Loop quantum gravity and black hole entropy quantization

Abstract

Using the spin networks and the asymptotic quasinormal mode frequencies of black holes given by loop quantum gravity, the minimum horizon area gap is obtained. Then the quantum area spectrum of black holes is derived and the black hole entropy is a realized quantization. The results show that the black hole entropy given by loop quantum gravity is in full accord with the Bekenstein-Hawking entropy with a suitable Immirzi.loop quantum gravity, quasinormal mode, quantum area spectrum, black hole entropy, quantization Ever since Hawking proved that the black hole has thermal radiation, much pioneer work has been done on the black hole physics, especially on the black hole entropy. Furthermore, it has long been argued by Bekenstein that the proportionality between entropy and area [1] , for large classical black holes, can be justified from the adiabatic invariance properties of horizon area. In 1974, Bekenstein further suggested that the horizon area, when quantized, should have a discrete, equidistant spectrum in the large horizon limit [2] :where l pl is the Planck length, N integer and k a pure number of order one. Because of the proportional relation between entropy and area, it is also important to study the black hole entropy, besides the quantum area spectrums, which has important practical significance to understand the intrinsic essence and structure of the black hole entropy [3] . Furthermore the black hole entropy would have a discrete spectrum, a property that might also be expected if the black hole entropy is associated with the number of microstates compatible with a given macrostate. So the quantization of horizon area must lead to the quantization of the black hole entropy [4] . Loop quantum gravity is a non-perturbative canonical quantum gravity [5] , which can offer a quantum canonical description to quantum horizon degrees of freedom [6] .

Initiating the Effective Unification of Black Hole Horizon Area and Entropy Quantization with Quasi-Normal Modes

“…agrees with the approach of [28,29] and additionally the LQG approaches of [9,10,11] to the same order of magnitude. Therefore, at level N (M ), it was expected that the number of possible BH micro-states (or "BH micro-state space cardinality") is [30] g(N ) ∝ e A/δ = e N ∆A/δ = e γN/4 .…”

“…For this work, we prefer this semiclassical, QG-based approach over existing unification candidates such as superstring theory [6], Yukawa (10) theory [13], and E8 theory [14] because their gravitational treatment adds too many spatial degrees of freedom. Moreover, a popular alternative to QG is LQG [7][8][9][10][11], which does have 4D space-time gravity built-in by default because it fundamentally operates on the principles of general relativity. Moreover, recent emerging LQG-based approaches do yield promising results for directly counting physical states with new quantization techniques and connections to semiclassical Bekenstein-Hawking entropy [7][8][9][10][11].…”

“…There is a vast array of modern attacks that aim to conquer BHs by establishing a unified field theory with a new set of physical laws. Among these approaches, numerous mainstream unification candidates (and variations of them) exist, including, super-string theory [6], QG, loop quantum gravity (LQG) [7,8,9,10,11], Chern-Simons theory [12], Yukawa SO(10) theory [13], E8 theory [14], and others. Frequently, components and ideas from different theories are combined, adjusted, and "hacked" together (i.e.…”

“…Moreover, a popular alternative to QG is LQG [7,8,9,10,11], which does have 4D space-time gravity built-in by default because it fundamentally operates on the principles of general relativity. Moreover, recent emerging LQG-based approaches do yield promising results for directly counting physical states with new quantization techniques and connections to semi-classical Bekenstein-Hawking entropy [7,8,9,10,11]. For example we refer the reader to the holography [17,18], the origin of thermodynamics [19,20,21], spin foams [22,23], and the many open questions concerning the classical limit of generalizing static uncharged BHs to encompass charged, rotating cases.…”

Bekenstein-Smarr formula and quantization of Kerr black holes

“…Since the 1970s, Hawking and Bekenstein's pioneering work [1][2][3][4] made the study of black holes a hot topic in theoretical physics. Lots of effort devotes to the research of quantum radiation from black hole [5][6][7][8][9][10][11][12][13][14][15][16][17][18], black hole entropy [19][20][21][22][23][24] and black hole quasinormal mode [25][26][27][28][29]. In 1974, Bekenstein first proposed that the area of the black hole event horizon has an equally spaced area spectrum [30] l A kN , 1…”