Thursday, December 6, 2018

Quantum theory of charged isolated horizons

Tuesday, Dec. 4th

Konstantin Eder, Hanno Sahlmann, FAU Erlangen
Title: Quantum theory of charged isolated horizons 
PDF of the talk (600K)
Audio+Slides of the talk (32M)

By Jorge Pullin, LSU

Thermodynamics is the branch of physics that deals with systems about which we have incomplete information. A prototypical thermodynamics system is a gas: we will never be able to follow the motion of all the molecules of a gas, there are too many. One describes such systems using macro variables. Some are well known like the volume, the pressure or the temperature. A less well known macro variable is the entropy, which is a measure of our ignorance about the system. When physical systems interact the total entropy always increases.
It came as a surprise when Bekenstein proposed that black holes had a thermodynamic description. Since the area of the horizon of a black hole is proportional to its mass and everything that falls into the black hole cannot get out, it means that when something interacts with a black hole its mass always grows. And since we cannot know what is in the interior of a black hole, the area of the horizon is a measure of that ignorance. So Bekenstein suggested that the entropy of a black hole was proportional to its area. The thermodynamic picture got completed when in 1975 Hawking showed that if one took into account quantum effects, black holes radiated as a black body with a given temperature.

Loop quantum gravity provides a detailed explanation of the entropy of a black hole. In loop quantum gravity finite surfaces can in principle have zero area. They get endowed with "quanta of area" when they are pierced by the loops that characterize the quantum states. A surface can be endowed with a certain value of the area by many different loop quantum gravity states. So just giving the area we have a certain ignorance of the quantum state that gave rise to it. A detailed counting of that ignorance is therefore a notion of entropy and it has been shown that it is proportional to the area.

This talks extends these results to the case in which black holes are in the presence of quantum fields, more specifically Yang-Mills fields, which are the theories that describe particle physics. It shows that the entropy is still proportional to the area, but that higher order corrections may depend on the charges of the Yang-Mills fields. This provides a nice consistency test that shows that the entropy is still mainly proportional to the area even if one is in a non-vacuum situation with the presence of fields.

Wednesday, November 28, 2018

A holographic description for boundary gravitons in 4D

Tuesday, Nov 20

Bianca Dittrich, Perimeter Institute
Title: A holographic description for boundary gravitons in 4D 
PDF of the talk (5M)
Audio+Slides< of the talk (38M)
By Jorge Pullin, LSU

Holography has become a central concept in gravity. It is the idea that the description of gravity in a region of spacetime can be mapped to the description of a quantum field theory on the boundary of the spacetime. It originated in string theory as part of the "Maldacena conjecture" but it proved to be a more fundamental concept that does not require string theory for its formulation.

In this talk, holography was first reviewed in the context of three dimensional spacetimes, where the theory of gravity is much simpler than in four space-time dimensions, as spacetimes are locally flat in 3D. In particular, the example of the torus was discussed in detail. It was presented how to use Regge calculus (an approximation to general relativity using a triangulation in terms of simplices) to construct the boundary theory.

The talk then moved to four dimensional spacetimes starting with the simpler example of the flat sector of gravity where one only considers flat spacetimes. Again, the boundary theory was constructed using Regge calculus and the example of the three torus was discussed. It concluded with some future directions for the full theory, discussion of the symmetry group of the theory at infinity and possible implications for black hole entropy.

Wednesday, October 24, 2018

A unified geometric framework for boundary charges and dressings

Tuesday, Oct 23rd

Aldo Riello, Perimeter Institute
Title: A unified geometric framework for boundary charges and dressings 
PDF of the talk (2M)
Audio+Slides of the talk (41M)
By Jorge Pullin, LSU (with some help from Aldo)

The electromagnetic force and all the subatomic interactions are described by a class of theories known as “gauge theories”. Even gravitation, in its modern formulation due to Einstein, is a gauge theory of sorts, although a more complicated one. The mathematical formulation of these theories is characterized by peculiar redundancies, as if the simplest way to describe the system is through a plethora of different descriptions rather than through a single “true” one. This is most often seen as a mathematical quirk rather than as a hint of some deep property of nature. This talk explores the latter possibility and build on the idea that the rationale for gauge theories must be found not so much in some property of a single system taken in isolation, but rather in the way systems can come together and talk to each other. The first hint of this can be found in the fact that the natural objects populating a gauge theory (“observables”) are intrinsically nonlocal and therefore can’t be easily localized in a given region, without carefully keeping track of what happens at its boundaries. The simplest example of this phenomenon can be found in the electron, that can never be separated from its electric field, which in turn can be detected even at a distance from the electron. This talk presents a novel mathematical framework that by embracing the relational perspective unifies many seemingly unrelated aspects of gauge theories and might – in its future developments – clarifies the analogous but harder conceptual issues one finds on their way to quantum gravity.

Thursday, October 18, 2018

Quantum extension of black holes

Tuesday, Oct 9th

Javier Olmedo, LSU
Title: Quantum Extension of Kruskal Black Holes 
PDF of the talk (500k)
Audio+Slides of the talk (17M)

By Jorge Pullin, LSU

In the interior of black holes the coordinates t and r swap roles. As one falls "towards the center" one is actually moving forward in time. This makes the interior of a black hole look like a contracting cosmology of a particular type, known as Kantowski-Sachs cosmology. This has allowed the use of loop quantum cosmology techniques to treat the interior of black holes. There have been several discussions of this, but they have some shortcomings. To begin with, they only cover the interior of the black hole. Moreover, some of the proposals have physical quantities with undesirable dependences on fiducial elements introduced in order to quantize or on the mass of the space-time.

