Narrow Results

For more than 30 years the discovery that black holes radiate like black bodies of specific temperature has triggered a multitude of puzzling questions concerning their nature and the fate of information that goes down the black hole during its lifetime. The most tricky issue in what is known as information loss paradox is the apparent violation of unitarity during the formation/evaporation process of black holes. A new idea is proposed based on the combination of our knowledge on Hawking radiation as well as the Einstein–Podolsky–Rosen phenomenon, that could resolve the paradox and spare physicists from the unpalatable idea that unitarity can ultimately be irreversibly violated even under special conditions.

Crystals, as quantum objects typically much larger than their lattice spacing, are counterexamples to a frequent prejudice that quantum effects should not be pronounced at macroscopic distances. We propose that the Einstein theory of gravity only describes a fluid phase and that a phase transition of crystallization can occur under extreme conditions such as those inside the black hole. Such a crystal phase with lattice spacing of the order of the Planck length offers a natural mechanism for pronounced quantum-gravity effects at distances much larger than the Planck length. A resolution of the black hole information paradox is proposed, according to which all information is stored in a crystal-phase remnant with size and mass much above the Planck scale.

This work analyzes the dynamical variables and information transfer of a collapsing string fluid in the theory of Rainbow gravity (RG). Modifications are made to the field equations for the anisotropic string fluid in spherical geometry with the necessary rainbow functions. We have calculated the radius and time when effective horizons formed. This calculation helps to estimate the time of the observer reaching the apparent horizon. Moreover, we have computed the dynamical variables concerning the string fluid including mass density, pressure and the string tension. The behavior of the dynamical quantities is presented graphically. It is found that the rainbow parameter $\eta$ affects the dynamical variables. The results enable us to understand the physics of a collapsing fluid and the information transfer in the collapsing scenario.

A sketchy review of the “island” paradigm in black hole evaporation theory, which actually brings us back to the old idea that interior of black hole decouples from our universe after Page time, so that Hawking radiation is entangled with emerging new universe, thus leaving no room for the information paradox. Instead this provides a self-consistent description of multiverse, where every black hole in a parent universe is a white hole — the origin — of a new one.

Christodoulou and Rovelli have shown that the interior volume of a Schwarzschild black hole grows linearly with time. The entropy of a scalar field in this interior volume of a Schwarzschild black hole has been calculated and shown to increase linearly with the advanced time too. In this paper, considering Hawking radiation from a d-dimensional charged black hole, we investigate the proportional relation between the entropy of the scalar field in the interior volume and the Bekenstein–Hawking entropy using the method of our previous work. We also derive this proportionality relation using Hamiltonian analysis and find a consistent result. We then investigate the proportionality coefficient with respect to d and find that it gradually decreases as the dimension of space–time increases.

By calculating the entropy of a scalar field in the interior volume of noncommutative black holes and considering an infinitesimal process of Hawking radiation, a proportion function is constructed that reflects the evolution relation between the scalar field entropy and Bekenstein–Hawking entropy under Hawking radiation. Comparing with the case of Schwarzschild black holes, the new physics of this research can be expanded to the later stage of Hawking radiation. From the result, we find that the proportion function is still a constant in the earlier stage of Hawking radiation, which is identical to the case of Schwarzschild black holes. As Hawking radiation goes into the later stage, the behavior of the function will be dominated by the noncommutative effect. In this circumstance, the proportion function is no longer a constant and decreases with the evaporation process. When the noncommutative black hole evolves into its final state with Hawking radiation, the interior volume will converge to a certain value, which implies that the loss of information of the black hole during the evaporation process will finally be stored in the limited interior volume.

In this talk, I would like to speak about two projects that Igor Volovich and I discussed several years ago and which were never completed. The first one concerns string field theory in term of string generalization of vierbein and the second is about possible relations between matrix models and knots. I also discuss our recent projects connected with information paradox.

In this work, we consider a special kind of space–time called AdS accelerating black holes. This is a kind of black holes which have a stringlike singularity along polar axis attached to the black hole and it accelerates the black hole. In these kind of space–times, the growth of Einstein–Hilbert action is independent of the acceleration as found in S. Chen and Y. Pei, Int. J. Theor. Phys. 60, 917 (2021). By using a string as a probe, we found the effect of the acceleration is captured by the string probe [K. Nagasaki, arXiv:2108.05429 [hep-th]]. Here in this work, we consider the case of rotating black holes. By the probe string, we clearly describe the effect of the acceleration and its relation to the rotation of the black holes.

