Two-dimensional Charged Black Holes Research Articles

Thermodynamics of a two-dimensional charged black hole in the geometric framework

In this paper, we study the thermodynamic features of a two-dimensional charged black hole. Weinhold curvature and Ruppeiner curvature are explored as information geometry, respectively. Moreover, based on the Legendre invariant proposed by Hernando Quevedo, the geometro-thermodynamics behavior of this black hole is investigated.

Dirac quasinormal modes of two-dimensional charged dilatonic black holes

We study charged fermionic perturbations in the background of two-dimensional charged Dilatonic black holes, and we present the exact Dirac quasinormal modes. Also, we study the stability of these black holes under charged fermionic perturbations.

Low-Noise Single-Photon Detector for the 1.5-??m Wavelength Region

A simple argument is given that a traversable Cauchy horizon inside a black hole is incompatible with unitary black hole evolution. The argument assumes the validity of black hole complementarity and applies to a generic black hole carrying angular momentum and/or charge. In the second part of the paper we review recent work on the semiclassical geometry of two-dimensional charged black holes.

Global geometry of two-dimensional charged black holes

The semiclassical geometry of charged black holes is studied in the context of a two-dimensional dilaton gravity model where effects due to pair-creation of charged particles can be included in a systematic way. The classical mass-inflation instability of the Cauchy horizon is amplified and we find that gravitational collapse of charged matter results in a spacelike singularity that precludes any extension of the spacetime geometry. At the classical level, a static solution describing an eternal black hole has timelike singularities and multiple asymptotic regions. The corresponding semiclassical solution, on the other hand, has a spacelike singularity and a Penrose diagram like that of an electrically neutral black hole. Extremal black holes are destabilized by pair-creation of charged particles. There is a maximally charged solution for a given black hole mass but the corresponding geometry is not extremal. Our numerical data exhibits critical behavior at the threshold for black hole formation.

Near-extremal and extremal quantum-corrected two-dimensional charged black holes

We consider charged black holes within dilaton gravity with exponential-linear dependence of action coefficients on dilaton and minimal coupling to quantum scalar fields. This includes, in particular, CGHS and RST black holes in the uncharged limit. For non-extremal configuration quantum correction to the total mass, Hawking temperature, electric potential and metric are found explicitly and shown to obey the first generalized law. We also demonstrate that quantum-corrected extremal black holes in these theories do exist and correspond to the classically forbidden region of parameters in the sense that the total mass Mtot < Q (Q is a charge). We show that in the limit TH → 0 (where TH is the Hawking temperature) the mass and geometry of the non-extremal configuration go smoothly to those of the extremal one, except from the narrow near-horizon region. In the vicinity of the horizon the quantum-corrected geometry (however small quantum the coupling parameter κ would be) of a non-extremal configuration does not tend to the quantum-corrected extremal one but to the special branch of solutions with the constant dilaton (2D analogue of the Bertotti–Robinson metric) instead. Meanwhile, if κ = 0 exactly, the near-extremal configuration tends to the extremal one. We also consider the dilaton theory which corresponds classically to the spherically symmetrical reduction from the 4D case and show that for the quantum-corrected extremal black hole Mtot > Q.

2dstringy black holes and varying constants

Motivated by the recent interest on models with varying constants and whether black hole physics can constrain such theories, two-dimensional charged stringy black holes are considered. We exploit the role of two-dimensional stringy black holes as toy models for exploring paradoxes which may lead to constrains on a theory. A two-dimensional charged stringy black hole is investigated in two different settings. Firstly, the two-dimensional black hole is treated as an isolated object and secondly, it is contained in a thermal environment. In both cases, it is shown that the temperature and the entropy of the two-dimensional charged stringy black hole are decreased when its electric charge is increased in time. By piecing together our results and previous ones, we conclude that in the context of black hole thermodynamics one cannot derive any model independent constraints for the varying constants. Therefore, it seems that there aren't any varying constant theories that are out of favor with black hole thermodynamics.

TWO-DIMENSIONAL DILATONIC BLACK HOLES AND HAWKING RADIATION

Hawking radiation emanating from two-dimensional charged and uncharged dilatonic black holes — dimensionally reduced from (2+1) spinning and spinless, respectively, BTZ black holes — is viewed as a tunneling process. Two-dimensional dilatonic black holes (AdS(2) included) are treated as dynamical background in contrast to the standard methodology where the background geometry is fixed when evaluating Hawking radiation. This modification to the geometry gives rise to a nonthermal part in the radiation spectrum. Nonzero temperature of the extremal two-dimensional charged black hole is found. The Bekenstein–Hawking area formula is easily derived for these dynamical geometries.

Casimir effect in 2D stringy black hole backgrounds

We consider the two-dimensional ``Schwarzschild'' and ``Reissner-Nordstr\"om'' stringy black holes as systems of Casimir type. We explicitly calculate the energy-momentum tensor of a massless scalar field satisfying Dirichlet boundary conditions on two one-dimensional ``walls.'' These results are obtained using the Wald's axioms. Thermodynamical quantities such as pressure, specific heat, isothermal compressibility and entropy of the two-dimensional stringy black holes are calculated. A comparison is made between the obtained results and the laws of thermodynamics. The results obtained for the extremal $(Q=M)$ stringy two-dimensional charged black hole are identical in all three different vacua used, a fact that indicates its quantum stability.

