The Immirzi parameter (also known as the Barbero-Immirzi parameter) is a numerical coefficient appearing in loop quantum gravity, a nonperturbative theory of quantum gravity. The Immirzi parameter measures the size of the quantum of area in Planck units. As a result, its value is currently fixed by matching the semiclassical black hole entropy, as calculated by Stephen Hawking, and the counting of microstates in loop quantum gravity. This article needs to be cleaned up to conform to a higher standard of article quality. ... Quantum gravity is the field of theoretical physics attempting to unify the theory of quantum mechanics, which describes three of the fundamental forces of nature, with general relativity, the theory of the fourth fundamental force: gravity. ... In physics, Planck units are physical units of measurement originally proposed by Max Planck. ... Black hole entropy is entropy carried by a black hole. ... Stephen Hawking in his classroom. ...

The reality conditions

The Immirzi parameter arises in the process of expressing a Lorentz connection with concompact group SO(3,1) in terms of a complex connection with values in a compact group of rotations, either SO(3) or its double cover SU(2). Although named after Giorgio Immirzi, the possibility of including this parameter was first pointed out by Fernando Barbero. The significance of this parameter remained obscure until the spectrum of the area operator in LQG was calculated. It turns out that the area spectrum is proportional to the Immirzi parameter.

Black hole thermodynamics

In the 1970s Hawking, motivated by the analogy between the law of increasing area of black hole event horizons and the second law of thermodynamics, carried out a semiclassical calculation showing that black holes are in equilibrium with thermal radiation outside them, and that black hole entropy (more properly, the entropy of the radiation in equilibrium with the black hole) equals This article is on the film Event Horizon. ... In physics, the second law of thermodynamics, in its many forms, is a statement about the quality and direction of energy flow, and it is closely related to the concept of entropy. ... For the 2002 science fiction movie see Equilibrium (2002 movie) Equilibrium or balance is any of a number of related phenomena in the natural and social sciences. ... Thermal radiation is electromagnetic radiation from an object that is simply caused by its temperature. ...

S = A / 4 (in Planck's units)

In 1997, Ashtekar, Baez, Corichi and Krasnov quantized the classical phase space of the exterior of a black hole in vacuum General Relativity. They showed that the geometry of spacetime outside a black hole is described by spin networks some of whose edges puncture the event horizon contributing area to it, and that the quantum geometry of the horizon can be described by a U(1) Chern-Simons theory. The appearance of the group U(1) is explained by the fact that two-dimensional geometry is described in terms of the rotation group SO(2), which is isomorphic to U(1). The relationship between area and rotations is explained by the Gauss relationship between the area of spherical triangles and their angular excess. Abhay Ashtekar is the Eberly Professor of Physics and the Director of the Center for Gravitational Physics and Geometry at Pennsylvania State University. ... John C. Baez is an American mathematical physicist who works on loop quantum gravity and applications of category theory to physics. ... Alejandro Corichi is a physicist working at the Department of Gravitation and Field Theory of the National University of Mexico (UNAM). ... A phase diagram or phase space is a useful construct used in mathematics and physics to demonstrate and visualise the changes in a given system. ... Two-dimensional visualisation of space-time distortion. ... This article just presents the basic definitions. ... In mathematics, the Chern-Simons forms are certain secondary characteristic classes. ...

By counting the number of spin-network states corresponding to a horizon of area A, the entropy of black holes is seen to equal

S = A / 4γ.

Here γ is the Immirzi parameter. It was thought to take the values

or

depending on the gauge group used in loop quantum gravity. However, Krzysztof Meissner [1] (http://arxiv.org/abs/gr-qc/0407052) and Marcin Dogamala with Jerzy Lewandowski [2] (http://arxiv.org/abs/gr-qc/0407051) have fixed an incorrect assumption that only the minimal values of the spin contributes. Their result involves the logarithm of a transcendental number instead of the logatithms of integers mentioned above. Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... In mathematics, a transcendental number is any irrational number that is not an algebraic number, i. ...

The Immirzi parameter appears in the denominator because the entropy counts the number of edges puncturing the event horizon, and the Immirzi parameter is proportional to the area contributed by each puncture.

Interpretation

The parameter may be viewed as a renormalization of Newton's constant. Various speculative proposals to explain this parameter have been suggested: for example, an argument due to Olaf Dreyer based on quasinormal modes. As of today, no alternative calculation of this constant exists. If a second match with experiment or theory (for example, the value of Newton's force at long distance) were found requiring a different value of the Immirzi parameter, it would constitute evidence that loop quantum gravity cannot reproduce the physics of general relativity at long distances. On the other hand, the Immirzi parameter seems to be the only free parameter of vacuum LQG, and once it is fixed by matching one calculation to an "experimental" result, it could in principle be used to predict other experimental results. Unfortunately, no such alternative calculations have been made so far. According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ... Olaf Dreyer is a German theoretical physicist, currently a postdoc at the Perimeter Institute in Waterloo, Canada. ... In theoretical physics, a quasinormal mode is a formal solution of linearized differential equations (such as the linearized equations of general relativity constraining perturbations around a black hole solution) with a complex eigenvalue (frequency). ... Two-dimensional visualisation of space-time distortion. ...

External links

• Quantum Geometry and Black Hole Entropy (http://xxx.lanl.gov/abs/gr-qc/9710007), the original vacuum LQG calculation of BH entropy.
• Quantum Geometry of Isolated Horizons and Black Hole Entropy (http://xxx.lanl.gov/abs/gr-qc/0005126), a calculation incorporating matter and the theory of isolated horizons from General Relativity.