Does matter take infinite time to leave a black hole?

To this question:

about the possibility of a sufficiently large black hole not containing a singularity John Rennie posted an answer containing information I had not seen before.

Here is John's quote: For the charged and rotating black holes things are more complicated, because there are timelike paths that take you through the event horizon, miss the singularity and back out again.

Quite clearly this refers to matter that crosses the Event Horizon to the interior and is expelled again because the time-like path avoids the singularity.

Now, in this question:

Can any object pass into the event horizon of a black hole and then escape?

the only answer on the page is from Bob Bee who is quoted now: possible to extract energy, charge and mass from a BH, without extracting any actual particles. Two reasons, besides the obvious one that no particle escapes the horizon.

Bob's answer seems to conflict with John's but are the two actually in agreement?

They might be if matter can enter and leave the black hole but not in the same form. That's the only reasoning I can come up with by myself.

Please excuse me though if I have misunderstood something entirely. The point of asking this question was to clarify the point that matter takes an infinite amount of time to cross the horizon from the perspective of an outside observer. In John's answer matter crosses and spends time within. Would this matter also take an infinite amount of time to re-enter into causal connection from the perspective of an outside observer?

• arxiv.org/pdf/1011.5399.pdf - This paper has many nice chars that show spacetime trajectories (geodesics) entering and leaving the outer horizon. Jan 31, 2020 at 23:23

In GR the equations are time symmetric. So if we calculate a geodesic for an object falling in a gravitational field the object could be moving in either direction. We can do this even for the simplest of black holes i.e. the uncharged, non-rotating Schwarzschild black hole. With time flowing in the usual direction objects fall into the black hole, but the same equations describe the time reversed version i.e. objects falling out of a white hole.

Just as an object falling inwards to a black hole takes infinite coordinate time to reach the horizon, an object moving outwards from a white hole takes an infinite time to leave the horizon - it is the same trajectory just in reverse. So the answer to your question is that yes matter takes an infinite time to leave a white hole.

Now you are asking about a charged or rotating black hole, i.e. the Reissner-Nordström or Kerr metrics, and with these geometries there are indeed trajectories that allow you to fall through the horizon and then back out again, missing the singularity on your way. And just as before we can reverse time to reverse the trajectory. So if you start at point A, fall through the black hole and back out to point B then we can time reverse to start at point B and end at point A. The significance of this is that the infall becomes the outfall when we do the reversal so if the infall takes infinite coordinate time so will the outward leg.

And the answer is that yes the infall does take infinite coordinate time, so it would also take infinite coordinate time for the outward leg. However the trip takes only a finite (and actually very short) for the falling observer. The difference between the coordinate and falling observer time has already been discussed to death in other questions on this site.

• I'm extrapolating here (and it's probably implied in your answer) that since there is no way to delay the matter along its trajectory through the interior there is also no way to boost it along its outward trajectory. Jan 30, 2020 at 12:58
• @BlackHoleSlice correct! :-) Jan 30, 2020 at 14:00
• matter takes an infinite time to leave a white hole” - It is a past infinity from the infinite past until now, not the future infinity. This time has already passed, so objects can come out of a white hole at any moment. (There is no infinite past in the real universe, of course, only in the Schwarzschild solution.) Jan 30, 2020 at 14:36
• @safesphere - so random information can spontaneously appear too - the white hole information creation paradox - only in the Schwarzschild : ) Jan 31, 2020 at 21:35
• @safesphere - As discussed at arxiv.org/abs/2006.07748. as well as elsewhere on PSE and in cosmological models that have included (per a footnote in the last--2003's--revision of the Borde-Guth-Vilenkin Theorem by BGV themselves) Aguirre & Gratton's "Steady-state eternal inflation", as well as in Nikodem J. Poplawski's "Cosmology with torsion", the possibility that the universe (or multiverse) is "past eternal" cannot be ruled out. Sep 15, 2020 at 15:27