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# If a black hole is moving, then is the horizon surface gravity constant ?

### 4 Answers

- 2 months ago
Yes, the event horizon surface gravity is not affected the black holes motion.

All motion at a constant velocity is equivalent to being at rest, because all motion is relative. Your coordinate system can be defined to move with the black hole. So it is at rest with respect to that coordinate system.

- nebLv 72 months ago
The usual solution for a black hole like the simple Schwarszchild black hole is done in a coordinate system (reference frame) defined far away and at rest with the black hole. So, if the black hole is moving with respect to an observer, it requires a transformation to a new coordinate system that incorporates that relative motion.

The solution to Einstein’s field equations is something called the metric tensor. The metric tensor defines the gravitational field in the various space and time directions. The metric tensor has components like a vector, and like a vector, the components of the metric tensor change under a coordinate change. So, if you now have motion with respect to the observer, the components of the metric tensor change in the direction of motion. So, a relative observer will no longer see a symmetric gravitational field. They will see changes in the gravitational field along the direction of motion.

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- Anonymous2 months ago
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I think the whole point of the question is what does an observer see that is in relative motion with respect to the black hole. Of course an observer with no relative motion will not see a difference, but observer with relative motion will see a difference.