论文标题
在同形不变重力中的动态4D BTZ黑洞溶液上
On the dynamical 4D BTZ black hole solution in conformally invariant gravity
论文作者
论文摘要
我们回顾了(2+1) - 维数二维体 - teitelboim-Zanelli黑洞溶液中的连形性重力,升至(3+1) - 维时空。作为内容,我们使用标量规范字段。公制写为$ g_ {μν} =ω^2 \ tilde g_ {μν} $,其中{\ it diLaton field fielat} $ω$包含所有比例依赖项,其中$ \ tilde g_ {μ才代表“非态” spaceTime。提出了数值溶液,并显示了如何与标量场相等的基础上处理DILATON。明显的地平线和Ergo表面的位置取决于模型的参数和初始值。找到合适的初始参数并不是一件很难的任务,以获取常规和{\ it单数免费} $ g_ {μν} $从btz-type解决方案中,用于$ \ tilde g_ {μν} $。在真空的情况下,发现了Eddington-finkelstein坐标中的{\ it Ception}时间依赖的解决方案,该解对(2+1)维BTZ时空以及对增强的(3+1)-Diblemensional BTZ时空有效。而$ \ tilde g_ {μν} $类似于标准BTZ解决方案,而$ g_ {μν} $ as {\ it Flat}。 Dilaton场成为一个无限的可重新分配量子场,该量子场将开关和关闭鹰辐射。该解决方案可用于研究模型的较小距离和黑洞互补性问题。它还可以用来描述问题如何映射遥远的观察者所见的即将辐射的量子状态,以及以一对一的方式绘制当地观察者的行为。两位观察者将使用不同的共形仪表。可能与反物质识别和单位性问题建立联系。
We review the (2+1)-dimensional Baunados-Teitelboim-Zanelli black hole solution in conformally invariant gravity, uplifted to (3+1)-dimensional spacetime. As matter content we use a scalar-gauge field. The metric is written as $g_{μν}=ω^2\tilde g_{μν}$, where the {\it dilaton field} $ω$ contains all the scale dependencies and where $\tilde g_{μν}$ represents the "un-physical" spacetime. A numerical solution is presented and shows how the dilaton can be treated on equal footing with the scalar field. The location of the apparent horizon and ergo-surface depends critically on the parameters and initial values of the model. It is not a hard task to find suitable initial parameters in order to obtain a regular and {\it singular free} $g_{μν}$ out of a BTZ-type solution for $\tilde g_{μν}$. In the vacuum situation, an {\it exact} time-dependent solution in the Eddington-Finkelstein coordinates is found, which is valid for the (2+1)-dimensional BTZ spacetime as well as for the uplifted (3+1)-dimensional BTZ spacetime. While $\tilde g_{μν}$ resembles the standard BTZ solution with its horizons, $g_{μν}$ is {\it flat}. The dilaton field becomes an infinitesimal renormalizable quantum field, which switches on and off Hawking radiation. This solution can be used to investigate the small distance scale of the model and the black hole complementarity issues. It can also be used to describe the problem how to map the quantum states of the outgoing radiation as seen by a distant observer and the ingoing by a local observer in a one-to-one way. The two observers will use a different conformal gauge. A possible connection is made with the antipodal identification and unitarity issues.