Dong-han Yeom

Black Hole Remnants and the Information Loss Paradox

Abstract Forty years after the discovery of Hawking radiation, its exact nature remains elusive. If Hawking radiation does not carry any information out from the ever shrinking black hole, it seems that unitarity is violated once the black hole completely evaporates. On the other hand, attempts to recover information via quantum entanglement lead to the firewall controversy. Amid the confusions, the possibility that black hole evaporation stops with a “remnant” has remained unpopular and is often dismissed due to some “undesired properties” of such an object. Nevertheless, as in any scientific debate, the pros and cons of any proposal must be carefully scrutinized. We fill in the void of the literature by providing a timely review of various types of black hole remnants, and provide some new thoughts regarding the challenges that black hole remnants face in the context of the information loss paradox and its latest incarnation, namely the firewall controversy. The importance of understanding the role of curvature singularity is also emphasized, after all there remains a possibility that the singularity cannot be cured even by quantum gravity. In this context a black hole remnant conveniently serves as a cosmic censor. We conclude that a remnant remains a possible end state of Hawking evaporation, and if it contains large interior geometry, may help to ameliorate the information loss paradox and the firewall controversy. We hope that this will raise some interests in the community to investigate remnants more critically but also more thoroughly.

Is the firewall consistent? Gedanken experiments on black hole complementarity and firewall proposal

In this paper, we discuss the black hole complementarity and the firewall proposal at length. Black hole complementarity is inevitable if we assume the following five things: unitarity, entropy-area formula, existence of an information observer, semi-classical quantum field theory for an asymptotic observer, and the general relativity for an in-falling observer. However, large N rescaling and the AMPS argument show that black hole complementarity is inconsistent. To salvage the basic philosophy of the black hole complementarity, AMPS introduced a firewall around the horizon. According to large N rescaling, the firewall should be located close to the apparent horizon. We investigate the consistency of the firewall with the two critical conditions: the firewall should be near the time-like apparent horizon and it should not affect the future infinity. Concerning this, we have introduced a gravitational collapse with a false vacuum lump which can generate a spacetime structure with disconnected apparent horizons. This reveals a situation that there is a firewall outside of the event horizon, while the apparent horizon is absent. Therefore, the firewall, if it exists, not only does modify the general relativity for an in-falling observer, but also modify the semi-classical quantum field theory for an asymptotic observer.

Mass inflation in f(R) gravity ? A conjecture on the resolution of the mass inflation singularity

We study gravitational collapse of a charged black hole in f(R) gravity using double-null formalism. We require cosmological stability to f(R) models; we used the Starobinsky model and the R+(1/2)cR2 model. Charged black holes in f(R) gravity can have a new type of singularity due to higher curvature corrections, the so-called f(R)-induced singularity, although it is highly model-dependent. As the advanced time increases, the internal structure will approach the Cauchy horizon, which may not be an inner apparent horizon. There is mass inflation as one approaches the Cauchy horizon and hence the Cauchy horizon may be a curvature singularity with nonzero area. However, the Ricci scalar is finite for an out-going null observer. This can be integrated as follows: Cosmologically stable higher curvature corrections of the Ricci scalar made it bounded even in the presence of mass inflation. Finally, we conjecture that if there is a general action including general higher curvature corrections with cosmological stability, then the corrections can make all curvature components finite even in the presence of mass inflation. This might help us to resolve the problem of inner horizon instability of regular black hole models.

Semi-classical black holes with large N re-scaling and information loss problem

We consider semiclassical black holes and related rescalings with N massless fields. For a given semiclassical solution of an N = 1 universe, we can find other solution of a large N universe by the rescaling. After the rescaling, any curvature quantity takes a sufficiently small value without changing its causal structure. Via the rescaling, we argue that black hole complementarity for semiclassical black holes cannot provide a fundamental resolution of the information loss problem, and the violation of black hole complementarity requires sufficiently reasonable amounts of N. Such N might be realized from some string inspired models. Finally, we claim that any fundamental resolution of the information loss problem should resolve the problem of the singularity.

Constructing a Counterexample to the Black Hole Complementarity

We propose a regular black hole whose inside generates a de Sitter space and then is finally frustrated into a singularity. It is a modified model which was suggested originally by Frolov, Markov, and Mukhanov. In our model, we could adjust a regular black hole so that its period before going into the extreme state is much longer than the information retention time. During this period an observer could exist who observes the information of the Hawking radiation, falls freely into the regular center of the black hole, and finally meets the free-falling information again. The existence of such an observer implies that the complementary view may not be consistent with a regular black hole, and therefore, is not appropriate as a generic principle of black hole physics.

