A summary of the black hole information loss problem and solution attempts, aimed at an audience mostly of philosophers of physics.

1. Black Hole Information
What’s the Problem?
Sabine Hossenfelder

2. What is a black hole
• Mathematically: It’s a solution to the field equations of general
relativity with an event horizon.
• But that’s an unphysical definition because the event horizon must be
eternal. We will never be able to establish its existence!
• Physically, therefore, a black hole is what looks like a mathematical
black hole for some while.
• This means it’ll have an “apparent horizon” or “trapped horizon”
which isn’t necessarily eternal

4. Black Holes are Real
• Black holes were originally thought to be mathematical curiosity, a
solution that can’t be created with physically realistic initial
conditions.
• Singularity theorems: Turned out the opposite is the case! Black holes
are hard to avoid with physically realistic initial conditions.
• Observational evidence confirms their existence:
Very compact dim objects that don’t seem to have
a hard surface
• We are presently waiting from data from the
EHT that’s supposed to show the shadow of Sag A*

5. What’s so interesting about black holes?
• For the experimentalist:
An extreme environment that allows precision tests of general
relativity and particle physics at high energies/densities
• For the theorist:
Black holes bring together many different
areas of physics: gravity, particle physics,
thermodynamics, stat mech, quantum gravity,
quantum information…
• For the public?

6. The Singularity
• At the center of the black hole is a singularity
• At that point, curvature and energy-density is infinitely large
• This is widely believed to be unphysical and a mathematical artifact
• When the curvature/density reaches the Planck scale, quantum
gravity should become important. GR breaks down.
• In a fully consistent theory, the singularity should be absent

7. Black Hole Thermodynamics
• Black holes have an entropy proportional to the surface area
• They have a temperature inversely proportional to the radius
• A body with a temperature must be able to radiate
• Hawking showed that indeed black holes emit particles
• This Hawking-effect is due to the quantum effects of matter, gravity is
not quantized
The black hole temperature for solar-mass and supermassive
black holes is tiny, below even the CMB temperature. It is
unobservable and will remain so for the foreseeable future.

8. The Black Hole Information Loss Problem
• Hawking radiation carries energy away from the black hole
• The black hole shrinks. As it shrinks it heats up. Eventually it’s gone
• Hawking radiation does not carry information besides the
temperature
• This means the endstate of the evaporation is always the same (for
black holes of the same initial mass)
• Black hole evaporation is fundamentally irreversible.
• It is the only such process that physicists know of and it’s
incompatible with quantum theory.

9. Is it a paradox?
• It’s not a paradox in the sense that we know what destroys
information: The singularity
• The singularity spoils the irreversibility (pretty much by definition)
because it’s the same infinity regardless of the initial state
• The horizon is not the problem. The horizon is merely where
information becomes practically unavailable. That’s inconvenient but
nothing paradoxical about that.
• If the singularity is removed, this means that information can’t be
destroyed. But that in itself doesn’t help: The problem is to find out
what happens with the information.

10. Solution Attempts
1. Denial: Nothing falls in/black holes don’t form
2. Hope: Information comes out with radiation
3. Desperation: Remnants, stable or quasi-stable
4. Acceptance: Non-unitarity

11. 1. Denial: Black holes don’t form
• Requires strong deviations from general relativity in regimes we have
tested.
• Extremely implausible.
• Most papers on this “solution”
are wrong.

12. 2. Hope: Information comes out
• Information starts leaking out long before the Planckian quantum
gravitational phase
• Unclear how that can happen. Requires some kind of non-locality or
causality violation
• Presently the most popular solution because supported by the
gauge/gravity duality

13. 3. Depression: Remnants
• Information just stays in the black hole
• Either eternally (stable) or for a very long time (quasi-stable)
• This requires that the black hole entropy does not count microstates
of the black hole but merely what’s accessible from the outside
• Has been criticized on the grounds of enabling infinite pair production
but these complaints are unfounded: In this regime quantum gravity
actually is strong
• Remains unpopular because nothing can be calculated

14. 4. Acceptance: Non-unitarity
• Black holes can be created in virtual processes. If their decay violates
unitarity, in principle all processes could
• Unitarity is an assumption to quantum field theory that we use, and it
would no longer be justified. Then what?
• But it’s unclear how bad violations of unitarity would be
• This solution has never been ruled out but is even more unpopular
than remnants

15. 5. – 3.320
• Loads of other solution attempts

16. What’s the Black Hole Firewall
• Equivalence principle requires infalling observer doesn’t notice
anything at the horizon
• Paper in 2012 claimed that if information is in the outgoing radiation
(early, long before Planck phase), then observer must notice because
the state can no longer be vacuum
• Instead of being empty, there’s a “firewall” at the horizon that burns
the observer
• Big headache for string theorists, hence the attention
• Imo, the claim is plainly wrong

17. My Conclusion
Math alone will not solve the problem