Black Hole Information Paradox, two variants comparedCompare two Black Hole Information Paradox variants

Five proposals for how information escapes a black hole. The 2019 Page curve calculations show unitarity can be recovered in simplified models of semiclassical gravity, but the question of what an infalling observer experiences at the horizon locally is still open.

Frontier

Basis: theoretical

Calculations since 2019 in simplified models show information can escape, but the mechanism in real black holes is open.

	Left Frontier Open the variant page	Right Frontier Open the variant page
Proposed	1993 and 2019 Don Page, Geoffrey Penington, Ahmed Almheiri, Netta Engelhardt, Donald Marolf, Henry Maxfield	2005 Samir D. Mathur
In one line	If quantum mechanics holds, the radiation's entropy must follow a precise curve over time.	String theory: the black hole has no interior. It's a fuzzy quantum surface.
The claim	If no information is lost, the entropy of Hawking radiation must rise and then fall. Calculations since 2019 reproduce that curve from gravity in simplified model universes.	The string-theory proposal that black holes have no interior and no event horizon at all. What appears to be a black hole is actually a fuzzy quantum-mechanical surface, a superposition of microstates that all look like a classical black hole from far away.
What would test it	4 predictions, first shown The fine-grained entropy of the radiation follows the Page curve, rising until the Page time and then falling to zero All 4	4 predictions, first shown There is no event horizon at the location predicted by classical general relativity; what is there is a quantum-stringy surface of finite area but no smooth interior beyond it All 4
Where it breaks	4 objections, first shown The calculations work in two-dimensional gravity and anti-de Sitter settings, and nobody has extended them to realistic four-dimensional black holes All 4	4 objections, first shown Most explicit fuzzball constructions are for supersymmetric or near-supersymmetric black holes; whether the construction generalizes to non-supersymmetric astrophysical Kerr black holes is contested, and no fully realistic example has been built All 4
Shared by both	4 shared objections, first shown The 2019 Page curve calculations using replica wormholes (Penington; Almheiri, Engelhardt, Marolf, Maxfield) show that unitarity can be recovered in simplified models of semiclassical gravity, but they are statements about the von Neumann entropy of the radiation, not direct statements about what an infalling observer experiences at the horizon locally. The original physical content of the paradox is partially separate from what the Page curve calculation resolves. All 4
Key unresolved problem	The realistic-black-hole problem: the calculations work only in simplified model universes, and no one has extended them to the four-dimensional black holes we observe.	The realistic-black-hole problem: every worked-out fuzzball, a black hole rebuilt as a tangle of strings with no smooth horizon, exists only in idealized symmetric settings, never for the spinning Kerr black holes we actually observe, so the central claim cannot yet be tested.
Sources	10, all established 8,531 INSPIRE citations, from 7 of 10 sources	1, established 1,133 INSPIRE citations, from its one source
Readers	No votes yet	No votes yet

In one line

If quantum mechanics holds, the radiation's entropy must follow a precise curve over time.

String theory: the black hole has no interior. It's a fuzzy quantum surface.

The claim

If no information is lost, the entropy of Hawking radiation must rise and then fall. Calculations since 2019 reproduce that curve from gravity in simplified model universes.

The string-theory proposal that black holes have no interior and no event horizon at all. What appears to be a black hole is actually a fuzzy quantum-mechanical surface, a superposition of microstates that all look like a classical black hole from far away.

What would test it

4 predictions, first shown

The fine-grained entropy of the radiation follows the Page curve, rising until the Page time and then falling to zero

All 4

4 predictions, first shown

There is no event horizon at the location predicted by classical general relativity; what is there is a quantum-stringy surface of finite area but no smooth interior beyond it

All 4

Where it breaks

4 objections, first shown

The calculations work in two-dimensional gravity and anti-de Sitter settings, and nobody has extended them to realistic four-dimensional black holes

All 4

4 objections, first shown

Most explicit fuzzball constructions are for supersymmetric or near-supersymmetric black holes; whether the construction generalizes to non-supersymmetric astrophysical Kerr black holes is contested, and no fully realistic example has been built

All 4

Shared by both

4 shared objections, first shown

The 2019 Page curve calculations using replica wormholes (Penington; Almheiri, Engelhardt, Marolf, Maxfield) show that unitarity can be recovered in simplified models of semiclassical gravity, but they are statements about the von Neumann entropy of the radiation, not direct statements about what an infalling observer experiences at the horizon locally. The original physical content of the paradox is partially separate from what the Page curve calculation resolves.

All 4

Key unresolved problem

The realistic-black-hole problem: the calculations work only in simplified model universes, and no one has extended them to the four-dimensional black holes we observe.

The realistic-black-hole problem: every worked-out fuzzball, a black hole rebuilt as a tangle of strings with no smooth horizon, exists only in idealized symmetric settings, never for the spinning Kerr black holes we actually observe, so the central claim cannot yet be tested.

Proposed

1993 and 2019

Don Page, Geoffrey Penington, Ahmed Almheiri, Netta Engelhardt, Donald Marolf, Henry Maxfield

2005

Samir D. Mathur

Sources

10, all established

8,531 INSPIRE citations, from 7 of 10 sources

1, established

1,133 INSPIRE citations, from its one source

Readers

No votes yet