Black-hole entropy from quantum geometry

By Marcin Domagala, J. Lewandowski. 2004

422 citations recorded by the source corpus.

Quantum geometry (the modern loop quantum gravity involving graphs and spin-networks instead of the loops) provides microscopic degrees of freedom that account for black-hole entropy. However, the procedure for state counting used in the literature contains an error and the number of the relevant horizon states is underestimated. In our paper a correct method of counting is presented. Our results lead to a revision of the literature of the subject. It turns out that the contribution of spins greater than 1/2 to the entropy is not negligible. Hence, the value of the Barbero–Immirzi parameter involved in the spectra of all the geometric and physical operators in this theory is different than previously derived. Also, the conjectured relation between quantum geometry and the black-hole quasi-normal modes should be understood again.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/498af287e87c6e39f174411df0cd6cab269e7683

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Citations in the corpus

On the classification of asymptotic quasinormal frequencies for $d$-dimensional black holes and quantum gravity (2004, methodology): “lly has that γobeys a complicated functional relationship and is a number which lies in the range [87] log2 π ≤ γ 1 ≤ log3 π . However, it does not seem that this number can be written as a logarithm [86, 87] which would even invalidate an attempt to match it against the Schwarzschild asymptotic qua”
Gravity and the quantum (2004, methodology): “ Lewandowski [ 47 ] and Meissner [48].”
Loop quantum gravity: an outside view (2005, background): “the horizon would imply a prediction for the value of the parameter γ. Unfortunately, the results obtained so far disagree; for instance, [36] obtains γ= ln2 π √ 3 , whereas a more recent calculation [83, 84] gives γ= 0.23753295.... We suspect that the ﬁnal word has not yet been spoken on this subje”
Introduction to loop quantum gravity and spin foams (2004, methodology): “rding to the previous deﬁnition. The graph consists of a single closed edge (e= γ) and an example is shown in Figure 2. Notice, however, that we can also deﬁne Wγ[A] as Wγ[A] := Tr[he 1 [A]he 2 [A]], (75) using (68) in which case W γ[A] ∈ Cyl ′ (γ′ is illustrated in the center of Figure 2). Moreover”
Isolated and Dynamical Horizons and Their Applications (2004, background): “of the dimension N of a well-deﬁned sub-space HBH S of the surface Hilbert space, namely the linear span of those surface states which occur in HBH. Entropy S∆ is given by lnN. A detailed calculation [83, 149] leads to the following expression of entropy: S∆ = γo γ ao 4ℓ2 Pl − 1 2 ln ao ℓ2 Pl +o(ln ”
Loop Quantum Cosmology (2005, background): “The spectrum depends on the value of the Barbero–Immirzi parameter, which can accordingly be fixed using implications of the spectrum such as black hole entropy, which gives a value of the order of but smaller than one [11, 12, 108, 155].”
Loop quantum cosmology of Bianchi type IX models (2009, background): “2375 due to black hole entropy calculations [37]).”
Quantum gravity in terms of topological observables (2005, background): “It affects the prediction of the spectra of geometrical operators and plays a key role in the black hole entropy calculation [11].”