Two-dimensional Black Hole Research Articles

Finite-mass correction to 2D black-hole evaporation rate

We numerically analyze the evolution of a two-dimensional dilatonic black hole, within the Callan-Giddings-Harvey-Strominger model. We focus our attention on the finite-mass corrections to the universal evaporation rate which applies at the large-mass limit. Our numerical results confirm a previous theoretical prediction for the first-order ($\ensuremath{\propto}1/M$) correction. In addition, our results strongly suggest that the next-order ($\ensuremath{\propto}1/{M}^{2}$) term vanishes and provide a rough estimate for the third-order term.

ENTROPY SPECTRA OF SINGLE HORIZON BLACK HOLES IN TWO DIMENSIONS

The Hod conjecture proposes that the asymptotic quasinormal frequencies determine the entropy quantum of a black hole. Considering the Maggiore modification of this conjecture, we calculate the entropy spectra of general, single horizon, asymptotically flat black holes in two-dimensional dilaton gravity. We also compute the entropy quanta of the two-dimensional Witten and AdS2 black holes. Using the results for the entropy quanta of these two-dimensional black holes, we discuss whether the produced values are generic. Finally we extend the results on the entropy spectra of other black holes.

Quasinormal frequencies of asymptotically anti-de Sitter black holes in two dimensions

We calculate exactly the quasinormal frequencies of Klein-Gordon and Dirac test fields propagating in two-dimensional uncharged Achucarro-Ortiz black hole. For both test fields we study whether the quasinormal frequencies are well defined in the massless limit. We use their values to discuss the classical stability of the quasinormal modes in uncharged Achucarro-Ortiz black hole and to check the recently proposed Time Times Temperature bound. Furthermore we extend some of these results to the charged Achucarro-Ortiz black hole.

Infrared radiative properties of two-dimensional square optical black holes

Optical black hole (OBH) is a special optical structure, in which the dielectric function or refractive index of media becomes gradually larger from the outside to the core. The circular optical black holes (COBH) have been proved remarkably useful for broadband omnidirectional light absorption. The main goal of this paper is to propose an alternative square structure of OBH due to fabrication consideration. The infrared radiative properties of two-dimensional SOBHs are numerically studied with geometric optics approximation (GOA) and the finite-difference time-domain (FDTD) method. A critical wavelength is found in this paper: when the wavelength is smaller than half of the inner core side length, the Poynting vectors obtained by the FDTD method agree well with the ray trajectories calculated by the GOA, and the absorptance is nearly 100% with a proper refractive index gradient. While the wavelength is increasing, the net energy flows do not agree with the ray trajectories and the absorptance will be decreased. The reason is attributed to the diffraction effect, which is discussed in detail in this paper.

A cylindrical optical black hole using graded index photonic crystals

The electromagnetic wave propagation of a two-dimensional optical black hole with graded index photonic crystals for transverse magnetic modes is studied. The implementation of the proposed system is validated in the metamaterial regime. The finite element method is employed in order to confirm the optical properties of the designed device. Numerical simulations show that the light incident on the device is bent toward the central area and absorbed by the inner core. As a result, the artificial optical black hole can effectively absorb the incident waves from all directions. The structure is composed of two kinds of real isotropic materials, which eases the experimental fabrication.

Quasinormal frequencies of asymptotically flat two-dimensional black holes

We discuss whether the minimally coupled massless Klein-Gordon and Dirac fields have well defined quasinormal modes in single horizon, asymptotically flat two-dimensional black holes. To get the result we solve the equations of motion in the massless limit and we also calculate the effective potentials of Schrodinger type equations. Furthermore we calculate exactly the quasinormal frequencies of the Dirac field propagating in the two-dimensional uncharged Witten black hole. We compare our results on its quasinormal frequencies with other already published.

