Quantum corrections to the spectroscopy of a BTZ black hole via periodicity

Quantum corrections to the area spectrum and the entropy spectrum of a BTZ black hole are calculated by equaling the motion period of an outgoing wave coming from the quantum corrections of the semiclassical action to the period of gravitational system with respect to the Euclidean time. We find that the area spectrum and the entropy spectrum are independent of the properties of particles. Furthermore, in the presence of higher-order quantum corrections, the area spectrum is found to be corrected by inverse area terms while the entropy spectrum is found to have a universal form, $\varDelta S_{BH}=2\pi $ . Both results show that the entropy spectrum is independent of not only the BTZ black hole parameters but also the higher-order quantum corrections, which implies that the entropy spectrum is more natural than the area spectrum in quantum gravity theory.     

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.     

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.     

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.     

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.     

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.     

Periodicity and area spectrum of black holes

The recent speculation of Maggiore that the periodicity of a black hole may be the origin of the area quantization law is confirmed. We exclusively utilize the period of motion of an outgoing wave, which is shown to be related to the vibrational frequency of the perturbed black hole, to quantize the horizon areas of a Schwarzschild black hole and a Kerr black hole. It is shown that the equally spaced area spectrum for both cases takes the same form and the spacing is the same as that obtained through the quasinormal mode frequencies. Particularly, for a Kerr black hole, the small angular momentum assumption, which is necessary from the perspective of quasinormal mode, is not employed as the general area spacing is reproduced.     

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.     

Black hole entropy and the modified uncertainty principle: A heuristic analysis

Recently Ali et al. (2009) proposed a Generalized Uncertainty Principle (or GUP) with a linear term in momentum (accompanied by Plank length). Inspired by this idea here we calculate the quantum corrected value of a Schwarzschild black hole entropy and a Reissner-Nordström black hole with double horizon by utilizing the proposed generalized uncertainty principle. We find that the leading order correction goes with the square root of the horizon area contributing positively. We also find that the prefactor of the logarithmic contribution is negative and the value exactly matches with some earlier existing calculations. With the Reissner-Nordström black hole we see that this model-independent procedure is not only valid for single horizon spacetime but also valid for spacetimes with inner and outer horizons.     

Single slepton production associated with a top quark at LHC in NLO QCD

Single slepton production in association with a top quark at the CERN Large Hadron Collider (LHC) is one of the important processes in probing the R-parity violation couplings. We calculate the QCD next-to-leading order (NLO) corrections to the $pp \to t\tilde{\ell}^{-}(\bar{t}\tilde{\ell}^{+})+X$ process at the LHC and discuss the impacts of the QCD corrections on kinematic distributions. We investigate the dependence of the leading order (LO) and the NLO QCD corrected integrated cross section on the factorization/renormalization energy scale, slepton, stop-quark and gluino masses. We find that the uncertainty of the LO cross section due to the energy scale is obviously improved by the NLO QCD corrections, and the exclusive jet event selection scheme keeps the convergence of the perturbative series better than the inclusive scheme. The results show that the polarization asymmetry of the top-quark will be reduced by the NLO QCD corrections, and the QCD corrections generally increase with the increment of the $\tilde{t}_{1}$ or $\tilde {g}$ mass value.     

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.     

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.     

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.     

A New Regular Black Hole

A spherically symmetric uncharged regular black hole is proposed in this paper. The black hole’s density in proportion to $r^{3n}e^{-r^{3n+3}}$ , and the curvature tensor in the region of r=0 keep finity. When n=0 in our model, this spacetime is no other than Dymnikova regular black hole. What’s more, there are better properties in this spacetime when n>0. We then discuss the temperature and Hawking radiation of the black hole’s horizon.     

