Qing-yu Cai

Hidden messenger revealed in Hawking radiation: A resolution to the paradox of black hole information loss

Using standard statistical method, we discover the existence of correlations among Hawking radiations (of tunneled particles) from a black hole. The information carried by such correlations is quantified by mutual information between sequential emissions. Through a careful counting of the entropy taken out by the emitted particles, we show that the black hole radiation as tunneling is an entropy conservation process. While information is leaked out through the radiation, the total entropy is conserved. Thus, we conclude the black hole evaporation process is unitary

Hawking radiation as tunneling derived from black hole thermodynamics through the quantum horizon

We show that the first law of the black hole thermodynamics can lead to the tunneling probability through the quantum horizon by calculating the change of entropy with the quantum gravity correction and the change of surface gravity is presented clearly in the calculation. The method is also applicable to the general situation which is independent on the form of black hole entropy and this verifies the connection of black hole tunneling with thermodynamics further. In the end we discuss the crucial role of the relation between the radiation temperature and surface gravity in this derivation

The temperature in Hawking radiation as tunneling

Abstract The quasi-classical method of deriving Hawking radiation under the consideration of canonical invariance is investigated. We find that the horizon should be regarded as a two-way barrier and the ingoing amplitude should be calculated according to the negative energy particles tunneling into the black hole because of the whole space–time interchange and thus the standard Hawking temperature is recovered. We also discuss the advantage of the Painleve coordinates in Hawking radiation as tunneling.

Noncommutative information is revealed from Hawking radiation as tunneling

We revisit the tunneling process from a Schwarzschild black hole in the noncommutative spacetime and obtain the nonthermal tunneling probability. In such nonthermal spectrum, the correlations are discovered, which can carry the information about the noncommutativity. Thus this enlightens a way to find the noncommutative information in the Hawking radiation. The entropy is also shown to be conserved in the whole radiation process, which implies that the unitarity is held even for the Hawking radiation from noncommutative black holes.

Spontaneous creation of the universe from nothing

An interesting idea is that the universe could be spontaneously created from nothingbut no rigorousproof has been given. In this paperwe present such a proof based on the analytic solutions of the Wheeler-DeWitt equation (WDWE). Explicit solutions of the WDWE for the special operator ordering factorp= -2 (or 4) show thatonce a small true vacuum bubble is created by quantum fluctuations of themetastable false vacuumit can expand exponentially no matter whether the bubble is closed,flat,or open.The exponential expansion will end when the bubble becomes large and thus the early universe appears.With the de Broglie-Bohm quantum trajectory theorywe show explicitly that it is the quantum potentialthat plays the role of the cosmological constant and provides the power for the exponential expansion of thetrue vacuum bubble. So it is clear that the birth of the early universe completely depends on the quantum nature of the theory.

An interpretation for the entropy of a black hole

We investigate the meaning of the entropy carried away by Hawking radiations from a black hole. We propose that the entropy for a black hole measures the uncertainty of the information about the black hole forming matter’s precollapsed configurations, self-collapsed configurations, and inter-collapsed configurations. We find that gravitational wave or gravitational radiation alone cannot carry all information about the processes of black hole coalescence and collapse, while the total information locked in the hole could be carried away completely by Hawking radiation as tunneling.

From a quantum to a classical description of intense laser-atom physics with Bohmian trajectories

In this paper, Bohmian mechanics is applied to intense laser-atom physics. The motion of an atomic electron in an intense laser field is obtained from the Bohm-Newton equation. We find that the quantum potential that dominates the quantum effect of a physical system becomes negligible as the electron is driven far from the parent ion by the intense laser field, i.e. the behavior of the electron smoothly tends towards classical soon after the electron is ionized. Our numerical calculations present direct positive evidence for semiclassical trajectory methods in intense laser-atom physics where the motion of the ionized electron is treated by classical mechanics, while quantum mechanics is needed before the ionization.

Dynamical interpretation of the wavefunction of the universe

a b s t r a c t In this paper, we study the physical meaning of the wavefunction of the universe. With the continuity equation derived from the Wheeler-DeWitt (WDW) equation in the minisuperspace model, we show that the quantity ρ(a) =| ψ(a)| 2 for the universe is inversely proportional to the Hubble parameter of the universe. Thus, ρ(a) represents the probability density of the universe staying in the state a during its evolution, which we call the dynamical interpretation of the wavefunction of the universe. We demonstrate that the dynamical interpretation can predict the evolution laws of the universe in the classical limit as those given by the Friedmann equation. Furthermore, we show that the value of the operator ordering factor p in the WDW equation can be determined to be p =− 2.

Correlation, entropy, and information transfer in black hole radiation

Since the discovery of Hawking radiation, its consistency with quantum theory has been widely questioned. In the widely described picture, irrespective of what initial state a black hole starts with before collapsing, it eventually evolves into a thermal state of Hawking radiations after the black hole is exhausted. This scenario violates the principle of unitarity as required for quantum mechanics and leads to the acclaimed “information loss paradox”. This paradox has become an obstacle or a reversed touchstone for any possible theory to unify the gravity and quantum mechanics. Based on the results from Hawking radiation as tunneling, we recently show that Hawking radiations can carry off all information about the collapsed matter in a black hole. After discovering the existence of information-carrying correlation, we show in great detail that entropy is conserved for Hawking radiation based on standard probability theory and statistics. We claim that information previously considered lost remains hidden inside Hawking radiation. More specifically, it is encoded into correlations between Hawking radiations. Our study thus establishes harmony between Hawking radiation and the unitarity of quantum mechanics, which establishes the basis for a significant milestone toward resolving the long-standing information loss paradox. The paper provides a brief review of the exciting development on Hawking radiation. In addition to summarize our own work on this subject, we compare and address other related studies.

Thermodynamics inducing massive particles’ tunneling and cosmic censorship

By calculating the change of entropy, we prove that the first law of black hole thermodynamics leads to the tunneling probability of massive particles through the horizon, including the tunneling probability of massive charged particles from the Reissner–Nordström black hole and the Kerr–Newman black hole. Novelly, we find the trajectories of massive particles are close to that of massless particles near the horizon, although the trajectories of massive charged particles may be affected by electromagnetic forces. We show that Hawking radiation as massive particles tunneling does not lead to violation of the weak cosmic-censorship conjecture.