We study the Hawking radiation emitted into the bulk by $(D+1)$-dimensional Schwarzschild black holes. It is well-known that the black-hole spectrum departs from exact blackbody form due to the frequency dependence of the `greybody' factors. For intermediate values of $D$ ($3\leq D\lesssim10$), these frequency-dependent factors may significantly modify the spectrum of the emitted radiation. However, we point out that for $D\gg1$, the typical wavelengths in the black-hole spectrum are much {\it shorter} than the size of the black hole. In this regime, the greybody factors are well described by the geometric-optics approximation according to which they are almost frequency-independent. Following this observation, we argue that for higher-dimensional black holes with $D\gg1$, the total power emitted into the bulk should be well approximated by the analytical formula for perfect blackbody radiation. We test the validity of this analytical prediction with numerical computations.
在膜宇宙学的背景下，我们的宇宙是一个3+1维的表面（“膜”）嵌入在一个五维时空（“体”）中，我们研究膜是各向异性的几何-更具体地说是Bianchi I -尽管仍然是均匀的。我们首先得到显式真空体解各向异性三维空间切片。大体积被假定为空的，但被赋予负的宇宙学常数。然后我们将Z_2对称膜嵌入到各向异性时空中，讨论了由于五维各向异性几何对膜能量动量张量的约束。我们表明，如果大部分是静态的，各向异性膜不能支持一个完美的流体。然而，我们发现，对于我们的一些体解，它是可能的嵌入膜与一个完美的流体，虽然它的能量密度和压力是完全由体几何形状。
我们探讨了在黑洞块中定位膜的可能性。我们明确地研究了BHTZ和Schwarzschild-anti de Sitter（AdS）黑洞的情况。我们的结果是，在这些情况下，膜不能仅仅由膜张力支撑，必须在膜上引入其他形式的物质。我们发现类完美流体的解决方案，遵守特殊的状态方程。对于BHTZ体几何的情况下，状态方程采取的正是一个'' Chaubergin气体''的形式，这是相关的膜上下文。在Schwarzschild-AdS的情况下，我们找到了新的状态方程，当膜位于视界附近时，这些状态方程简化为Chaubergin形式。
