Mass curves space. All mass curves space all the time. You are bending the fabric of spacetime even now! Don’t try to deny it!
What does curvature mean? It means that the direction of time’s arrow is different in different places. To an observer outside of a large gravitational field, events inside the field appear to move more slowly than they would have outside of it. Black holes merely take this to an extreme. To an observer far from a black hole, a clock entering the black hole appears to slow down and finally _stop_ as it crosses the event horizon¹. But simultaneously an observer traveling with the clock observes something different. They see everything outside the black hole slow down and stop instead, while they continue to coast smoothly along. They notice nothing strange at the horizon itself; it is simply empty space with weird visuals in the distance.
This almost seems like a paradox, since the two observers each believe that the other’s clock has stopped. The reason why it’s not a paradox is that the space around the black hole is strongly curved, so strongly that the axis of time swaps place with one direction of space. At the horizon the axis of time flips over and points down into the black hole. The distant observer sees time stop because time is now edge–on, as it were. The observer falling into the black hole notices nothing weird near themselves, because both time and space still exist. Only the images of distant objects show any evidence of curvature. But the falling observer is doomed, for their own time axis now points at the singularity. Their timeline now ends abruptly, while the timeline of the distant observer extends potentially a vigintillion years.
For some edutainment on the subject, I recommend The Science Asylum. He’s done a bunch of videos on gravity and relativity, but here are two in particular:
* Explaining Gravity Using Relativistic Time Dilation <https://www.youtube.com/watch?v=F5PfjsPdBzg&list=PLOVL_fPox2K83_36YgnGisn4rxNvgq1iR&index=7>
* Why Can't You Escape a Black Hole? <https://www.youtube.com/watch?v=yPQUtuTraxs&list=PLOVL_fPox2K-zpTeryROTkmzzsMssSMWp&index=6>
¹ There are other effects too. The image of the clock _lingers_ on the horizon forever, since for it time has apparently stopped. But the redshift increases to infinity too, as the gravitational well becomes steeper, so no matter what wavelengths we observe in the image of the clock fades away beyond sight. Worse, the tidal forces caused by a real stellar–mass black hole will tear apart solid objects into a stream of plasma, even small objects. So the hypothetical black hole in our thought experiment must be very large indeed, to minimize the tidal forces enough that the clock survives the trip to the horizon intact and functional. And it can't be rotating either, since the rotation causes its own weirdness. This is the spherical cow of black holes.
What does curvature mean? It means that the direction of time’s arrow is different in different places. To an observer outside of a large gravitational field, events inside the field appear to move more slowly than they would have outside of it. Black holes merely take this to an extreme. To an observer far from a black hole, a clock entering the black hole appears to slow down and finally _stop_ as it crosses the event horizon¹. But simultaneously an observer traveling with the clock observes something different. They see everything outside the black hole slow down and stop instead, while they continue to coast smoothly along. They notice nothing strange at the horizon itself; it is simply empty space with weird visuals in the distance.
This almost seems like a paradox, since the two observers each believe that the other’s clock has stopped. The reason why it’s not a paradox is that the space around the black hole is strongly curved, so strongly that the axis of time swaps place with one direction of space. At the horizon the axis of time flips over and points down into the black hole. The distant observer sees time stop because time is now edge–on, as it were. The observer falling into the black hole notices nothing weird near themselves, because both time and space still exist. Only the images of distant objects show any evidence of curvature. But the falling observer is doomed, for their own time axis now points at the singularity. Their timeline now ends abruptly, while the timeline of the distant observer extends potentially a vigintillion years.
For some edutainment on the subject, I recommend The Science Asylum. He’s done a bunch of videos on gravity and relativity, but here are two in particular:
¹ There are other effects too. The image of the clock _lingers_ on the horizon forever, since for it time has apparently stopped. But the redshift increases to infinity too, as the gravitational well becomes steeper, so no matter what wavelengths we observe in the image of the clock fades away beyond sight. Worse, the tidal forces caused by a real stellar–mass black hole will tear apart solid objects into a stream of plasma, even small objects. So the hypothetical black hole in our thought experiment must be very large indeed, to minimize the tidal forces enough that the clock survives the trip to the horizon intact and functional. And it can't be rotating either, since the rotation causes its own weirdness. This is the spherical cow of black holes.