XXV Brazilian National Meeting on particles and fields

The celebrated area-entropy formula for black holes has provided the most important clue in the search for the elusive theory of quantum gravity. We explore the possibility that the (linear) areaentropy relation acquires some smaller corrections. Using the Boltzmann-Einstein formula, we rule out the possibility for a power-law correction, and provide severe constraints on the coefficient of a possible log-area correction. We argue that a non-zero logarithmic correction to the area-entropy relation, would also imply a modification of the area-mass relation for quantum black holes.The necessity in a quantum theory of gravity was already recognized in the 1930s. However, despite the flurry of research we still lack a complete theory of quantum gravity. It is believed that black holes may play a major role in our attempts to shed some light on the nature of a quantum theory of gravity (such as the role played by atoms in the early development of quantum mechanics).In particular, the area-entropy relation S BH = A/4ℓ2 P[1] for black holes has served as a valuable element of guidance for the quantum-gravity research. The intuition that has led Bekenstein to this discovery is actually based on very simple ingredients. In particular, to elucidate the relation between area and entropy, it is instructive to use a semiclassical version of Christodoulou's reversible processes [2,3], in which a particle is absorbed by a black hole. Bekenstein [1,4] has shown that the Heisenberg quantum uncertainty principle imposes a lower bound on the increase in black hole surface areawhere γ is a dimensionless constant of order unity, and ℓ P = G c 3 1/2h 1/2 is the Planck length. Remarkably, this bound is universal in the sense that it is independent of the black-hole parameters [5]. The universality of the fundamental lower bound is clearly a strong evidence in favor of a uniformly spaced area spectrum for quantum black holes (see Ref. [7]). Hence, one concludes that the quantization condition of the black-hole surface area should be of the formFurthermore, using the fact that the minimum increase in black-hole surface area should correspond to a minimum increase of its entropy (in order to compensate for the loss of the particle's entropy), one arrives to the proportionality between black-hole surface area and entropy S BH = ηA/ℓ 2 P . It should be recognized however that the precise values of the proportionality constants γ and η cannot be inferred from this simple line of reasoning. The very nature of Heisenberg quantum uncertainty principle allows only an order-of-magnitude estimate of the minimal increase in black-hole surface area. As a consequence, the proportionality constant η was fixed only few years later by Hawking, who determined the characteristic temperature of black holes [8].Mukhanov and Bekenstein [9,10,7] have suggested an independent argument in order to determine the value of the coefficient γ. In the spirit of Boltzmann-Einstein formula in statistical physics, they relate g n ≡ exp[S BH (n)] to the number of micro...

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confidence: 99%

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confidence: 99%

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High-order corrections to the entropy and area of quantum black holes

Hod¹

2004

“…Following the intriguing analogy of 'QBHs as atoms' [51,52,66], it is easy to derive the energy spectrum of such a QBH. The idea is to identify the quantum prediction for the outer horizon area with the classical one:…”

Section: Bekenstein-mukhanov Conjecture: Qnm Spectrummentioning

confidence: 99%

“…Notable features are the Hawking radiation and the entropy-area relation, expected to be distinctive trademarks of a full quantum BH (QBH) theory. In a tentative heuristic description of QBHs, one would expect that the fundamental quantities describing macroscopic classical BHs could play the role of unique quantum numbers characterizing their properties [51,52]. This route was undertaken by Bekenstein who, since the discovery of the entropy-area law, adopted a partial scheme to quantize BHs through the quantisation of the classical hairs of a BH: mass, electric charge, magnetic monopole, and angular momentum (which, in agreement with GW physics conventions, we will refer to as 'spin'), deriving their eigenstates for a non-extremal and stationary BH [16,53].…”

Section: Introductionmentioning

confidence: 99%

Quantum black hole spectroscopy: probing the quantum nature of the black hole area using LIGO–Virgo ringdown detections

