标题： 具有曲率修正项的高维引力理论中的黑洞 显示英文标题

标题： Black Holes in Higher Dimensional Gravity Theory with Quadratic in Curvature Corrections

摘要： 静态球对称黑洞在高维引力框架下，考虑曲率平方项时进行了讨论。 这类项自然地作为由量子场在引力背景中传播所诱导的量子修正的结果而出现。 我们将注意力集中在形式为${\cal C}^2=C_{\alpha\beta\gamma\delta} C^{\alpha\beta\gamma\delta}$的修正上。 四维（4D）时空中的高斯-博内方程使得这一项可以在作用量中简化为里奇张量和标量曲率的二次项。 因此，里奇平坦的史瓦西解也是具有 Weyl 标量${\cal C}^2$修正的理论解。 具有维度$D > 4$的空间的一个重要新特征是，在存在 Weyl 曲率平方项的情况下，解必然不同于相应的‘经典’真空 Tangherlini 度规。 这种差异与存在{\em 次要的}或{\em 引发的}‘毛发’有关。 我们探讨了 Tangherlini 解如何受到‘量子修正’的影响，假设引力半径$r_0$远大于量子修正的尺度。 我们还证明了，超出微扰方法寻找一般解可以归结为求解一个三阶常微分方程（主方程）。 显示英文摘要

摘要： Static spherically symmetric black holes are discussed in the framework of higher dimensional gravity with quadratic in curvature terms. Such terms naturally arise as a result of quantum corrections induced by quantum fields propagating in the gravitational background. We focus our attention on the correction of the form ${\cal C}^2=C_{\alpha\beta\gamma\delta} C^{\alpha\beta\gamma\delta}$. The Gauss-Bonnet equation in four-dimensional (4D) spacetime enables one to reduce this term in the action to the terms quadratic in the Ricci tensor and scalar curvature. As a result the Schwarzschild solution which is Ricci flat will be also a solution of the theory with the Weyl scalar ${\cal C}^2$ correction. An important new feature of the spaces with dimension $D > 4$ is that in the presence of the Weyl curvature-squared term a solution necessary differs from the corresponding `classical' vacuum Tangherlini metric. This difference is related to the presence of {\em secondary} or {\em induced} hair. We explore how the Tangherlini solution is modified by `quantum corrections', assuming that the gravitational radius $r_0$ is much larger than the scale of the quantum corrections. We also demonstrated that finding a general solution beyond the perturbation method can be reduced to solving a single third order ODE (master equation).