**Konstantin Eder, Hanno Sahlmann, FAU Erlangen**

**Title: Quantum theory of charged isolated horizons**

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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.