Laghi

Carullo

Veitch

et al. 2021

We present a thorough observational investigation of the heuristic quantised ringdown model presented by Foit and Kleban (2019 Class. Quantum Grav. 36 035006). This model is based on the Bekenstein–Mukhanov conjecture, stating that the area of a black hole (BH) horizon is an integer multiple of the Planck area l P 2 multiplied by a phenomenological constant, α, which can be viewed as an additional BH intrinsic parameter. Our approach is based on a time-domain analysis of the gravitational wave (GW) signals produced by the ringdown phase of binary BH mergers detected by the LIGO and Virgo collaboration. Employing a full Bayesian formalism and taking into account the complete correlation structure among the BH parameters, we show that the value of α cannot be constrained using only GW150914, in contrast to what was suggested by Foit and Kleban (2019 Class. Quantum Grav. 36 035006). We proceed to repeat the same analysis on the new GW events detected by the LIGO and Virgo Collaboration up to 1 October 2019, obtaining a combined-event measure equal to α = 15 . 6 − 13.3 + 20.5 and a combined log odds ratio of 0.1 ± 0.6, implying that current data are not informative enough to favor or discard this model against general relativity. We then show that using a population of O ( 20 ) GW150914-like simulated events—detected by the current infrastructure of ground-based detectors at their design sensitivity—it is possible to confidently falsify the quantised model or prove its validity, in which case probing α at the few % level. Finally we classify the stealth biases that may show up in a population study.

Quasinormal spectrum and quantization of charged black holes

Hod¹

2006

Black-hole quasinormal modes have been the subject of much recent attention, with the hope that these oscillation frequencies may shed some light on the elusive theory of quantum gravity. We study analytically the asymptotic quasinormal spectrum of a charged scalar field in the (charged) ReissnerNordström spacetime. We find an analytic expression for these black-hole resonances in terms of the black-hole physical parameters: its Bekenstein-Hawking temperature TBH , and its electric potential Φ. We discuss the applicability of the results in the context of black-hole quantization. In particular, we show that according to Bohr's correspondence principle, the asymptotic resonance corresponds to a fundamental area unit ∆A = 4h ln 2.Everything in our past experience in physics tell us that general relativity and quantum theory are approximations, special limits of a single, universal theory. However, despite the flurry of research in this field we still lack a complete theory of quantum gravity. In many respects the black hole plays the same role in gravitation that the atom played in the nascent of quantum mechanics [1]. It is therefore believed that black holes may play a major role in our attempts to shed light on the nature of a quantum theory of gravity.The quantization of black holes was proposed long ago by Bekenstein [2,3], based on the remarkable observation that the horizon area of a non-extremal black hole behaves as a classical adiabatic invariant. In the spirit of the Ehrenfest principle [4] -any classical adiabatic invariant corresponds to a quantum entity with a discrete spectrum, and based on the idea of a minimal increase in black-hole surface area [2], Bekenstein conjectured that the horizon area of a quantum black hole should have a discrete spectrum of the formwhere γ is a dimensionless constant, andis the Planck length (we use units in which G = c =h = 1 henceforth). This type of area quantization has since been reproduced based on various other considerations (see e.g., [5] for a detailed list of references). In order to determine the value of the coefficient γ, Mukhanov and Bekenstein [6][7][8] have suggested, in the spirit of the Boltzmann-Einstein formula in statistical physics, to relate g n ≡ exp[S BH (n)] to the number of the black hole microstates that correspond to a particular external macro-state, where S BH is the black-hole entropy. In other words, g n is the degeneracy of the nth area eigenvalue. Now, the thermodynamic relation between black-hole surface area and entropy, S BH = A/4h, can be met with the requirement that g n has to be an integer for every n only whenwhere k is some natural number.Identifying the specific value of k requires further input. This information may emerge by applying Bohr's correspondence principle to the (discrete) quasinormal mode (QNM) spectrum of black holes [9]. Gravitational waves emitted by a perturbed black hole are dominated by this 'quasinormal ringing', damped oscillations with a discrete spectrum (see e.g., [10] for a detailed review). At late...