标题： 共形标量引力与五维扭曲时空 显示英文标题

标题： Conformal Dilaton Gravity and Warped Spacetimes in 5D

摘要： 在保形不变引力理论中，在扭曲的Randall-Sundrum时空上找到了一个黑洞的时间相关精确解，通过写出度规$g_{\mu\nu}=\omega^{\frac{4}{n-2}}\tilde g_{\mu\nu}$。 这里$\tilde g_{\mu\nu}$表示“非物理”时空，而$\omega$表示标量场，它将与任何可重整化的标量场同等对待。 对于五维扭曲时空的情况，我们写出$ ^{(4)}{\tilde g_{\mu\nu}}=\bar\omega^2{ ^{(4)}\bar g_{\mu\nu}}$。两种形式$\omega$和$\bar\omega$都可以用来描述内向观察者和外部观察者对霍金辐射的不同理解，利用不同的共形规范自由度。 黑洞内部的分歧可以通过视界上点的抗极图映射来解释。 解的自由参数可以选择为使得即使对于$\omega\rightarrow 0$，$\bar g_{\mu\nu}$无奇点且拓扑规则。 值得注意的是，度规分量和标量场的5维和4维有效场方程可以写成一般维度下的$ n= 4,5$。 据推测，在视界附近的量子化过程中，只有当额外维度尺度较大时，幺正性问题才会出现在整个体积内部。 在有效理论中的减去点仅在体积内部处于紫外区域，因为使用大额外维度会导致基本的 Planck 尺度与电弱尺度相当。 显示英文摘要

摘要： An exact time-dependent solution of a black hole is found in conformally invariant gravity on a warped Randall-Sundrum spacetime, by writing the metric $g_{\mu\nu}=\omega^{\frac{4}{n-2}}\tilde g_{\mu\nu}$. Here $\tilde g_{\mu\nu}$ represents the "un-physical" spacetime and $\omega$ the dilaton field, which will be treated on equal footing as any renormalizable scalar field. In the case of a five-dimensional warped spacetime, we write $ ^{(4)}{\tilde g_{\mu\nu}}=\bar\omega^2{ ^{(4)}\bar g_{\mu\nu}}$ Both $\omega$ and $\bar\omega$ can be used to describe the different notion the in-going and outside observers have of the Hawking radiation by using different conformal gauge freedom. The disagreement about the interior of the black hole is explained by the antipodal map of points on the horizon. The free parameters of the solution can be chosen in such a way that $\bar g_{\mu\nu}$ is singular-free and topologically regular, even for $\omega\rightarrow 0$. It is remarkable that the 5D and 4D effective field equations for the metric components and dilaton fields can be written in general dimension $ n= 4,5$. It is conjectured that, in context of quantization procedures in the vicinity of the horizon, unitarity problems only occur in the bulk at large extra-dimension scale. The subtraction point in an effective theory will be in the UV only in the bulk, because the use of a large extra dimension results in a fundamental Planck scale comparable with the electroweak scale.