Evaporation of two-dimensional black holes

We present a detailed analysis of results from a new study of the quantum evaporation of Callan-Giddings-Harvey-Strominger black holes within the mean-field approximation. This semiclassical theory incorporates backreaction. Our analytical and numerical calculations show that, while some of the assumptions underlying the standard evaporation paradigm are borne out, several are not. One of the anticipated properties we confirm is that the semiclassical space-time is asymptotically flat at right future null infinity ${\mathcal{I}}_{\mathrm{R}}^{+}$ yet incomplete in the sense that null observers reach a future Cauchy horizon in finite affine time. Unexpected behavior includes that the Bondi mass traditionally used in the literature can become negative even when the area of the horizon is macroscopic; an improved Bondi mass remains positive until the end of semiclassical evaporation, yet the final value can be arbitrarily large relative to the Planck mass; and the flux of the quantum radiation at ${\mathcal{I}}_{\mathrm{R}}^{+}$ is nonthermal even when the horizon area is large compared to the Planck scale. Furthermore, if the black hole is initially macroscopic, the evaporation process exhibits remarkable universal properties. Although the literature on Callan-Giddings-Harvey-Strominger black holes is quite rich, these features had escaped previous analyses, in part because of the lack of required numerical precision and in part due to misinterpretation of certain properties and symmetries of the model. Finally, our results provide support for the full quantum scenario recently developed by Ashtekar, Taveras, and Varadarajan and also offer a number of interesting problems to the mathematical relativity and geometric analysis communities.

Two-dimensional quantum black holes: numerical methods

We present details of a new numerical code designed to study the formation and evaporation of two-dimensional black holes within the Callan–Giddings–Harvey–Strominger model. We explain several elements of the scheme that are crucial to resolve the late-time behavior of the spacetime, including regularization of the field variables, compactification of the coordinates, the algebraic form of the discretized equations of motion and the use of a modified Richardson extrapolation scheme to achieve high-order convergence. Physical interpretation of our results will be discussed in detail elsewhere.

Functional integrals and energy density fluctuations on black hole background

The propagator and effective action in quantum Thirring model are derived by using variational functional integrals method. The energy density fluctuations of weak and strong coupling Fermi matter are calculated in two-dimensional black hole model, scalar field fluctuations are calculated in the same physics background. The relative ratios of density fluctuations for Fermi and scalar matter are also estimated.

Entropy and temperature from black-hole/near-horizon-CFT duality

We construct a two-dimensional CFT, in the form of a Liouville theory, in the near-horizon limit of four- and three-dimensional black holes. The near-horizon CFT assumes two-dimensional black hole solutions first introduced by Christensen and Fulling (1977 Phys. Rev. D 15 2088–104) and expanded to a greater class of black holes via Robinson and Wilczek (2005 Phys. Rev. Lett. 95 011303). The two-dimensional black holes admit a Diff(S1) subalgebra, which upon quantization in the horizon limit becomes Virasoro with calculable central charge. This charge and the lowest Virasoro eigen-mode reproduce the correct Bekenstein–Hawking entropy of the four- and three-dimensional black holes via the known Cardy formula (Blöte et al 1986 Phys. Rev. Lett. 56 742; Cardy 1986 Nucl. Phys. B 270 186). Furthermore, the two-dimensional CFT's energy–momentum tensor is anomalous. However, in the horizon limit the energy–momentum tensor becomes holomorphic equaling the Hawking flux of the four- and three-dimensional black holes. This encoding of both entropy and temperature provides a uniformity in the calculation of black hole thermodynamic and statistical quantities for the non-local effective action approach.

Interior design of a two-dimensional semiclassical black hole: Quantum transition across the singularity

We study the internal structure of a two-dimensional dilatonic evaporating black hole based on the Callan, Giddings, Harvey, and Strominger model. At the semiclassical level, a (weak) spacelike singularity was previously found to develop inside the black hole. We employ here a simplified quantum formulation of spacetime dynamics in the neighborhood of this singularity, using a minisuperspace-like approach. Quantum evolution is found to be regular and well defined at the semiclassical singularity. A well-localized initial wave packet propagating towards the singularity bounces off the latter and retains its well-localized form. Our simplified quantum treatment thus suggests that spacetime may extend semiclassically beyond the singularity, and also signifies the specific extension.

Calculation of energy density fluctuations for Fermi matter on black hole background

In this paper, the propagator and the effective potential in quantum Thirring model are derived by using the functional integral method, and the energy density fluctuations for coupled Fermi matter are calculated in two-dimensional point matter black hole and dilaton black hole models separately. We find that energy density fluctuation outside dilaton black hole is stronger under the same physical conditions.

Interior design of a two-dimensional semiclassical black hole

We look into the inner structure of a two-dimensional dilatonic evaporating black hole. We establish and employ the homogenous approximation for the black-hole interior. Two kinds of spacelike singularities are found inside the black hole, and their structure is investigated. We also study the evolution of spacetime from the horizon to the singularity.

Functional Integrals and Quantum Fluctuations on Two-Dimensional Noncommutative Space-Time

The generalized Thirring model with impurity coupling is defined on two-dimensional noncommutative space-time, a modified propagator and free energy are derived by means of functional integrals method. Moreover, quantum fluctuations and excitation energies are calculated on two-dimensional black hole and soliton background.

