this section of the Usenet Physics FAQ:

How does the gravity get out of the black hole?

Purely in terms of general relativity, there is no problem here. The gravity doesn't have to get out of the black hole. General relativity is a local theory, which means that the field at a certain point in spacetime is determined entirely by things going on at places that can communicate with it at speeds less than or equal to c. If a star collapses into a black hole, the gravitational field outside the black hole may be calculated entirely from the properties of the star and its external gravitational field before it becomes a black hole. Just as the light registering late stages in my fall takes longer and longer to get out to you at a large distance, the gravitational consequences of events late in the star's collapse take longer and longer to ripple out to the world at large. In this sense the black hole is a kind of "frozen star": the gravitational field is a fossil field. The same is true of the electromagnetic field that a black hole may possess.

This is the classical answer, they go on to explain that in terms of virtual photons, or "virtual gravitons" if such things exist, the explanation for the black hole's electromagnetic/gravitational field would be a little different.

If that is true, can a black hole's gravitational pull ever increase? Would it be possible to have the object's (delayed) gravitational field exist near the event horizon, and have the black hole's gravity increase?

A BH's gravity does increase as more mass falls into it, so I'd guess that something along the lines of your second suggestion would be the explanation.

One additional complication is that although gravitational waves travel at the speed of light, gravitational waves are only produced by changes in acceleration, in general relativity the gravitational field acts like it can "extrapolate" the motion of objects which are accelerating at a constant rate. So, for example, the Earth is pulled towards Jupiter's current position (in the frame where both are orbiting at approximately constant speed), not the position it was a few minutes ago. Similarly, electromagnetic fields can "extrapolate" the motion of charges which are moving at constant velocity. See this post along with some of the subsequent posts by pervect for more details.

 

[wangyi]

If an object is falling into a black hole, a remote observer will find:
1. beams of light from the object gets redder and redder, i.e. it's wavelength gets longer and longer.
2. if the object send a pulse of light per second according to the clock falling with it,
the observer will find the interval of pulse longer and longer.
I guess you mixed the two together.