Responses of the Brans-Dicke field due to gravitational collapses

We study responses of the Brans–Dicke field due to gravitational collapses of scalar field pulses using numerical simulations. Double-null formalism is employed to implement the numerical simulations. If we supply a scalar field pulse, it will asymptotically form a black hole via dynamical interactions of the Brans–Dicke field. Hence, we can observe the responses of the Brans–Dicke field by two different regions. First, we observe the late time behaviors after the gravitational collapse, which include formations of a singularity and an apparent horizon. Second, we observe the fully dynamical behaviors during the gravitational collapse and view the energy–momentum tensor components. For the late time behaviors, if the Brans–Dicke coupling is greater (or smaller) than −1.5, the Brans–Dicke field decreases (or increases) during the gravitational collapse. Since the Brans–Dicke field should be relaxed to the asymptotic value with the elapse of time, the final apparent horizon becomes time-like (or space-like). For the dynamical behaviors, we observed the energy–momentum tensors around ω ~ −1.5. If the Brans–Dicke coupling is greater than −1.5, the Tuu component can be negative at the outside of the black hole. This can allow an instantaneous inflating region during the gravitational collapse. If the Brans–Dicke coupling is less than −1.5, the oscillation of the Tvv component allows the apparent horizon to shrink. This allows a combination that violates weak cosmic censorship. Finally, we discuss the implications of the violation of the null energy condition and weak cosmic censorship.

SPHERICALLY SYMMETRIC TRAPPING HORIZONS, THE MISNER–SHARP MASS AND BLACK HOLE EVAPORATION

We discuss some of the issues relating to information loss and black hole thermodynamics in the light of recent work on local black hole horizons. Understood in terms of pure states evolving into mixed states, the possibility of information loss in black holes is closely related to the global causal structure of space–time, as is the existence of event horizons. However, black holes need not be defined by event horizons, and in fact we argue that in order to have a fully unitary evolution for black holes, they should be defined in terms of something else, such as a trapping horizon. The Misner–Sharp mass in spherical symmetry shows very simply how trapping horizons can give rise to black hole thermodynamics, Hawking radiation and singularities. We show how the Misner–Sharp mass can also be used to give insights into the process of collapse and evaporation of locally defined black holes.

Generation of a bubble universe using a negative energy bath

This paper suggests a model for a bubble universe using buildable false vacuum bubbles. We study the causal structures of collapsing false vacuum bubbles using double-null simulations. False vacuum bubbles violate the null energy condition and emit negative energy along the outgoing direction through semi-classical effects. If there are a few collapsing false vacuum bubbles and they emit negative energy to a certain region, then the region can be approximated by a negative energy bath, which means that the region is homogeneously filled by negative energy. If a false vacuum bubble is generated in the negative energy bath and the tension of the bubble effectively becomes negative in the bath, then the bubble can expand and form an inflating bubble universe. This scenario uses a set of assumptions different from those in previous studies because it does not require tunneling to unbuildable bubbles.

Bubble collision with gravitation

In this paper, we study vacuum bubble collisions with various potentials including gravitation, assuming spherical, planar, and hyperbolic symmetry. We use numerical calculations from double-null formalism. Spherical symmetry can mimic the formation of a black hole via multiple bubble collisions. Planar and especially hyperbolic symmetry describes two bubble collisions. We study both cases, when two true vacuum regions have the same field value or different field values, by varying tensions. For the latter case, we also test symmetric and asymmetric bubble collisions, and see details of causal structures. If the colliding energy is sufficient, then the vacuum can be destabilized, and it is also demonstrated. This double-null formalism can be a complementary approach in the context of bubble collisions.

Internal structure of charged black holes

We investigate the internal structure of charged black holes with a spherically symmetric model including Hawking radiation and discharge. In the stage of formation, the internal structure is determined by the mass and charge of collapsing matter. When the charge–mass ratio is small, a wormhole–like internal structure is observed. However, the structure becomes analogous to the static limit as the ratio reaches unity. After the formation, mass inflation induces large curvatures in the internal structure, which makes the structure insensitive to the late–time perturbations. The internal structure determined from the formation seems to be maintained during evaporation. The discharge and neutralization of charged black holes is also investigated for both non–evaporating and evaporating cases. Finally, we discuss the implications of the wormhole structure inside of charged black holes.