Black Hole Information
What’s the Problem?
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
Black Holes are Real
• Black holes were originally thought to be mathematical curiosity, a
solution that can’t be created with physically realistic initial
• 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*
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,
• For the public?
• 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
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
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.
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
• 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.
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.
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
1. Denial: Black holes don’t form
• Requires strong deviations from general relativity in regimes we have
• Extremely implausible.
• Most papers on this “solution”
2. Hope: Information comes out
• Information starts leaking out long before the Planckian quantum
• Unclear how that can happen. Requires some kind of non-locality or
• Presently the most popular solution because supported by the
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
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
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
• Big headache for string theorists, hence the attention
• Imo, the claim is plainly wrong
Math alone will not solve the problem