标题： 黑洞时空中的重正化应力-能量计算的通用方法 显示英文标题

标题： Versatile method for renormalized stress-energy computation in black-hole spacetimes

摘要： 我们在此报告一种用于计算黑洞（BH）时空中的重整化应力-能量张量（RSET）的新方法，该方法也应该适用于动态黑洞和旋转黑洞。 此新方法仅要求时空具有单一对称性。 到目前为止，我们已经发展了三种方法变体，分别针对静态、球对称或轴对称黑洞。 我们使用这种方法计算了施瓦茨希尔德和雷斯勒-诺斯特罗姆背景下的极小耦合无质量标量场的RSET，对于几种量子态进行了计算。 这里我们给出了施瓦茨希尔德情况下的RSET结果，在Unruh态（描述黑洞蒸发的状态）下。 在弱场情况下，RSET为I型，在 $r\lesssim2.78M$ 处变为IV型。 然后我们利用RSET的结果来探讨弱能条件和零能条件的违反。 我们发现这两个条件从 $r\simeq4.9M$ 到视界都被违反。 我们还发现平均弱能条件被一类（不稳定的）圆周类时测地线违反。 最显著的是， $r=3M$ 处的圆周零测地线违反了平均零能条件。 显示英文摘要

摘要： We report here on a new method for calculating the renormalized stress-energy tensor (RSET) in black-hole (BH) spacetimes, which should also be applicable to dynamical BHs and to spinning BHs. This new method only requires the spacetime to admit a single symmetry. So far we developed three variants of the method, aimed for stationary, spherically symmetric, or axially symmetric BHs. We used this method to calculate the RSET of a minimally-coupled massless scalar field in Schwarzschild and Reissner-Nordstrom backgrounds, for several quantum states. We present here the results for the RSET in the Schwarzschild case in Unruh state (the state describing BH evaporation). The RSET is type I at weak field, and becomes type IV at $r\lesssim2.78M$. Then we use the RSET results to explore violation of the weak and null Energy conditions. We find that both conditions are violated all the way from $r\simeq4.9M$ to the horizon. We also find that the averaged weak energy condition is violated by a class of (unstable) circular timelike geodesics. Most remarkably, the circular null geodesic at $r=3M$ violates the averaged null energy condition.