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

Abstract

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 $r\lesssim 2.78M$. 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 $r\simeq 4.9M$ 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.

arXiv comment5 pages, 3 figures. V2: Added two important references (Refs. [18] and [19]), which already showed ANEC violations previously, although for different fields. Title was consequently changed, and also various modifications were made in the text. Overall, the paper's content is unchanged. V3: Typo corrected. V4: Updated to match the version in PRL

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