Periodicity and area spectrum of the three dimensional BTZ black hole

Very recently, a new scheme to quantize the horizon area of a black hole has been proposed by Zeng and Liu et?al. In this paper, we further apply the analysis to investigate area spectrum of three dimensional BTZ black hole with the cosmological constant ${\Lambda=-1/l^{2}}$ . The results show that the area spectrum and entropy spectrum are independent of the cosmological constant. The area spectrum of the black hole is ${\Delta A=8\pi l_{P}^{2}}$ , which confirms the initial proposal of Bekenstein that the area spectrum is independent of the black hole parameters and the spacing is ${8\pi l_{P}^{2}}$ . This result also confirms the speculation of Maggiore that the periodicity of a black hole may be the origin of the area quantization. In addition, for the rotating and non-rotating BTZ black holes, we obtain the same entropy spectrum ${\triangle S=2\pi}$ , which is consistent with the result for other black holes. This implies that the entropy spectrum is more fundamental than the area spectrum.     

Area Spectrum of Black Holes with Quantum Corrections via Periodicity

Using the Heisenberg uncertainty principle, Bekenstein once claimed that the horizon area of a black hole is quantized with uniform spacing $8\pi l_{p}^{2}$ . This spacing is shown to be corrected with inverse area terms from the perspective of periodicity, which indicates that the area spectrum in this case is no longer evenly spaced. Concretely we study the corrected area spectrum by equaling the motion period of an outgoing wave to the period of gravitational system in Kruskal coordinate with respect to the Euclidean time with consideration of quantum corrections to the semiclassical action. To check our result, we also study the corrected area spectrum in the framework of Generalized Uncertainty Principle. We find the area spectrum produced from the perspective of periodicity takes the same form as the one obtained by the Generalized Uncertainty Principle. As examples, area spectrum with quantum corrections of a Schwarzschild black hole and a Kerr black hole are studied. Our result shows that the formula for area spectrum with quantum corrections is universal though it is not independent of the black hole parameters. In addition, we also discuss the motion period of fermions and find that the area spectrum of a black hole is independent of particle statistics when the black hole is perturbed by an outgoing fermion.     

Approximation of the naive black hole degeneracy

In 1996, Rovelli suggested a connection between black hole entropy and the area spectrum. Using this formalism and a theorem we prove in this paper, we briefly show the procedure to calculate the quantum corrections to the Bekenstein–Hawking entropy. One can do this by two steps. First, one can calculate the “naive” black hole degeneracy without the projection constraint (in case of the $U(1)$ symmetry reduced framework) or the $SU(2)$ invariant subspace constraint (in case of the fully $SU(2)$ framework). Second, then one can impose the projection constraint or the $SU(2)$ invariant subspace constraint, obtaining logarithmic corrections to the Bekenstein–Hawking entropy. In this paper, we focus on the first step and show that we obtain infinite relations between the area spectrum and the naive black hole degeneracy. Promoting the naive black hole degeneracy into its approximation, we obtain the full solution to the infinite relations.     

The Schwarzschild black hole’s remnant via the Bohr-Sommerfeld quantization rule

A d-dimensional Schwarzschild black hole is quantized by the action variable and the Bohr-Sommerfeld quantization rule in this paper. We find that the spectra of the horizon area and the entropy are evenly spaced. The black hole mass is also quantized and it’s spectrum spacing is proportional inversely to the mass. The ground state appears and has a constant entropy $\pi k_B$ . The ground state mass is shown to be the black hole remnant predicted by the generalized uncertainty principle and may be a candidate of dark matter.     

Quantization of Horizon Area from the NUT-Kerr-Newman Black Hole

The aim of this Letter is to investigate the spectroscopy of the NUT-Kerr-Newman black hole by improving the method of revisited adiabatic invariant quantity. We present the modified expression of the adiabatic invariant quantity in the dragged–Painlevé coordinate system, and derive the spectroscopy of the black hole via revisited adiabatic invariant quantity, using Bohr–Sommerfeld quantization rule and the first law of the black hole thermodynamics. The result shows that the area and entropy spectra are respectively equally spaced and independent of black hole parameters and the area spectrum of the black hole is $\Delta A=8\pi l_{P}^{2}$ , which confirms the initial proposal of Bekenstein. It is noteworthy that there is no need to impose the small angular momentum limit and small charge limit in contrast to the quasinormal mode method.     

