There are some arcane problems with black hole in the realm of fundamental physics. They are tricky and yours truly is mostly ignorant and there are NO generally accepted solutions. We will largely just skirt them, but NOT forget them entirely. Here we just give a brief introduction to them.

Arcane Problems:

1. The arcane problems all seem to be cases of fundamental physics theories being applied to extreme limits in black holes where they give seemingly inconsistent answers. Solving these problems means finding consistent answers somehow. At present, the black hole information paradox seems to combine all the problems. The best intro to the black hole information paradox that yours truly knows of is the video Has the Black Hole Information Paradox Finally Been Solved? SciAm | 3:50.

2. No-hair theorem: The no-hair theorem (i.e., John A. Wheeler's (1911--2008) "black holes have no hair" rule) has been challenged since circa 2012 by black hole firewall paradox. See "Scientists claim hairy black holes explain Hawking paradox", Pallab Ghosh, 2022 Mar17, BBC.

   The no-hair theorem is summarized in a famous aphorism of John A. Wheeler (1911--2008): "black holes have no hair" which just means they are simple objects---in a certain sense---without a lot of features like hair, fingers, toes, etc.

   By the way, "Every aphorism is both true and false including this one."

   The no-hair theorem itself: If one can ignore astronomical perturbations from other astronomical objects, then aside from its location in spacetime a black hole is fully specified by just 3 parameters: mass, angular momentum (a measure of rotation often call spin in the case of black holes), and net electric charge.

   In fact, the no-hair theorem even if NOT fundamentally true is probably a useful model of black holes for many purposes, but NOT those deep in the realm of fundamental physics.

3. Faster-than-light travel: It seems that wormholes (which may exist inside the event horizons of black holes: see "How the Inside of a Black Hole Is Secretly on the Outside", Ahmed Almheiri, 2022 Sep01, SciAm) may allow faster-than-light travel in a sense. Locally, there is no faster-than-light travel as one moves through a wormhole connecting two points in spacetime, but from outside the wormhole, there is faster-than-light travel (see Wikipedia: Wormhole: Faster-than-light travel. Yours truly wonders how causality would NOT be violated by such faster-than-light travel. Maybe it is because there is NO local faster-than-light travel. But some megamind will have to explain.

   See Wikipedia: Special relativity: Causality and prohibition of motion faster than light.

4. Time travel: There are some theories that wormholes allow time travel to the past and future. But they all sound very complex. See Wikipedia: Wormhole: Time travel.

5. The Black Hole Firewall Paradox:

   Actually, since 2012, there been renewed controversy about Hawking radiation.

   Hawking radiation it has been realized leads to the black hole firewall paradox:

   1. According to general relativity nothing special should happen to an observer falling through an event horizon from his/her point of view.

   2. But it is now understood that quantum mechanics seems to imply that there will an invisible-to-the-outside region of intense heat at or near the event horizon because of Hawking radiation. This region is the black hole firewall that would fry an observer falling through the event horizon.

   Which event actually happens? There is no certainty circa 2024. People are very perplexed. The resolution of the black hole firewall paradox could lead to an important advance in our understanding of black holes.

6. Relevant keywords:
   black hole, black hole firewall paradox, black hole information paradox, event horizon, Hawking radiation, no-hair theorem, wormhole, yes-hair theorem (2022), etc.
   

7. Relevant scientific articles:
   1. "Black Hole Firewalls Confound Theoretical Physicists", Jennifer Ouellete, 2012, SciAm.
   2. "Information Preservation and Weather Forecasting for Black Holes", Stephen Hawking, 2014.
   3. "Black Holes, Firewalls and Chaos from Gravitational Collapse", Pankaj S. Joshi & Ramesh Narayan, 2014.
   4. "Scientists claim hairy black holes explain Hawking paradox", Pallab Ghosh, 2022 Mar17, BBC.
   5. "What Is the Black Hole Information Paradox? A Primer", Jason Drakeford, et al. 2022 Aug16, SciAm.
   6. "What are wormholes? An astrophysicist explains these shortcuts through space-time", Dejan Stojkovic, 2022 Aug23, The Conversation: For young readers.
   7. "How the Inside of a Black Hole Is Secretly on the Outside", Ahmed Almheiri, 2022 Sep01, SciAm: This is probably the fullest general public explanation of wormholes existing inside black holes.

8. Black hole, Wormhole, Black hole Information Paradox, Firewall videos (i.e., Black hole Wormhole, Black hole information paradox Firewall videos):
   
   1. Has the Black Hole Information Paradox Finally Been Solved? SciAm | 3:50: Well, has the black hole information paradox been solved? Maybe. OK for the classroom if the instructor wants do give some idea about this.