Geometrothermodynamics of black holes in two dimensions

We study the properties of two-dimensional dilatonic black holes from the viewpoint of geometrothermodynamics. We show that the thermodynamic curvature of the equilibrium space vanishes only in the case of a flat spacetime, and it reproduces correctly the behavior of the thermodynamic interaction and phase transition structure of the corresponding black hole configurations.

A twisted FZZ-like dual for the 2D black hole

We study the duality between string theory formulated on a curved exact background (the two-dimensional black hole) and string theory in flat space with a tachyon-like potential. We generalize previous results on this subject by discussing a twisted version of the Fateev-Zamolodchikov-Zamolodchikov conjecture (FZZ). This duality is shown to hold at the level of N -point correlation functions on the sphere topology, and connects tree-level string amplitudes in the Euclidean version of the 2D black hole to correlation functions in a nonlinear sigma-model in flat space but in presence of a tachyon wall potential and a linear dilaton. The dual CFT we propose here corresponds to the perturbed 2D quantum gravity coupled to c n = 2 momentum mode perturbation, while the usual sine-Liouville potential involved in the FZZ duality would correspond to the vortex sector n = 1. We give a precise prescription for computing correlation functions in the twisted model.

Orientifolds in 𝒩 = 2 Liouville theory and its mirror

We consider unoriented strings in the supersymmetric SL(2, )/U(1) coset, which describes the two-dimensional Euclidean black hole, and its mirror dual = 2 Liouville theory. We analyze the orientifolds of these theories from several complementary points of view: the parity symmetries of the worldsheet actions, descent from known AdS3 parities, and the modular bootstrap method (in some cases we can also check our results against known constraints coming from the conformal bootstrap method). Our analysis extends previous work on orientifolds in Liouville theory, the AdS3 and SU(2) WZW models and minimal models. Compared to these cases, we find that the orientifolds of the two dimensional Euclidean black hole exhibit new intriguing features. Our results are relevant for the study of orientifolds in the neighborhood of NS5-branes and for the engineering of four-dimensional chiral gauge theories and gauge theories with SO and Sp gauge groups with suitable configurations of D-branes and orientifolds. As an illustration, we discuss an example related to a configuration of D4-branes and O4-planes in the presence of two parallel fivebranes.

Two-dimensional black holes in a higher derivative gravity and matrix model

We construct perturbatively a class of charged black hole solutions in type 0A string theory with higher derivative terms. They have extremal limit, where the solution interpolates smoothly between near horizon AdS 2 geometry and the asymptotic linear dilaton geometry. We compute the free energy and the entropy of those solutions using various methods. In particular, we show that there is no correction in the leading term of the free energy in the large charge limit. This supports the duality of the type 0A strings on the extremal black hole and the 0A matrix model in which the tree level free energy is exact without any α ′ corrections in the leading order.

Anomalies and Hawking radiation from the Reissner–Nordström black hole with a global monopole

We extend the work by Iso, Umetsu and Wilczek (2006 Phys. Rev. Lett. 96 151302) to derive the Hawking flux via gauge and gravitational anomalies of a most general two-dimensional non-extremal black hole spacetime with the determinant of its diagonal metric differing from unity and use it to investigate Hawking radiation from the Reissner–Nordström black hole with a global monopole by requiring the cancellation of anomalies at the horizon. It is shown that the compensating energy–momentum and gauge fluxes required to cancel gravitational and gauge anomalies at the horizon are precisely equivalent to the (1 + 1)-dimensional thermal fluxes associated with Hawking radiation emanating from the horizon at the Hawking temperature. These fluxes are universally determined by the value of anomalies at the horizon.

Entanglement entropy of two-dimensional anti-de Sitter black holes

Using the AdS/CFT correspondence we derive a formula for the entanglement entropy of the anti-de Sitter black hole in two spacetime dimensions. The leading term in the large black hole mass expansion of our formula reproduces exactly the Bekenstein–Hawking entropy SBH, whereas the subleading term behaves as lnSBH. This subleading term has the universal form typical for the entanglement entropy of physical systems described by effective conformal fields theories (e.g. one-dimensional statistical models at the critical point). The well-known form of the entanglement entropy for a two-dimensional conformal field theory is obtained as analytic continuation of our result and is related with the entanglement entropy of a black hole with negative mass.