I Can Gravity Escape a Black Hole? | GR Learning

[Mahesh]

TL;DR Summary

If light cannot escape a black hole and gravity cannot transmit information faster than light, how does gravity exerted by matter within the black hole affect matter outside the event horizon?

I was learning GR and I got to the point where I learned about worldlines and their structure within a Schwarzschild black hole, that space-time itself is curved so that all future worldlines from an event point inward. Since a massive object cannot exert gravity into its past, how does the gravity exerted by matter in the black hole affect matter outside the event horizon? (am I correct so far?)

I considered this thought experiment: consider a nearly ideal Schwarzschild black hole in which a massive but extremely light particle resides, within the event horizon. Can an extremely precise gravity probe (outside the horizon) pick up details about the particle that is within the horizon(such as position and velocity)? As far as I can tell it cannot, because of the worldlines going inward, and also that no information being able to escape a black hole, (I am not very sure about this), but if all influence that the particle has on the outside world can be detected and does not exist, how does the singularity exert gravity outside the event horizon?
Also,this is my second post,is my preview/formatting/etc correct?

 

[Janus]

What can't escape the event horizon is information about changes in the gravitational field. The gravitational field outside the event horizon was there before the event horizon formed, and remains after it forms.

 

[PeterDonis]

What can't escape the event horizon is information about changes in the gravitational field.

More precisely, information about changes in spacetime geometry inside the horizon.

 

[Mahesh]

But since all future-direction of worldlines point inward inside of the event horizon, how does gravity affect what is outside the event horizon, when it is always in the past of the particle?

 

[PeterDonis]

Can an extremely precise gravity probe (outside the horizon) pick up details about the particle that is within the horizon(such as position and velocity)?

No.

how does the singularity exert gravity outside the event horizon?

It doesn't. The mass of the black hole is not contained in the singularity (although pop science sources often make it seem like it is). The mass of the hole is a global property of the spacetime geometry. If you want to view it as caused by the presence of matter in the past, the matter in question will be the matter that collapsed to form the hole, prior to it going inside the horizon. The spacetime geometry outside the horizon that is left behind by the collapse process maintains the effects of the collapsing matter even after that matter has fallen inside the horizon.

 

[PeterDonis]

all future-direction of worldlines point inward inside of the event horizon

This is not true as you state it. What is true is that all future-directed worldlines from events inside the horizon point inward. But future-directed worldlines from events outside the horizon do not have to point inward.

 

[Mahesh]

My particle is inside the event horizon. Does that affect its ability to cause changes in space-time outside the black hole?

Edit: More precisely, my particle is at a point A inside the horizon when the experiment starts, and falls to point B during the experiment. Can not gravity probes detect the change in gravity at many points C as the particle falls, and hence deduce the position if the particle as it falls from A to B? Or is the space-time curvature at C constant over the particle falling in?

 

[Mahesh]

worldlines from events outside the horizon do not have to point inward

This is true, the world doesn't all end up in a single black hole, haha

 

[Nugatory]

More precisely, my particle is at a point A inside the horizon when the experiment starts, and falls to point B during the experiment. Can not gravity probes detect the change in gravity at many points C as the particle falls, and hence deduce the position if the particle as it falls from A to B?

Not if the points C are outside the horizon. Nothing that happens inside the horizon will affect what happens outside.