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It is known that when one crosses the event horizon of a Schwarzschild black hole, one cannot return and is destined to hit the $r=0$ horizon. My understanding is that this can be seen from the Eddington-Finkelstein coordinate where the future light cone always tilts toward $r=0$ when $r < 2GM$. My impression is that when something is in the light-cone, it is time-like separated, so how is the singularity called space-like when it lives in the light cone?

Another confusion that I have is that I read the singularity of a Reissner-Nordstrom black hole is time-like, which means that it lives in the light cone. Why do people say that going into $r=0$ is avoidable if it is a time-like singularity?

user1372002
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  • https://physics.stackexchange.com/questions/60869/what-is-the-definition-of-a-timelike-and-spacelike-singularity – Rexcirus May 24 '22 at 18:10
  • Is the r=0 horizon the singularity? – MatterGauge May 24 '22 at 19:38
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    Your house at midnight is spacelike, but you can take a timelike path to step into your kitchen exactly at midnight. What contradiction do you see here? – safesphere May 24 '22 at 21:06
  • @Rexcirus This answer of Ben Crowell is challenged in the comments. – safesphere May 24 '22 at 21:10
  • A point in space is timelike, but you can go around it. Why wouldn’t you be able to go around a timelike singularity? – safesphere May 24 '22 at 21:17
  • @safesphere Your house at midnight is spacelike safesphere! WTF? :;) – MatterGauge May 24 '22 at 22:08
  • @Felicia I mean at any chosen moment of time like midnight, noon, or any particular time. For example, the spacetime interval between your living room at midnight and your kitchen at midnight is spacelike. – safesphere May 25 '22 at 03:51

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