We exhibit an explicit foliation of Schwarzschild space–time by spacelike hypersurfaces which extend from Schwarzschild r=0 to r=∞. This allows us to compute the values of a massless scalar field for all space–time points which lie in the future of the surface on which we initially quantize the theory. This is to be contrasted with approaches which start at past null infinity and propagate to future null infinity. One of its virtues is that this method allows us to discuss both asymptotic Hawking radiation and what is happening at finite distances from the black hole.

In order to explain the techniques we use, we begin by discussing variants of the flat-space moving mirror⁹ problem. Then we discuss the canonical quantization of the massless scalar field theory and the geometric optics approximation which we use to solve the Heisenberg equations of motion in the black hole background. Using the example of an infalling mirror, an analogue of the moving mirror problem, we show that, although our spacelike slices extend to r=0, we can avoid discussing an initial state which extends through the horizon. Furthermore, we show that in the same way we avoid having to deal with the singularity at r=0 when we first quantize the system. This discussion naturally leads to a suggestion of how to handle the question of what is happening when the mirror hits the singularity. In the last section of the paper we discuss a discretization of the computation which behaves in the manner we suggest and yet exhibits Hawking radiation.⁵ This formulation of the problem allows us to discuss all the issues in an explicitly unitary setting. The resulting picture raises some interesting questions about the information paradox.

A brief review on virtual black holes is presented, with special emphasis on phenomenologically relevant issues like their influence on scattering or on the specific heat of (real) black holes. Regarding theoretical topics, the results important for (the avoidance of) information loss are summarized.

After recalling Hawking's Euclidean notion of virtual black holes and a Minkowskian notion which emerged in studies of 2D models, the importance of virtual black holes for scattering experiments is addressed. Among the key features is that virtual black holes tend to regularize divergences of quantum field theory and that a unitary S-matrix may be constructed. Also, the thermodynamical behavior of real evaporating black holes may be ameliorated by interactions with virtual black holes. Open experimental and theoretical challenges are mentioned briefly.

We point out that nonperturbative effects in quantum gravity are sufficient to reconcile the process of black hole evaporation with quantum mechanics. In ordinary processes, these corrections are unimportant because they are suppressed by e^-S. However, they gain relevance in information-theoretic considerations because their small size is offset by the corresponding largeness of the Hilbert space. In particular, we show how such corrections can cause the von Neumann entropy of the emitted Hawking quanta to decrease after the Page time, without modifying the thermal nature of each emitted quantum. Second, we show that exponentially suppressed commutators between operators inside and outside the black hole are sufficient to resolve paradoxes associated with the strong subadditivity of entropy without any dramatic modifications of the geometry near the horizon.

Recently, it was argued [A. Almheiri et al., arXiv: 1207.3123, A. Almheiri et al., arXiv: 1304.6483], via a delicate thought experiment, that it is not consistent to simultaneously require that (a) Hawking radiation is pure, (b) effective field theory is valid outside a stretched horizon and (c) infalling observers encounter nothing unusual as they cross the horizon. These are the three fundamental assumptions underlying Black Hole Complementarity and the authors proposed that the most conservative resolution of the paradox is that (c) is false and the infalling observer burns up at the horizon (the horizon acts as a "firewall"). However, the firewall violates the equivalence principle and breaks the CPT invariance of quantum gravity. This led Hawking to propose recently that gravitational collapse may not end up producing event horizons, although he did not give a mechanism for how this may happen. Here we will support Hawking's conclusion in a quantum gravitational model of dust collapse. We will show that continued collapse to a singularity can only be achieved by combining two independent and entire solutions of the Wheeler–DeWitt equation. We interpret the paradox as simply forbidding such a combination. This leads naturally to a picture in which matter condenses on the apparent horizon during quantum collapse.

The black hole final state proposal implements manifest unitarity in the process of black hole formation and evaporation in quantum gravity, by postulating a unique final state boundary condition at the singularity. We argue that this proposal can be embedded in the gauge/gravity context by invoking a path integral formalism inspired by the Schwinger–Keldysh like thermo-field double construction in the dual field theory. This allows us to realize the gravitational quantum channels for information retrieval to specific deformations of the field theory path integrals and opens up new connections between geometry and information theory.

