# Thread: simultaneity and black holes

1. How you define simultaneity between A very far from the black hole, and B very close to the event horizon.
What about inside the event horizon?

Because the black hole is evaporating, it could be for example, that free fall inside the event horizon takes longer then the evaporation time of the black hole for point A.

2.

3. How do you define it?

4. I'm not qualified to offer an opinion on your question, but it did lead me to this Wikipedia article which I found quite interesting.

Relativity of simultaneity

5. Originally Posted by Quantum immortal
How you define simultaneity between A very far from the black hole, and B very close to the event horizon.
The short answer is - you can't. In a curved space-time, the notions of "time" and "simultaneity" are strictly observer-dependent. The only physically meaningful thing you can do is compare accumulated proper times on clocks which travel between the same two fixed events on different trajectories.

What about inside the event horizon?
The region beyond the horizon is not causally connected to the rest of the universe, so this is meaningless.

6. Originally Posted by Quantum immortal
How you define simultaneity between A very far from the black hole, and B very close to the event horizon.
The notion of simultaneity is defined with respect to a single observer at an given instant in time. Specifically, it is defined for a single point on a world-line. Let be a specified point on the observer's world-line parametised by proper time. Let and be the two points on the world-line equidistant from in terms of proper time . From the past point , construct the future light-cone, and from the future point , construct the past light-cone. The intersection of these two light-cones is a (generally deformed) spherical surface parametrised by . Taken over all values of , the set of all the surfaces of intersection is the three-dimensional space that is simultaneous to . Different observers will generally have different three-dimensional spaces of simultaneity even to the extent that point being simultaneous to point does not imply that point is simultaneous to point .

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