Quantum models of black holes:

Marios Christodoulou, CPT Marseille: Black to White Hole transition and Gravitational Tunneling in Spinfoams

An overview of recent progress in covariant LQG regarding the calculation of the lifetime of a trapped region before it transitions to an anti-trapped region. We review the conceptual setup and present the results of an explicit estimation from EPRL amplitudes.

William Cuervo, Universidad Nacional Autonoma de Mexico: Loop quantum effective geometry and Schwarschild singularity: exact results

Quantum Geometry effects Ă  la Loops is applied to the region where classical general relativity fails and the Schwarzschild singularity appears. Using an effective semiclassical geometry as well as the qualitative theory of ordinary differential equations we show that at this regime the spacetime is not singular:
i) Effective Hamilton's equations for the geometry fulfill the conditions of a theorem for extendibility of solutions to first order differential equations and hence the corresponding space-time can be extended to arbitrary large proper times.
ii) The Raychauduri equation is finite term by term, resolving the singularities of classical geodesic congruences.
iii) All effective curvature invariants are bounded and hence curvature singularities are absent.
iv) The volume does not evolve towards zero in a finite proper time ruling out strong singularities.

Tommaso De Lorenzo, Centre de Physique Theorique, Marseille, CNRS: Light Cone Thermodynamics

We show that to null surfaces emanating from a sphere in Minkowski spacetime can be assigned thermodynamical properties that are in strict formal correspondence with those of black holes in curved spacetimes. Such null surfaces, made of pieces of light cones, are bifurcating conformal Killing horizons for suitable conformally stationary observers. Those observers perceive the Minkowski vacuum state as a thermal state at a given light cone temperature, given by the standard expression in terms of the (generalisation of) surface gravity for conformal Killing horizons. Exchanges of conformally invariant energy as measured by these special observers across the conformal horizon are described by a first law with an entropy term that is given by 1/4 of the area of the bifurcating surface--the shining sphere--in Planck units. These conformal horizons can be extremal and non-extremal. They satisfy the zeroth to the third laws of thermodynamics in an appropriate way. Extremal horizons are horizons emanating from a single event; they have zero temperature and zero entropy.

Konstantin Eder, Ludwig-Maximilians-Universität München: Title: The entropy of charged black holes

We describe the quantum theory of isolated horizons with charge in a setting in which both electromagnetic and gravitational field are quantized. We consider the spherically symmetric and the distorted case. The resulting picture depends significantly on the choices made for the quantization and the definition of the state counting. We show that there is a choice such that the Bekenstein-Hawking relation holds.

Mohammed Ezzi, Quantum black holes, Foundations of quantum gravity: Black Hole Theorem for the Non-Extensive Entropy in Loop Quantum Gravity

We apply non-extensive statistical mechanics, characterized by a free parameter q, to calculate black hole entropy in loop quantum gravity. For a given horizon area, the entropy of the black hole is given by the Bekenstein-Hawking area law for arbitrary real positive values of the Barbero-Immirzi parameter γ. In this work, we find a correlation between γ, q and s (where s=j_{max}). We conclud in our result that Hawking radiation for 0≺q≺1 is important also for massive black holes, is therefore possible That those Black Holes have also been a source of radiation since the beginning of the universe without being eroded by the decline of mass. For black holes that have M>M_{min} lose their mass over time due to Hawking radiation at a rate proportional to its mass. For the non-extensive entropy, Hawking radiation is important for the small masses and also for the supermassive black hole. This result can explain to us that there are premordial supermassive black holes still present today, and even massive black holes formed at the center of the galaxies would be much larger than the current predicted mass, otherwise they would be consumed by Hawking radiation, which may represent explanation of the dark matter problem

Rodolfo Gambini, Instituto de Fisica, Facultad de Ciencias, Igua 4225 esa Mataojo, C.C.11400, Montevideo Uruguay: Quantum fluctuating geometries and the information paradox

We study Hawking radiation on the quantum space-time of a collapsing null shell. We show that there are departures from thermality in the radiation even though we are not considering back reaction. One recovers the usual profile for the Hawking radiation as a function of frequency in the limit where the space-time is classical.

However, when quantum corrections are taken into account, the profile of the Hawking radiation as a function of time contains information about the initial state of the collapsing shell.

Hal Haggard, Bard College: Complex Quantum Tunneling and the Decay of Black Holes

Quantum effects render black holes unstable. In addition to Hawking radiation, which leads to the prediction of an extraordinary lifetime for black holes, there is the possibility of quantum tunneling of the black hole geometry itself. A robust possibility for treating the quantum tunneling of a spacetime geometry is to complexify the gravitational variables. I will illustrate this technique with an analytically solvable 1D quantum potential and describe the present state of the calculation for spherically symmetric black holes.

Antonino Marciano, Fudan University: Kac-Moody instantons in space-time foam on black holes

In an ongoing collaboration with Andrea Addazi, Pisin Chen and Yong-Shi Wu, we propose an alternative scenario to the one developed by Hawking, Perry and Strominger, and elaborate on the role of the Kac- Moody charges — in stead of BMS symmetries charges — in the resolution of the black hole information paradox. The same role of BMS charges may be indeed played by an infinite set of symmetries that emerge in the space-time foam predicted by quantum gravity. Specifically, we focus on Yang-Mills theories and on the Holst formulation of gravity, and argue that the Yang-Mills and gravitational self-duality conditions in space-time bubbles are related to a new infinite dimensional global symmetry, hidden in the Lagrangian. Such a symmetry is manifested by the Kac-Moody algebra, with zero central charges. This implies the existence, in the space-time foam, of an infinite number of different instantons that are interconnected by the Kac-Moody symmetry. These solutions punctures the horizons of the building block of the space-time bubbles. The new result carries consequences on the no-hair theorem and on the study of quantum black holes.

Yuki Yokokura, RIKEN: A Model of Black Hole Evaporation and 4D Weyl Anomaly

We analyze time evolution of a spherically-symmetric collapsing matter from a point of view that black holes evaporate by nature. We consider conformal matters and solve the semi-classical Einstein equation by using the 4-dimensional Weyl anomaly with a large c coefficient. Here the expectation value of energy-momentum tensor contains the contribution from both the collapsing matter and Hawking radiation. 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. [arxiv: 1701.03455]

Thomas Zilker, Friedrich-Alexander-Universität Erlangen-Nürnberg: Surface holonomies and their quantization

Exponentiating the isolated horizon boundary condition (IHBC), one obtains an expression in terms of the E-field on the right hand side, which corresponds to the surface holonomies known from higher gauge theory. The main part of the talk will be dedicated to the quantization of these surface holonomies with the use of the Duflo-Kirillov map. In order to estimate our chances of finding solutions to the quantized IHBC we study the determinant of the quantized surface holonomies.