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

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          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 \(r\lesssim2.78M\). 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.

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          Proof of the averaged null energy condition in a classical curved spacetime using a null-projected quantum inequality

          , (2015)
          Quantum inequalities are constraints on how negative the weighted average of the renormalized stress-energy tensor of a quantum field can be. A null-projected quantum inequality can be used to prove the averaged null energy condition (ANEC), which would then rule out exotic phenomena such as wormholes and time machines. In this work we derive such an inequality for a massless minimally coupled scalar field, working to first order of the Riemann tensor and its derivatives. We then use this inequality to prove ANEC on achronal geodesics in a curved background that obeys the null convergence condition.
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            Quantum inequality in spacetimes with small curvature

            , (2014)
            Quantum inequalities bound the extent to which weighted time averages of the renormalized energy density of a quantum field can be negative. They have mostly been proved in flat spacetime, but we need curved-spacetime inequalities to disprove the existence of exotic phenomena, such as closed timelike curves. In this work we derive such an inequality for a minimally-coupled scalar field on a geodesic in a spacetime with small curvature, working to first order in the Ricci tensor and its derivatives. Since only the Ricci tensor enters, there are no first-order corrections to the flat-space quantum inequalities on paths which do not encounter any matter or energy.
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              Author and article information

              Journal
              2016-08-12
              2016-11-24
              Article
              1608.03806
              de89003a-94bf-458e-9e4f-a19e478a2b22

              http://arxiv.org/licenses/nonexclusive-distrib/1.0/

              History
              Custom metadata
              5 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
              gr-qc hep-th

              General relativity & Quantum cosmology,High energy & Particle physics
              General relativity & Quantum cosmology, High energy & Particle physics

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