Area spectrum and thermodynamics of KS black holes in Hořava gravity

We investigate the area spectrum of Kehagias–Sfetsos black hole in Ho?ava–Lifshitz gravity via modified adiabatic invariant $I=\oint p_i d q_i$ I = ∮ p i d q i and Bohr–Sommerfeld quantization rule. We find that the area spectrum is equally spaced with a spacing of $ \Delta A=4 \pi l_p ^2$ Δ A = 4 π l p 2 . We have also studied the thermodynamic behavior of KS black hole by deriving different thermodynamic quantities.     

Stability of the massive graviton around a BTZ black hole in three dimensions

We investigate the massive graviton stability of the BTZ black hole obtained from three dimensional massive gravities which are classified into the parity-even and parity-odd gravity theories. In the parity-even gravity theory, we perform the $s$ -mode stability analysis by using the BTZ black string perturbations, which gives two Schrödinger equations with frequency-dependent potentials. The $s$ -mode stability is consistent with the generalized Breitenlohner-Freedman bound for spin-2 field. It seems that for the parity-odd massive gravity theory, the BTZ black hole is stable when the imaginary part of quasinormal frequencies of massive graviton is negative. However, this condition is not consistent with the $s$ -mode stability based on the second-order equation obtained after squaring the first-order equation. Finally, we explore the black hole stability connection between the parity-odd and parity-even massive gravity theories.     

Quantum tunneling of Park black hole in IR modified Ho\check{\mathrm{r}}ava gravity with cosmological constant

In this paper, we study the quantum tunneling of non-asymptotically flat Park black hole in IR modified Ho?ava gravity, as well as its thermodynamical stability. In order to calculate the quantum tunneling more comprehensively, Kraus–Parikh–Wilczek method and Hamilton–Jacoby method are used together. The results show that two methods give us the same logarithmic modified entropy, namely $S = (\alpha - \Lambda _W) A/4\alpha + \pi /\alpha \ln A/4$ . This kind of logarithmic entropy is explained well by the effect of self-gravitation in quantum tunneling picture. At tow that the thermodynamics is stable for small case ( $r_+ < r_3$ ) and unstable for large case ( $r_+ > r_3$ ) where $r_3$ is the critical position of Park solution, which is concordant with asymptotically flat case shown by Kehagias–Sfetsos (Phys. Lett. B 678:127, 2009).     

Thermodynamics and spectroscopy of charged dilaton black holes

The Bohr–Sommerfeld quantization rule is useful to study the area spectrum of black holes by employing adiabatic invariants. This method is extended to charged dilaton black holes in 2 $+$ + 1 dimensions. We put the background space-time into the Kruskal-like coordinate to find the period with respect to Euclidian time. Also assuming that the adiabatic invariant obeys Bohr–Sommerfeld quantization rule, detailed study of area and entropy spectrum has been done. It is dependent on the charge and is equally spaced as well. We also investigate the thermodynamics of the charged dilaton black hole.     

Spin and mass of the nearest supermassive black hole

Quasi-periodic oscillations (QPOs) of the hot plasma spots or clumps orbiting an accreting black hole contain information on the black hole mass and spin. The promising observational signatures for the measurement of black hole mass and spin are the latitudinal oscillation frequency of the bright spots in the accretion flow and the frequency of black hole event horizon rotation. Both of these frequencies are independent of the accretion model and defined completely by the properties of the black hole gravitational field. Interpretation of the known QPO data by dint of a signal modulation from the hot spots in the accreting plasma reveals the Kerr metric rotation parameter, \(a=0.65\pm 0.05\) , and mass, \(M=(4.2\pm 0.2)10^6M_\odot \) , of the supermassive black hole in the Galactic center. At the same time, the observed 11.5 min QPO period is identified with a period of the black hole event horizon rotation, and, respectively, the 19 min period is identified with a latitudinal oscillation period of hot spots in the accretion flow. The described approach is applicable to black holes with a low accretion rate, when accreting plasma is transparent up to the event horizon region.     

