标题： 半经典黑洞蒸发中平均null能量条件的破坏 显示英文标题

标题： Violation of the averaged null energy condition in semiclassical black-hole evaporation

摘要： 我们在这里报告一种计算黑洞（BH）时空中重正化应力-能量张量（RSET）的新方法，该方法也应适用于动态黑洞。 我们使用此方法计算了在史瓦西和雷斯纳-诺德斯特罗姆背景下的无质量、最小耦合标量场的RSET，针对几种量子态。 我们在此呈现史瓦西情况下的RSET结果，处于厄努克状态（描述黑洞蒸发的状态）。 在弱场区域，RSET为类型I，在$r\lesssim2.78M$处变为类型IV。 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情况。 我们发现这两种条件从$r\simeq4.9M$到视界一直被违反。 我们还发现，一类（不稳定的）圆形类时测地线会违反平均弱能条件。 最显著的是，在$r=3M$处的圆形零测地线被发现违反平均零能条件（ANEC）。 据我们所知，这是首次在蒸发黑洞的物理时空中展示ANEC的违反。 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 be applicable to dynamical BHs as well. We used this method to calculate the RSET of a massless, minimally coupled 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 $r=3M$ is found to violate the averaged null energy condition (ANEC). To the best of our knowledge this is the first demonstration of ANEC violation in the physical spacetime of evaporating BH.