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- 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
- 3. 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*
- 4. 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?
- 5. 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
- 6. 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.
- 7. 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.
- 8. 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.
- 9. 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
- 10. 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.
- 11. 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
- 12. 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
- 13. 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
- 14. 5. – 3.320 • Loads of other solution attempts
- 15. 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
- 16. My Conclusion Math alone will not solve the problem

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