Event Horizon vs Singularity: Are They the Same Thing in Black Hole Physics?

[Ray Eston Smith Jr]

Is the event horizon of a black hole (as seen by an observer at rest relative to the singularity) equivalent to the singularity (as seen by a free-falling observer)? In other words, if the stationary observer watches a rocketship free-fall to near the event horizon then turn on its rockets and return (much later), would the occupant of that rocket report that he saw no event horizon when he was free-falling but he did see himself approach close to the singularity? In other words, does space-time near the event-horizon in the stationary frame map to space-time near the singularity in the free-falling frame?

 

[pervect]

There's nothing particularly special about the event horizion as far as the geometry of space-time itself goes. Some coordinate systems (specifically, the typical Scwarzschild coordinates) are ill behaved there, but this is a property of the coordinates. The situation is roughly similar to using standard latitude and longitude coordiantes at the north pole of the Earth - there is nothing special about the shape of the Earth there, but a coordinate system based on lattitude and longitude goes a bit "wonky".

 

[R0man]

The event horizon and the singularity are two distinct concepts in black hole physics. The event horizon is the boundary beyond which nothing, including light, can escape the gravitational pull of a black hole. It is defined as the point of no return for any object falling into a black hole. On the other hand, the singularity is a point of infinite density and zero volume at the center of a black hole, where the laws of physics as we know them break down.

To answer the question, the event horizon and the singularity are not equivalent. The event horizon is a physical boundary that can be observed by an external observer, whereas the singularity is a mathematical concept that cannot be directly observed. An observer at rest relative to the singularity would see the event horizon as a physical boundary, but they would not see the singularity itself.

In the scenario described, the occupant of the rocketship would indeed report that they did not see the event horizon while free-falling towards the black hole, but they did see themselves approach close to the singularity. This is because the event horizon is a boundary in space-time, and as the rocketship approaches it, the space-time around it becomes increasingly distorted. However, the singularity is a point in space-time, and it is not something that can be seen or approached.

In conclusion, the event horizon and the singularity are not equivalent. The event horizon is a physical boundary that can be observed, while the singularity is a mathematical concept. The space-time near the event horizon may appear similar to the space-time near the singularity, but they are not the same thing.