This talk discusses overcoming these problems. To begin with, it is shown that the quantum treatment eliminates the singularity inside black holes and replaces with a region of large curvature. The value of the maximum curvature is universal and independent on the mass of the space-time. Moreover, it gives the same mass for the black hole to the past and to the future (unlike other treatments). In addition, the quantum theory is extended to the exterior region of the black hole. In the future it is expected to extend these ideas to other type of black hole space-times, like those with charge, spin and cosmological constant.

Monday, October 8, 2018

Computing volumes in spin foams

Tuesday, Sep 25th

Benjamin Bahr, DESY
Title: 4-volume in spin foam models from knotted boundary graphs 
PDF of the talk (3M)
Audio+Slides of the talk (15M)

by Jorge Pullin, LSU

There is an approach to quantum mechanics known as the path integral approach. In it, one considers all possible classical trajectories, not only the ones satisfying the equations of motion and assigns probabilities to each of them using a formula. The probabilities are summed and that gives the quantum probability to go from an initial state to a final state. In loop quantum gravity the initial and final states are given by spin networks, which are graphs with intersections and "colors" (a number) assigned to each edge. The trajectories connecting initial and final states therefore resemble a "foam" and are given the names of spin foams.

In this talk it was shown how to compute volumes of polytopes (regions of space-time bounded by flat sides, a generalization to higher dimensions of polyhedra of 3d) in spin foam quantum gravity. The calculation has nice connections with knot theory, the branch of math that studies how curves entangle with each other.

One of the central elements of spin foams is the formula that assigns the probabilities, known as a "vertex". The construction in this talk gives ideas for extending the current candidates for vertices, including the possibility of adding a cosmological constant and suggests possible connections with Chern-Simons theories (a special type of field theories) and also with quantum groups.

Tuesday, May 1, 2018

Cosmological perturbations in terms of observables and physical clocks

Tuesday, Apr 17th

Kristina Giesel, FAU Erlangen-Nürnberg
Title: Gauge invariant observables for cosmological perturbations 
PDF of the talk (8M)
Audio+Slides of the talk (15M)

By Jorge Pullin, LSU

When one sets up to quantize general relativity something unusual happens. When one constructs a key quantity for describing the evolution called the Hamiltonian, it turns out it vanishes. What the framework is telling us is that since in general relativity one can choose arbitrary coordinates, the coordinate t that one normally associated with time is arbitrary. That means that the evolution described in terms of it is arbitrary.

Of course this does not mean that the evolution predicted by general relativity is arbitrary. It is just that one is choosing to describe it in terms of a coordinate that is arbitrary. So how can one get to the invariant part of the evolution? Basically one needs to construct a clock out of physical quantities. Then one asks how other variables evolve in terms of the variable of the clock. The relational information between such variables is coordinate independent and therefore characterizes the evolution in an invariant way.

Cosmological perturbation theory is an approximation in which one assumes that the universe at large scales is homogeneous and isotropic plus small perturbations. One can then expand the Einstein equations keeping only the lower order terms in the small perturbations. That makes the equations much more manageable. Up to now most studies of cosmological perturbations were done in coordinate dependent fashion, in particular the evolution was described in terms of a coordinate t. This talk discusses how to formulate cosmological perturbation theory in terms of physical clocks and physically observable quantities. Several choices of clocks are discussed.

Sunday, April 22, 2018

Quantum gravity inside and outside black holes

Tuesday, Apr 3rd

Hal Haggard, Bard College
Title: Quantum Gravity Inside and Outside Black Holes 
PDF of the talk (5M)
Audio+Slides of the talk (19M)
By Jorge Pullin, Louisiana State University

The talk consisted of two distinct parts. The second part discussed black holes exploding into white holes. We have covered the topic in this blog before, and the new results were a bit technical for a new update, mainly a better handle on the time the process takes, so we will not discuss them here.

The first part concerned itself with how the interior of a black hole would look like in a quantum theory. Black holes are regions of space-time from which nothing can escape and are bounded by a spherical surface called the horizon. Anything that ventures beyond the horizon can never escape the black hole. Black holes develop when stars exhaust their nuclear fuel and start to contract under the attraction of gravity. Eventually gravity becomes too intense for anything to escape and a horizon forms.

The interior of the horizon however, is drastically different if a black hole has rotation or not. If the black hole does not rotate, anything that falls into the black hole is crushed in a central singularity where, presumably, all the mass of the initial star concentrated. If the black hole has rotation however, the structure is more complicated and infalling matter can avoid hitting the singularity and move into further regions of space-time inside the black hole.

This raises the question: what happens with all this in a quantum theory of gravity. Presumably a state representing a non-rotating black hole will consist of a superposition of black holes with rotation, peaked around zero rotation, but with contributions from black holes with small amounts of rotation. How does the interior of a non-rotating quantum black hole look when it is formed through a superposition of rotating black holes? This is an interesting question since the interior of rotating black holes are so different from their non-rotating relatives.

The talk concludes that the resulting interior actually does resemble that of a non-rotating black hole. The key observation is that one cannot trust the classical theory all the way to the singularity and that leads to the superposition having large curvatures where one would have expected the singularity of the non-rotating black hole to be.