On the conformal equivalence between 2D black holes and Rind(6)

发布时间:2021-06-06

We study a two-dimensional dilaton gravity model related by a conformal transformation of the metric to the Callan-Giddings-Harvey-Strominger model. We find that most of the features and problems of the latter can be simply understood in terms of the class

which is in agreement with the CGHS result.Our results simply state that the semiclassical behavior of our black holes is described by a quantumfield theory of accelerated observers in Minkowski space.The physical interpretation of the associated thermal radiation deserves however careful analysis.It is in fact evident that it cannot be interpreted in the usual way, as the Hawking radiation seen by an observer in an asymptoticallyflat spacetime region. This prevents the usual interpretation of the Hawking effect as the distortion,due to the black hole geometry,of incoming quantum modes defined in aflat region into outcoming ones defined in anotherflat region.The point is that in our model the black hole geometry is truly equivalent to that seen by accelerated observers in Minkowski space.The event horizon of the black hole has to be considered as an acceleration horizon.This discussion clarifies a point which appears rather puzzling in the CGHS model.The CGHS black holes have temperature and Hawkingflux,given by(6)and(12)respectively,independent of the mass of the black hole;there is no explanation of this fact in CGHS theory.In our model a natural explanation of this fact is at hand:the thermal properties are independent of the mass because the semiclassical dynamics of the black hole is equivalent to that of accelerated observers,they depend only on the parameterλwhich defines the proper acceleration of these observers.Moreover our results restore some of the physical intuition about the equivalence of the models under the rescaling of the metric(2).What we have found is that the models(1)and(3)have an equivalent classical and semiclassical dynamics.Indeed the two metrics,being related by a Weyl rescaling,have the same causal structure(the same Penrose diagram)and at the semiclassical level have the same thermal properties.

Atfirst glance our result seems to contradict the well-known relationship between conformal anomaly and Hawking radiation.Being the black hole spacetime everywhere flat the conformal anomaly vanishes and there should be no Hawking radiation.However the presence of thermal radiation in our model is related to a topological effect which is independent of the presence of a conformal anomaly.On the other hand the possibility of having Hawking radiation in globallyflat spaces is related to the anomalous transformation law of the quantum energy-momentum tensor T−−under coordinates change.

To conclude this letter let us comment about the question of the stability of the ground state in our model and in the related CGHS model.Soon after the discovery of the CGHS model it was realised that the semiclassical ground state of this model is unstable and plagued by the presence of naked singularities[2].The meaning and the origin of this instability has been further clarified in Ref.[5],where a dynamical moving mirror inflat spacetime was used to model the semiclassical evolution of a CGHS black hole. It was found that vacuum solution do exist which describe a forever accelerating mirror resulting in an unphysical process of a forever radiating black hole.These features have a natural explanation in the context of our model.Differently from the CGHS case,for which the classical vacuum(the so called linear dilaton vacuum)is a perfectly regular and geodesically complete spacetime,in our model one can define consistently a classical ground state only using a cosmic censorship conjecture to rule out the states with negative mass. Moreover this vacuum does not describe a complete spacetime but Minkowsky space with a light-like boundary.The presence of this boundary is a potential source of instability of the vacuum.This can be easily understood if one allows in the spectrum the states

5

On the conformal equivalence between 2D black holes and Rind(6).doc 将本文的Word文档下载到电脑

精彩图片

热门精选

大家正在看

× 游客快捷下载通道(下载后可以自由复制和排版)

限时特价:7 元/份 原价:20元

支付方式:

开通VIP包月会员 特价:29元/月

注:下载文档有可能“只有目录或者内容不全”等情况,请下载之前注意辨别,如果您已付费且无法下载或内容有问题,请联系我们协助你处理。
微信:fanwen365 QQ:370150219