Black hole entropy with minimal length in tunneling formalism

Here we study the effects of the Generalized Uncertainty Principle in the tunneling formalism for Hawking radiation to evaluate the quantum-corrected Hawking temperature and entropy for a Schwarzschild black hole. We compare our results with the existing results given by other candidate theories of quantum gravity. In the entropy-area relation we found some new correction terms and in the leading order we found a term which varies as $\sim \sqrt{Area}$ ～ A r e a . We also get the well known logarithmic correction in the sub-leading order. We discuss the significance of this new quantum corrected leading order term.     

Quantization of Horizon Area from Accelerating and Rotating Black Hole

Based on the ideas of adiabatic invariant quantity, and as a further study, adopting near horizon approximation, we attempt to quantize the horizon area of an accelerating and rotating black hole in two different coordinate frames. The area spectrum is obtained by imposing Bohr-Sommerfeld quantization rule and the laws of black hole thermodynamics to the modified adiabatic covariant action of the rotating black hole. The results show that the area spectrum of the black hole is \(\Delta A=8\pi {l_{p}^{2}}\) , which confirms the initial proposal of Bekenstein.     

Absorption of scalars by extremal black holes in string theory

We show that the low frequency absorption cross section of minimally coupled test massless scalar fields by extremal spherically symmetric black holes in d dimensions is equal to the horizon area, even in the presence of string-theoretical \(\alpha '\) corrections. Classically one has the relation \(\sigma = 4 GS\) between that absorption cross section and the black hole entropy. By comparing in each case the values of the horizon area and Wald’s entropy, we discuss the validity of such relation in the presence of higher derivative corrections for extremal black holes in many different contexts: in the presence of electric and magnetic charges; for nonsupersymmetric and supersymmetric black holes; in \(d=4\) and \(d=5\) dimensions. The examples we consider seem to indicate that this relation is not verified in the presence of \(\alpha '\) corrections in general, although being valid in some specific cases (electrically charged maximally supersymmetric black holes in \(d=5\)). We argue that the relation \(\sigma = 4 GS\) should in general be valid for the absorption cross section of scalar fields which, although being independent from the black hole solution, have their origin from string theory, and therefore are not minimally coupled.     

Interacting Ricci Logarithmic Entropy-Corrected Holographic Dark Energy in Brans-Dicke Cosmology

In the derivation of Holographic Dark Energy (HDE), the area law of the black hole entropy assumes a crucial role. However, the entropy-area relation can be modified including some quantum effects, motivated from the Loop Quantum Gravity (LQG), string theory and black hole physics. In this paper, we study the cosmological implications of the interacting logarithmic entropy-corrected HDE (LECHDE) model in the framework of Brans-Dicke (BD) cosmology. As system’s infrared (IR) cut-off, we choose the average radius of Ricci scalar curvature, i.e. R ^?1/2. We obtain the Equation of State (EoS) parameter ω _D , the deceleration parameter q and the evolution of energy density parameter $\varOmega'_{D}$ of our model in a non-flat universe. Moreover, we study the limiting cases corresponding to our model without corrections and to the Einstein’s gravity.     

Cold, ultracold and Nariai black holes with quintessence

In this paper, we study the properties of the charged black hole surrounded by the quintessence. The solution space for the horizons for various values of the mass $M$ M , charge $Q$ Q , and the quintessence parameter $\alpha $ α are studied in detail. Special focus in given to the degenerate horizons: we obtain cold, ultracold and Nariai black holes which has similar topologies as for the Reissner–Nordstrom-de Sitter black holes. We also study the lukewarm black hole with the quintessence in this paper.     

