arXiv subjects

Kirill Krasnov

Publications and source records attributed to Kirill Krasnov.

113 records · Page 7Linked to original sources

arXiv1999

Quanta of Geometry and Rotating Black Holes

In the loop approach to quantum gravity the spectra of operators corresponding to such geometrical quantities as length, area and volume become quantized. However, the size of arising quanta of geometry in Planck units is not fixed by the theory itself: a free parameter, sometimes referred to as Immirzi parameter, is known to affect the spectrum of all geometrical operators. In this paper I propose an argument that fixes the value of this parameter. I consider rotating black holes, in particular the extremal ones. For such black holes the ``no naked singularity condition'' bounds the total angular momentum J by A_H/8 pi G, where A_H is the horizon area and G Newton's constant. A similar bound on J comes from the quantum theory. The requirement that these two bounds are the same fixes the value of Immirzi parameter to be unity. A byproduct of this argument is the picture of the quantum extremal rotating black hole in which all the spin entering the extremal hole is concentrated in a single puncture.

gr-qc↗

arXiv1998

The Area Spectrum in Quantum Gravity

We show that, apart from the usual area operator of non-perturbative quantum gravity, there exists another, closely related, operator that measures areas of surfaces. Both corresponding classical expressions yield the area. Quantum mechanically, however, the spectra of the two operators are different, coinciding only in the limit when the spins labelling the state are large. We argue that both operators are legitimate quantum operators, and which one to use depends on the context of a physical problem of interest. Thus, for example, we argue that it is the operator proposed here that is relevant in the black hole context to measure the area of black hole horizon. We show that the difference between the two operators is due to non-commutativity that is known to arise in the quantum theory. We give a heuristic picture explaining the difference between the two area spectra in terms of quantum fluctuations of the surface whose area is being measured.

gr-qc↗

arXiv1998

Discrete Space-Time Volume for 3-Dimensional BF Theory and Quantum Gravity

The Turaev-Viro state sum invariant is known to give the transition amplitude for the three dimensional BF theory with cosmological term, and its deformation parameter hbar is related with the cosmological constant via hbar=sqrt{Lambda}. This suggests a way to find the expectation value of the spacetime volume by differentiating the Turaev-Viro amplitude with respect to the cosmological constant. Using this idea, we find an explicit expression for the spacetime volume in BF theory. According to our results, each labelled triangulation carries a volume that depends on the labelling spins. This volume is explicitly discrete. We also show how the Turaev-Viro model can be used to obtain the spacetime volume for (2+1) dimensional quantum gravity.

hep-th↗

arXiv1997

On the Constant that Fixes the Area Spectrum in Canonical Quantum Gravity

The formula for the area eigenvalues that was obtained by many authors within the approach known as loop quantum gravity states that each edge of a spin network contributes an area proportional to sqrt{j(j+1)} times Planck length squared to any surface it transversely intersects. However, some confusion exists in the literature as to a value of the proportionality coefficient. The purpose of this rather technical note is to fix this coefficient. We present a calculation which shows that in a sector of quantum theory based on the connection A=Gamma-gamma*K, where Gamma is the spin connection compatible with the triad field, K is the extrinsic curvature and gamma is Immirzi parameter, the value of the multiplicative factor is 8*pi*gamma. In other words, each edge of a spin network contributes an area 8*pi*gamma*l_p^2*sqrt{j(j+1)} to any surface it transversely intersects.

gr-qc↗

arXiv1997

Loop Quantization of Maxwell Theory and Electric Charge Quantization

We consider the loop quantization of Maxwell theory. A quantization of this type leads to a quantum theory in which the fundamental excitations are loop-like rather than particle-like. Each such loop plays the role of a quantized Faraday's line of electric flux. We find that the quantization depends on an arbitrary choice of a parameter e that carries the dimension of electric charge. For each value of e an electric charge that can be contained inside a bounded spatial region is automatically quantized in units of hbar/4*pi*e. The requirement of consistency with the quantization of electric charge observed in our Universe fixes a value of the, so far arbitrary, parameter e of the theory. Finally, we compare the ambiguity in the choice of parameter e with the beta-ambiguity that, as pointed by Immirzi, arises in the loop quantization of general relativity, and comment on a possible way this ambiguity can be fixed.

hep-th↗