The black hole information loss paradox epitomizes the contradictions between general relativity and quantum field theory. The AdS/conformal field theory (CFT) correspondence provides an implicit answer for the information loss paradox in black hole physics by equating a gravity theory with an explicitly unitary field theory. Gravitational collapse in asymptotically AdS spacetimes is generically turbulent. Given that the mechanism to read out the information about correlations functions in the field theory side is plagued by deterministic classical chaos, we argue that quantum chaos might provide the true Rosetta Stone for answering the information paradox in the context of the AdS/CFT correspondence.

The aim of this paper is to give an overview to nonspecialists of recent arguments from fundamental physics in favor and disfavor of quantum corrections to black hole horizons. I will mainly discuss the black hole information paradox, its possible resolutions and shortly address its relevance or irrelevance to astronomy.

We start by looking at why we believe that black holes have entropy. According to Boltzmann, the entropy is a measure of the number of microstates of a system. We suggest here that the entropy arises from a holographic conformal field theory on the black hole horizon. Finally, we discuss some of the implications for the information paradox.

We explain how Hawking radiation stores significant amount of information in high-order correlations of quantum fields. This information can be retrieved by multi-time measurements on the quantum fields close to the black hole horizon. This result requires no assumptions about quantum gravity, it takes into account the differences between Gibbs’s and Boltzmann’s accounts of thermodynamics, and it clarifies misconceptions about key aspects of Hawking radiation and about informational notions in QFT.

Based on the definition of the interior volume of spherically symmetry black holes, the interior volume of Schwarzschild–(Anti) de Sitter black holes is calculated. It is shown that with the cosmological constant ($\mathrm{\Lambda }$) increasing, the changing behaviors of both the position of the largest hypersurface and the interior volume for the Schwarzschild–Anti de Sitter black hole are the same as the Schwarzschild–de Sitter black hole. Considering a scalar field in the interior volume and Hawking radiation with only energy, the evolution relation between the scalar field entropy and Bekenstein–Hawking entropy is constructed. The results show that the scalar field entropy is approximately proportional to Bekenstein–Hawking entropy during Hawking radiation. Meanwhile, the proportionality coefficient is also regarded as a constant approximately with the increasing $\mathrm{\Lambda }$. Furthermore, considering $\mathrm{\Lambda }$ as a dynamical variable, the modified Stefan–Boltzmann law is proposed which can be used to describe the variation of both the mass and $\mathrm{\Lambda }$ under Hawking radiation. Using this modified law, the evolution relation between the two types of entropy is also constructed. The results show that the coefficient for Schwarzschild–de Sitter black holes is closer to a constant than the one for Schwarzschild–Anti de Sitter black holes during the evaporation process. Moreover, we find that for Hawking radiation carrying only energy, the evolution relation is a special case compared with the situation that the mass and $\mathrm{\Lambda }$ are both considered as dynamical variables.

We argue that the vacuum of quantum gravity must contain a hierarchical structure of correlations spanning all length scales. These correlated domains (called “vecros”) correspond to virtual fluctuations of black hole microstates. Larger fluctuations are suppressed by their larger action, but this suppression is offset by a correspondingly larger phase space of possible configurations. We give an explicit lattice model of these vecro fluctuations, noting how their distribution changes as the gravitational pull of a star becomes stronger. At the threshold of formation of a closed trapped surface, these virtual fluctuations transition into on-shell black hole microstates (fuzzballs). Fuzzballs radiate from their surface like normal bodies, resolving the information paradox. We also argue that any model without vecro-type extended vacuum correlations cannot resolve the paradox.

I discuss how five reasonably sounding assumptions lead to a dilemma — the Page-time paradox — which appears to challenge a conventional statistical mechanical underpinning of black hole thermodynamics. By inspecting the conceptual subtleties behind each hypothesis, I list questions that require clarification before the puzzle can be deemed paradoxical. I devote particular attention to using thermodynamic arguments for a system that never reaches equilibrium. As a proof of concept, I show that the paradox is absent in a modified setting that admits an equilibrium thermodynamics formulation.