Negative Entropy and Black Hole Information

Based on negative entropy in entanglement, it is shown that a single-system Copenhagen measurement protocol is equivalent to the two-system von Neumann scheme with the memory filling up the system with negative information similar to the Dirac sea of negative energy. After equating the two quantum measurement protocols, we then apply this equivalence to the black hole radiation. That is, the black hole evaporation corresponds to the quantum measurement process and the two evaporation approaches, the observable-based single-system and the two-system entanglement-based protocols, can be made equivalent using quantum memory. In particular, the measurement choice θ with the memory state inside the horizon in the entanglement-based scheme is shown to correspond to the observable of the measurement choice θ outside the horizon in the single-system protocol, that is, $\mathcal{O}_{\theta}^{\mathrm{out}} = Q_{\theta}^{\mathrm{in}}$ . This indicates that the black hole as quantum memory is filling up with negative information outside the horizon, and its entropy corresponds to the logarithm of a number of equally probable measurement choices. This shows that the black hole radiation is no different than ordinary quantum theory.     

Determination of the mass spectrum and the decay constant mesons consisting of c and b quarks

On the basis of an investigation into the asymptotic behavior of the correlation functions of the corresponding field currents with the necessary quantum numbers, an analytic method for determining the mass spectrum and decay constants of mesons consisting of c and b quarks with relativistic corrections is proposed. The dependence of the constituent mass of quarks on the current mass and on the orbital and radial quantum numbers is analytically derived. The mass and the wave function (WF) mesons are determined from the Schrodinger equation with a mass of constituent components particles. We calculate the splitting of the mass spectrum for the singlet and triplet states mesons, as well as to determine the width of the lepton and radiation decays due E1 transition for $\left( {\bar cc} \right)$ , $\left( {\bar bb} \right)$ , $\left( {\bar bc} \right)$ systems. Our results for the mass spectrum of mesons consisting of c and b quarks are in satisfactory agreement with the available experimental data.     

P–V criticality of topological black holes in Lovelock–Born–Infeld gravity

To understand the effect of third order Lovelock gravity, $P$ – $V$ criticality of topological AdS black holes in Lovelock–Born–Infeld gravity is investigated. The thermodynamics is further explored with some more extensions and in some more detail than the previous literature. A detailed analysis of the limit case $\beta \rightarrow \infty $ is performed for the seven-dimensional black holes. It is shown that, for the spherical topology, $P$ – $V$ criticality exists for both the uncharged and the charged cases. Our results demonstrate again that the charge is not the indispensable condition of $P$ – $V$ criticality. It may be attributed to the effect of higher derivative terms of the curvature because similar phenomenon was also found for Gauss–Bonnet black holes. For $k=0$ , there would be no $P$ – $V$ criticality. Interesting findings occur in the case $k=-1$ , in which positive solutions of critical points are found for both the uncharged and the charged cases. However, the $P$ – $v$ diagram is quite strange. To check whether these findings are physical, we give the analysis on the non-negative definiteness condition of the entropy. It is shown that, for any nontrivial value of $\alpha $ , the entropy is always positive for any specific volume $v$ . Since no $P$ – $V$ criticality exists for $k=-1$ in Einstein gravity and Gauss–Bonnet gravity, we can relate our findings with the peculiar property of third order Lovelock gravity. The entropy in third order Lovelock gravity consists of extra terms which are absent in the Gauss–Bonnet black holes, which makes the critical points satisfy the constraint of non-negative definiteness condition of the entropy. We also check the Gibbs free energy graph and “swallow tail” behavior can be observed. Moreover, the effect of nonlinear electrodynamics is also included in our research.     

Entropic Fluctuations of Quantum Dynamical Semigroups

We study a class of finite dimensional quantum dynamical semigroups $\{\mathrm {e}^{t\mathcal{L}}\}_{t\geq0}$ whose generators $\mathcal{L}$ are sums of Lindbladians satisfying the detailed balance condition. Such semigroups arise in the weak coupling (van Hove) limit of Hamiltonian dynamical systems describing open quantum systems out of equilibrium. We prove a general entropic fluctuation theorem for this class of semigroups by relating the cumulant generating function of entropy transport to the spectrum of a family of deformations of the generator ${\mathcal{L}}$ . We show that, besides the celebrated Evans-Searles symmetry, this cumulant generating function also satisfies the translation symmetry recently discovered by Andrieux et al., and that in the linear regime near equilibrium these two symmetries yield Kubo’s and Onsager’s linear response relations.