Evaporation of a two-dimensional charged black hole

We construct a dilatonic two-dimensional model of a charged black hole. The classical solution is a static charged black hole, characterized by two parameters m and q representing the black hole's mass and charge. Then we study the semiclassical effects, and calculate the evaporation rate of both m and q, as a function of these two quantities. Analyzing this dynamical system, we find two qualitatively different regimes, depending on the electromagnetic coupling constant ${g}_{A}.$ If the latter is greater than a certain critical value, the charge-to-mass ratio decays to zero upon evaporation. On the other hand, for ${g}_{A}$ smaller than the critical value, the charge-to-mass ratio approaches a non-zero constant that depends on ${g}_{A}$ but not on the initial values of m and q.

Bogoliubov coefficients of 2D charged black holes

We exactly calculate the thermal distribution and temperature of Hawking radiation for a two-dimensional charged dilatonic black hole after it has settled down to an “equilibrium” state. The calculation is carried out using the Bogoliubov coefficients. The background of the process is furnished by a preexisting black hole and not by collapsing matter as considered by Giddings and Nelson for the case of a Schwarzschild black hole. Furthermore, the vanishing of the temperature and/or the Hawking radiation in the extremal case is obtained as a regular limit of the general case.

Are extremal 2D black holes really frozen?

In the standard methodology for evaluating the Hawking radiation emanating from a black hole, the background geometry is fixed. Trying to be more realistic we consider a dynamical geometry for a two-dimensional charged black hole and we evaluate the Hawking radiation as a tunneling process. This modification to the geometry gives rise to a nonthermal part in the radiation spectrum. We explore the consequences of this new term for the extremal case.

Quantum entropy of two-dimensional extreme charged dilaton black hole

By using Hawking's treatment as well as Zaslavskii's treatment respectively and the brick wall model, two different values of classical entropy and quantum entropy of scalar fields in the two-dimensional extreme charged dilaton black hole backgrounds have been obtained. A new divergent term emerges in the quantum entropy under the extreme limit for Zaslavskii's treatment and its connection with the phase transition has been addressed.

Charged heterotic black holes in four and two dimensions

We consider four-dimensional charged black holes occuring in toroidally compactified heterotic string theory, whose ten-dimensional interpretation involves a Kaluza-Klein monopole and a five-brane. We show that these four-dimensional black holes can be connected to two-dimensional charged heterotic black holes upon removal of the constants appearing in the harmonic functions associated with the Kaluza-Klein monopole and the five-brane.

Statistical entropy of charged two-dimensional black holes

The statistical entropy of a five-dimensional black hole in Type II string theory was recently derived by showing that it is U-dual to the three-dimensional Banados-Teitelboim-Zanelli black hole, and using Carlip's method to count the microstates of the latter. This is valid even for the non-extremal case, unlike the derivation which relies on D-brane techniques. In this letter, I shall exploit the U-duality that exists between the five-dimensional black hole and the two-dimensional charged black hole of McGuigan, Nappi and Yost, to microscopically compute the entropy of the latter. It is shown that this result agrees with previous calculations using thermodynamic arguments.

Quantized fields and temperature in charged dilatonic black hole spacetimes

The stress-energy tensor of a quantized scalar field is computed in the reduced two-dimensional charged dilatonic black hole spacetime of Garfinkle, Horowitz, and Strominger. In order for the stress-energy of quantized fields to be regular on the event horizon in both the extreme string metric and the conformally associated physical metric, it is necessary to assign a nonzero temperature, T = (8 pi e^{phi_0} M)^{-1}, to the extreme string metric, contrary to the expectation that this horizonless spacetime would have a natural temperature of zero.

Blueshift of a tachyon in the charged two-dimensional black hole.

We study the propagation of string fields (metric ${\mathit{G}}_{\mathrm{\ensuremath{\mu}}\ensuremath{\nu}}$, Maxwell gauge potential ${\mathit{A}}_{\mathrm{\ensuremath{\mu}}}$, dilaton \ensuremath{\Phi}, and tachyon T) in a two-dimensional charged black hole. It is shown that the tachyon is a propagating field both inside and outside the black hole. This becomes infinitely blueshifted at the inner horizon. We confirm that the inner horizon is unstable, whereas the outer horizon is stable.

Phase Transition in 1+1 Dimensional Charged Dilaton Black Holes

Using the Landau phase transition theory, we calculate some second moments of thermodynamical quantities for two-dimensional charged dilaton black holes. We find that some second moments diverge, and a nonequilibrium phase transition occurs when the two-dimensional charged black holes are from the nonextreme to the extreme.

Mass inflation in 2d dilaton gravity

Recently two-dimensional dilaton gravity has received great attention. We investigate two-dimensional charged black holes. These solutions possess two horizons, an event horizon and an inner, so-called Cauchy horizon. It has been argued on general grounds that the inner horizon must be unstable. We show that a minimally coupled scalar field indeed causes a mass inflation singularity to be formed at the Cauchy horizon, in striking similarity to the four-dimensional case.

Symmetries of string-effective action and spacetime geometry

A two-dimensional charged black hole solution is obtained by implementing a (2,2) transformation on the three-dimensional black string solution. Two different monopole backgrounds in five dimensions are related through an O(2,2) transformation. It has been shown in these examples that the particular O(2,2) transformation corresponds to a duality transformation.

One-loop renormalization in two-dimensional matter-dilaton quantum gravity and charged black holes

The quantum properties of two-dimensional matter-dilaton gravity — which includes a large family of actions for two-dimensional gravity (in particular, string-inspired models) — are investigated. The one-loop divergences in linear covariant gauges are calculated and the structure of the one-loop renormalization is studied. The explicit forms of the dilaton potential, dilaton-Maxwell, and dilaton-scalar couplings for which the theory is one-loop multiplicatively renormalizable are found. A comparison with the one-loop renormalization structure of four-dimensional gravity-matter theory is given. Charged multiple-horizon black holes which appear in the model are also considered.