Some Properties of Generalized Quantum Operations

Let $\mathcal{B}(\mathcal{H})$ be the set of all bounded linear operators on the separable Hilbert space  $\mathcal{H}$ . A (generalized) quantum operation is a bounded linear operator defined on  $\mathcal{B}(\mathcal{H})$ , which has the form $\varPhi_{\mathcal{A}}(X)=\sum_{i=1}^{\infty}A_{i}XA_{i}^{*}$ , where $A_{i}\in\mathcal{B}(\mathcal{H})$ (i=1,2,…) satisfy $\sum_{i=1}^{\infty}A_{i}A_{i}^{*}\leq \nobreak I$ in the strong operator topology. In this paper, we establish the relationship between the (generalized) quantum operation $\varPhi_{\mathcal{A}}$ and its dual $\varPhi_{\mathcal {A}}^{\dag}$ with respect to the set of fixed points and the noiseless subspace. In particular, we also partially characterize the extreme points of the set of all (generalized) quantum operations and give some equivalent conditions for the correctable quantum channel.     

Stability of Black Holes and Black Branes

We establish a new criterion for the dynamical stability of black holes in D ≥ 4 spacetime dimensions in general relativity with respect to axisymmetric perturbations: Dynamical stability is equivalent to the positivity of the canonical energy, ${\mathcal{E}}$ , on a subspace, ${\mathcal{T}}$ , of linearized solutions that have vanishing linearized ADM mass, momentum, and angular momentum at infinity and satisfy certain gauge conditions at the horizon. This is shown by proving that—apart from pure gauge perturbations and perturbations towards other stationary black holes— ${\mathcal{E}}$ is nondegenerate on ${\mathcal{T}}$ and that, for axisymmetric perturbations, ${\mathcal{E}}$ has positive flux properties at both infinity and the horizon. We further show that ${\mathcal{E}}$ is related to the second order variations of mass, angular momentum, and horizon area by ${\mathcal{E} = \delta^2 M -\sum_A \Omega_A \delta^2 J_A - \frac{\kappa}{8\pi}\delta^2 A}$ , thereby establishing a close connection between dynamical stability and thermodynamic stability. Thermodynamic instability of a family of black holes need not imply dynamical instability because the perturbations towards other members of the family will not, in general, have vanishing linearized ADM mass and/or angular momentum. However, we prove that for any black brane corresponding to a thermodynamically unstable black hole, sufficiently long wavelength perturbations can be found with ${\mathcal{E} < 0}$ and vanishing linearized ADM quantities. Thus, all black branes corresponding to thermodynmically unstable black holes are dynamically unstable, as conjectured by Gubser and Mitra. We also prove that positivity of ${\mathcal{E}}$ on ${\mathcal{T}}$ is equivalent to the satisfaction of a “ local Penrose inequality,” thus showing that satisfaction of this local Penrose inequality is necessary and sufficient for dynamical stability. Although we restrict our considerations in this paper to vacuum general relativity, most of the results of this paper are derived using general Lagrangian and Hamiltonian methods and therefore can be straightforwardly generalized to allow for the presence of matter fields and/or to the case of an arbitrary diffeomorphism covariant gravitational action.     

Comprehensive Bayesian analysis of rare (semi)leptonic and radiative \varvec{B} decays

The available data on \(|\Delta B| = |\Delta S| = 1\) decays are in good agreement with the Standard Model when permitting subleading power corrections of about \(15\,\%\) at large hadronic recoil. Constraining new-physics effects in \(\mathcal {C}_{7}^{\mathrm {}}\) , \(\mathcal {C}_{9}^{\mathrm {}}\) , \(\mathcal {C}_{10}^{\mathrm {}}\) , the data still demand the same size of power corrections as in the Standard Model. In the presence of chirality-flipped operators, all but one of the power corrections reduce substantially. The Bayes factors are in favor of the Standard Model. Using new lattice inputs for \(B\rightarrow K^*\) form factors and under our minimal prior assumption for the power corrections, the favor shifts toward models with chirality-flipped operators. We use the data to further constrain the hadronic form factors in \(B\rightarrow K\) and \(B\rightarrow K^*\) transitions.     

Topological static spherically symmetric vacuum solutions in gravity \mathcal{F }(R,G)

The Lagrangian derivation of the Equations of Motion for topological static spherically symmetric metrics in $\mathcal{F }(R,G)$ -modified gravity is presented and the related solutions are discussed. In particular, a new topological solution for the model $\mathcal{F }(R,G)=R+\sqrt{G}$ is found. The black hole solutions and the First Law of thermodynamic are analyzed. Furthermore, the coupling with electromagnetic field is also considered and a Maxwell solution is derived.