How does gravity travel faster than the speed of light in a gravitational field?

[Myslius]

Let's say i state following things:
1) c decreases in gravitational field (Shapiro delay)
2) gravity travels at the speed of light
3) gravity is inner force
4) black holes do have gravitational effect

When light approaches event horizon, it's speed approaches 0, and inside black hole light can't escape. So how gravity can? We are in gravitational field, so gravity propagates faster then c by c + delta c where delta c is c change in gravitational field. Any ideas on the insight?

 

[DrGreg]

It's only changes in gravity that need to travel. When an event horizon forms, the gravity outside it is already there and will remain there without anything having to travel outwards through the horizon.

 

[Myslius]

Well yes. But let's ask how fast does the gravity of the sun reaches earth? It's the same time as the light reaches earth. But light in a presence of massive body travels slower (takes longer or distance increase - no matter what interpretation you prefer)
How gravity can be outside black hole if gravity is inner force and mass lies inside black hole?

 

[DrGreg]

While the Sun just sits there doing nothing, its gravity doesn't change, so nothing needs to travel from Sun to Earth to maintain the constant gravity. The Sun's gravity is already here on the Earth, and has been here ever since the Sun was formed.

Suppose the Sun were to suddenly explode and divide into two pieces that shot off at high speed in opposite directions. That change would change the gravity, and it would take 8 minutes for the change in gravity to reach Earth.

But if gravity is static, nothing changes and nothing needs to travel.

In the case of a black hole, the gravity around it already existed before the event horizon was formed. This gravity was caused by the mass (or more accurately the stress-energy-momentum) of the material that was collapsing to form the black hole. Nothing happened after that to change the gravity, so the gravity is still there. Nothing needs to travel out of the event horizon to maintain a static gravity.

 

[Dale]

let's ask how fast does the gravity of the sun reaches earth? It's the same time as the light reaches earth.

If you mean the static gravitational field this is incorrect. The Earth is attracted towards the sun's current position, not the retarded position. Otherwise the Earth's orbit would not be stable.

 

[Myslius]

DrGreg, BH mass isn't static. If the light reaches an object at the same time as the gravity reaches object, then what if the light can't reach us? The incorrect assumption would be to say that BH that appeared in observable universe has no gravitational force.


Another incorrect assumption would be:
If the light from more massive body takes longer to reach an object, then the gravity does the same, because gravity reaches at the same time as light does. All I'm saying that we see gravity first, and light a little bit later (by shapiro effect), same for gravitational changes.

 

[Dale]

All I'm saying that we see gravity first, and light a little bit later (by shapiro effect), same for gravitational changes.

Please show your derivation from the Einstein field equations.

 

[DrGreg]

DrGreg, BH mass isn't static. If the light reaches an object at the same time as the gravity reaches object, then what if the light can't reach us? The incorrect assumption would be to say that BH that appeared in observable universe has no gravitational force.

Black holes don't just magically appear from nowhere. They occur as a result of matter collapsing. The matter that originally forms a black hole was already there before the event horizon formed, and the gravity due that matter already existed. When the event horizon formed, as far as any distant observer was concerned, there was no change. The gravity before and after was exactly the same. So nothing has to travel outward. The gravity doesn't need to "reach us" if it's already there.

If the black hole grows, the growth comes from more matter falling in from outside. While this matter is still outside it "increases the gravity", and that increase can propagate at the speed of light to distant objects. Once the matter falls through the event horizon, there is no further change to the gravity so nothing further needs to travel to distant objects.

Another incorrect assumption would be:
If the light from more massive body takes longer to reach an object, then the gravity does the same, because gravity reaches at the same time as light does. All I'm saying that we see gravity first, and light a little bit later (by shapiro effect), same for gravitational changes.

I think you misunderstand the Shapiro effect, which says that light travels slower out of a gravitational "hole" than it would if there was no gravity. It says nothing about the speed of changes in gravity, which would be the same speed as any light making the same journey.