General Relativity & Quantum Cosmology

We propose that a large Schwarzschild black hole (BH) is a bound state of highly excited, long, closed strings just above the Hagedorn temperature. The effective free-energy density is expressed as a function of its entropy density and contains only linear and quadratic terms, in analogy with that of collapsed living polymers. Classically, the horizon of such BH’s is completely opaque, hiding any clues about the state and very existence of its interior. Quantum mechanically and in equilibrium, the situation is not much different: Hawking radiation will now be emitted, but it carries a minimal amount of information. The situation is significantly different when such a quantum BH is out of equilibrium. The BH can then emit ``supersized" Hawking radiation with a much larger amplitude than that emitted in equilibrium. The result is a new type of quantum hair that can reveal the state and composition of the BH interior to an external observer.

Kento Osuga and I give an explicit toy qubit transport model for transferring information from the gravitational field of a black hole to the Hawking radiation by a continuous unitary transformation of the outgoing radiation and the black hole gravitational field.  The model has no firewalls or other drama at the event horizon and fits the set of six physical constraints that Giddings has proposed for models of black hole evaporation.  It does utilize nonlocal qubits for the gravitational field but assumes that the radiation interacts locally with these nonlocal qubits, so in some sense the nonlocality is confined to the gravitational sector.  Although the qubit model is too crude to be quantitively correct for the detailed spectrum of Hawking radiation, it fits qualitatively with what is expected.

Event horizons are the defining feature of classical black holes. They are the key ingredient of the information loss paradox which, as paradoxes in quantum foundations, is built on a combination of predictions of quantum theory and counterfactual classical features. Within the semi-classical theory we investigate the possibility that black hole radiation still does not allow for a finite time crossing of the Schwarzschild radius of collapsing matter as seen by distant observers. The exact form of the pre-Hawking radiation is not yet settled, and we make only minimal assumptions about its nature.

We analyze the time evolution of a spherically-symmetric collapsing matter from the point of view that black holes evaporate by nature. We obtain a self-consistent solution of the semi-classical Einstein equation. The solution indicates that the collapsing matter forms a dense object and evaporates without horizon or singularity, and it has a surface but looks like an ordinary black hole from the outside. Any object we recognize as a black hole should be such an object. In the case of stationary black holes that are formed adiabatically in the heat bath, the area law is reproduced by integrating the entropy density over the interior volume. This result implies that the information is stored inside the object.

A quantum system behaves classically when quantum probabilities are high for coarse-grained histories correlated in time by deterministic laws. That is as true for the flight of a tennis ball as for the behavior of spacetime geometry in gravitational collapse. Classical spacetime may be available only in patches of configuration space with quantum transitions between them. Global structures of general relativity. such as event horizons may not be available. We consider the quantum dynamics of gravitational collapse in a model in which classical spacetime breaks down because the wave function spreads over a large ensemble of classical end states as envisioned in the fuzzball proposal. Probabilities of coarse-grained observables are highly peaked around the classical black hole values. By contrast, probabilities for finer-grained observables probing the near horizon region are broadly distributed, and no notion of `averaging' applies. This means that the formation of fuzzballs may result significant observational features including a novel type of gravitational wave burst associated with tunneling between classical solutions.