Black hole information paradox
He also argued that the detailed form of the radiation would be independent of the initial state of the black hole,[2] and depend only on its mass, electric charge and angular momentum.
The Schrödinger equation obeys two principles that are relevant to the paradox—quantum determinism, which means that given a present wave function, its future changes are uniquely determined by the evolution operator, and reversibility, which refers to the fact that the evolution operator has an inverse, meaning that the past wave functions are similarly unique.
Starting in the mid-1970s, Stephen Hawking and Jacob Bekenstein put forward theoretical arguments that suggested that black-hole evaporation loses information, and is therefore inconsistent with unitarity.
[2] The arguments for microscopic irreversibility were backed by Hawking's calculation of the spectrum of radiation that isolated black holes emit.
Today, some physicists believe that the holographic principle (specifically the AdS/CFT duality) demonstrates that Hawking's conclusion was incorrect, and that information is in fact preserved.
[16][17] In 1973–1975, Stephen Hawking showed that black holes should slowly radiate away energy, and he later argued that this leads to a contradiction with unitarity.
The important aspect of these formulas is that they suggest that the final gas of radiation formed through this process depends only on the black hole's temperature and is independent of other details of the initial state.
Lacking the ability to make a full quantum analysis, he nonetheless made a powerful observation: If a black hole starts in a pure quantum state and evaporates completely by a unitary process, the von Neumann entropy or entanglement entropy of the Hawking radiation initially increases from zero and then must decrease back to zero when the black hole to which the radiation is entangled has totally evaporated.
[6] Recent progress in deriving the Page curve for unitary black hole evaporation is a significant step towards finding both a resolution to the information paradox and a more general understanding of unitarity in quantum gravity.
Some of this coverage resulted from a widely publicized bet made in 1997 between John Preskill on the one hand with Hawking and Kip Thorne on the other that information was not lost in black holes.
Within what might broadly be termed the "string theory community", the dominant idea is that Hawking radiation is not precisely thermal but receives quantum correlations that encode information about the black hole's interior.
The GISR (Gravity Induced Spontaneous Radiation) mechanism of references[28][29] can be considered an implementation of this idea but with the quantum perturbations of the event horizon replaced by the microscopic states of the black hole.
This coupling mimics the photon-atom coupling in the Jaynes–Cummings model of atomic physics, replacing the photon's vector potential with the binding energy of particles to be radiated in the black hole case, and the dipole moment of initial-to-final state transitions in atoms with the similarity factor of the initial and final states' wave functions in black holes.
Despite its ad hoc nature, this coupling introduces no new interactions beyond gravity, and it is deemed necessary irrespective of the future development of quantum gravitational theories.
In the case of short time evolution or single quantum emission, Wigner-Wiesskopf approximation allows one[28][29] to show that the power spectrum of GISR is exactly of thermal type and the corresponding temperature equals that of Hawking radiation.
The observers far away can retrieve the information stored in the initial black hole from this mass or temperature versus time curve.
The hamiltonian and wave function description of GISR allows one to calculate the entanglement entropy between the black hole and its Hawking particles explicitly.
The most important lesson from this calculation is that the intermediate state of an evaporating black hole cannot be considered a semiclassical object with a time-dependent mass.
This idea suggests that Hawking's computation fails to keep track of small corrections that are eventually sufficient to preserve information about the initial state.
[30][31][9] This can be thought of as analogous to what happens during the mundane process of "burning": the radiation produced appears to be thermal, but its fine-grained features encode the precise details of the object that was burnt.
The mechanism that allowed the right small corrections to form was initially postulated in terms of a loss of exact locality in quantum gravity so that the black-hole interior and the radiation were described by the same degrees of freedom.
Within what might be termed the loop-quantum-gravity approach to black holes, it is believed that understanding this phase of evaporation is crucial to resolving the information paradox.
A minority view in the theoretical physics community is that information is genuinely lost when black holes form and evaporate.
Banks, Susskind and Peskin argue that, in some cases, loss of unitarity also implies violation of energy–momentum conservation or locality, but this argument may possibly be evaded in systems with a large number of degrees of freedom.
Penrose claims that quantum systems will in fact no longer evolve unitarily as soon as gravitation comes into play, precisely as in black holes.
The Conformal Cyclic Cosmology Penrose advocates critically depends on the condition that information is in fact lost in black holes.
[57] The original motivation of these studies was Penrose's long-standing proposal wherein collapse of the wave-function is said to be inevitable in the presence of black holes (and even under the influence of gravitational field).
Significant progress was made in 2019, when, starting with work by Penington[70] and Almheiri, Engelhardt, Marolf and Maxfield,[71] researchers were able to compute the von Neumann entropy of the radiation black holes emit in specific models of quantum gravity.
It has also been argued that a key technique used in the Page-curve computations, the "island proposal", is inconsistent in standard theories of gravity with a Gauss law.
[74] This would suggest that the Page curve computations are inapplicable to realistic black holes and work only in special toy models of gravity.
