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Re:Neutron stars may be bigger than expected, measurement of... by colechristensen on Wednesday April 28, 2021 @02:08AM (#26966203)
Thank you for your reply, going back to my original question that sparked all of this uninformed speculation... how much extra time and distance is covered/experienced traveling to an event horizon? (It's not exactly easy to construct the question correctly)
Re:Neutron stars may be bigger than expected, measurement of... by pdonis on Wednesday April 28, 2021 @02:10PM (#26972305)
> how much extra time and distance is covered/experienced traveling to an event horizon?

I'm not sure what "extra" means, but a general rule of thumb is that the time to fall goes like the 3/2 power of the radial coordinate you are falling from. (Strictly speaking, this is the time to fall to the singularity, not the horizon, but for falling in from large radial coordinates, which will be the case for virtually all cases of interest, the difference is small.) The only technical complication is that this rule is true if the time and radial coordinate are in units of the Schwarzschild radius of the hole; you then have to convert to conventional units. A couple of specific examples:

Black hole of one solar mass, observer falling into the hole from a distance of 3 million kilometers (which is about 4.3 times the radius of the actual Sun--the distance is chosen for reasons that will appear in a moment). This makes the radial coordinate 1 million, 10^6, in units of the Schwarzschild radius of the hole (which is 3 km), so the time to fall will be 10^9, 1 billion, times the light-travel time across that distance, which is 10 microseconds (10^-5 seconds). So the time to fall will be 10^4 seconds, or about 3 hours.

Black hole of one million solar masses, observer falling into the hole from a distance of 30 billion kilometers (or about 5 times the semi-major axis of the orbit of Pluto around the Sun). Here the radial coordinate is only 10^4 in units of the Schwarzschild radius, so the time to fall will be 10^6 times the light travel time across that radius, which is 10 seconds (a million times 10 microseconds). So the time to fall will be about 10^7 seconds, or about 4 months.