One of the most remarkable aspects of physics is that Newtonian gravity calculations are quite spot on for all the parts of black holes layfolk consider important.
1. Both predict the same critical radius, now called the Schwarzschild radius.
2. Both predict a central singularity with formally infinite density in idealised collapse.
3. Both predict exactly the same finite time to fall into the singularity under equivalent idealised conditions.
4. Both give the same equation for radial free fall, using different definitions of time.
What GR added was meaning to these things (and of course precise calculations outside of very idealised scenarios and symmetric conditions).
Both have finite time falling in to the singularity. If you use a point test particle Newton and GR agree on that finite time.
That's proper time I.e. the infalling particles wristwatch time.
In GR, external observers would never see the infalling particle cross the event horizon but that's a coordinate artifact. If using our wrist watch time for that particle.
What I find really interesting is that black holes don't really "require" infinite density; the mass density inside the event horizon never exceeds neutron star levels, and becomes in fact lower the heavier the black hole gets (=> event horizon enclosed volume grows faster than mass).
1. Both predict the same critical radius, now called the Schwarzschild radius.
2. Both predict a central singularity with formally infinite density in idealised collapse.
3. Both predict exactly the same finite time to fall into the singularity under equivalent idealised conditions.
4. Both give the same equation for radial free fall, using different definitions of time.
What GR added was meaning to these things (and of course precise calculations outside of very idealised scenarios and symmetric conditions).
I thought you need at least special relativity for time dilution.
That's proper time I.e. the infalling particles wristwatch time.
In GR, external observers would never see the infalling particle cross the event horizon but that's a coordinate artifact. If using our wrist watch time for that particle.
https://www.si.edu/newsdesk/releases/astronomers-reveal-firs...