The Coordination Chemistry of Tungsten

Approximate solution to the Callan-Giddings-Harvey-Strominger field equations for two-dimensional evaporating black holes

“…It will be interesting to check this approximate solution against numerical simulations of the CGHS field equations. Such numerical simulations are currently being conducted by several groups [5,6]. A preliminary comparison with the numerical results [5] shows nice agreement, though a more comprehensive check still needs to be carried out.…”

“…This scaling makes it obvious that the relative magnitude of semiclassical effects in various regions of spacetime will not be determined by K or R separately, but only through (dimensionless 4 ) combinations like K/R or K/e S , which are invariant to the rescaling. 5 One can easily verify that in the above scaling transformation the BH original mass M 0 is multiplied by c. It is a common wisdom that when a BH is "macroscopic", semiclassical effects will be locally weak 6 (except in the neighborhood of the singularity). The above scaling law makes it obvious that whether a BH may be regarded as "macroscopic" or not, would only depend on the ratio of M 0 and K: A CGHS BH should be regarded as macroscopic if M 0 K-which we indeed assume throughout this paper.…”

“…5 One can easily verify that in the above scaling transformation the BH original mass M 0 is multiplied by c. It is a common wisdom that when a BH is macroscopic, semiclassical effects will be locally weak 6 (except in the neighborhood of the singularity). The above scaling law makes it obvious that whether a BH may be regarded as macroscopic or not would only depend on the ratio of M 0 and K: A CGHS BH should be regarded as macroscopic if M 0 ) K-which we indeed assume throughout this paper.…”

“…The general analytical solution to the CGHS field equations is not known. Nevertheless, these equations can be explored analytically [3] as well as numerically [4,5,6]. The global structure which emerges from these studies is depicted in Fig.…”

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

“…In both stages (ii) and (iii), the evolution can be analyzed either numerically or by certain analytic approximations (which are beyond the scope of the present paper). A numerical simulation of the semiclassical CGHS field equations is underway [10,11], and perhaps it will be possible to extend this numerics to the post-singularity region as well. By this way it should be possible to determine the semiclassical spacetime [particularly the functions R(u, v) and S(u, v)] in the entire future "domain of dependence" of the spacelike line R = 0, the triangle-like region denoted by D [which is actually D + (R = 0)] in Fig.…”