Averaged null energy condition in spacetimes with boundaries

Fewster, Christopher J.; Olum, Ken D.; Pfenning, Michael J.

doi:10.1103/physrevd.75.025007

Cited by 39 publications

(68 citation statements)

References 34 publications

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“…For a broader discussion on ANEC violations see [25,26]. Here we use our RSET results to examine the various energy conditions for a MCMSF in the Unruh state (for first time as far as we know).…”

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confidence: 99%

Versatile Method for Renormalized Stress-Energy Computation in Black-Hole Spacetimes

Levi

Ori

2016

Phys. Rev. Lett.

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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 the Unruh state (the state describing BH evaporation). The RSET is type I at weak field, and becomes type IV at r 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 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.Semiclassical gravity is a theory that describes the interaction of quantum fields with a classical spacetime metric, and their coupled evolution. One of the central goals of semiclassical gravity is to allow detailed understanding of black-hole (BH) evaporation. Since Hawking's discovery in 1974 that BHs emit quantum radiation [1] and evaporate, many efforts have been made to properly formulate and analyze this dynamical process of semiclassical BH evaporation. This phenomenon is directly related to a number of profound issues like the information puzzle and loss of unitarity.To properly address semiclassical BH evaporation one should (at least in principle) solve the semiclassical Einstein equation [36] where G αβ is the Einstein tensor and T αβ ren is the quantum field's renormalized stress-energy tensor (RSET). Both sides depend on the evolving spacetime metric g αβ (x), which is the unknown in this equation. The RSET, which emerges from the field's quantum fluctuations, also depends on the type of matter field as well as on its quantum state. Throughout this paper we shall consider a minimally-coupled massless scalar field (MCMSF) φ(x), satisfying φ = 0.One of the hardest aspects in dealing with Eq. (1) is the computation of the RSET. In this paper we shall mostly address this aspect: computation of T αβ ren (and analysis thereof) for a prescribed spacetime metric g αβ (x).In principle, this computation involves summation (and integration) of the contributions to T αβ from the individual field's modes. The naive mode sum is divergent and requires regularization. This is not surprising, as the naive expectation value diverges already in flat spacetime. In flat spacetime, however, one can use the normal ordering procedure. Unfortunately, this simple procedure is not applicable in curved spacetime.Instead, in curved spacetime one can use the pointsplitting regularization which was developed by ...

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confidence: 99%

Versatile Method for Renormalized Stress-Energy Computation in Black-Hole Spacetimes

Levi

Ori

2016

Phys. Rev. Lett.

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“…Reference [2] proved that the averaged null energy condition (ANEC) holds for geodesics traveling through empty, flat space, even if elsewhere in the spacetime there are boundaries or spacetime curvature, providing that these stay some minimum distance from the geodesic and do not affect the causal structure of the spacetime near the geodesic. Here we will extend this work to geodesics traveling in curved spacetime, with the restriction that the spacetime near the geodesic must obey the null convergence condition,…”

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confidence: 99%

“…Equation (2) holds whenever the curvature is generated by a "classical background" whose stress tensor obeys the null energy condition (NEC),…”

Section: Introductionmentioning

confidence: 99%

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Averaged null energy condition in a classical curved background

Kontou

Olum

2013

Phys. Rev. D

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The Averaged Null Energy Condition (ANEC) states that the integral along a complete null geodesic of the projection of the stress-energy tensor onto the tangent vector to the geodesic cannot be negative. Exotic spacetimes, such as those allow wormholes or the construction of time machines are possible in general relativity only if ANEC is violated along achronal geodesics. Starting from a conjecture that flat-space quantum inequalities apply with small corrections in spacetimes with small curvature, we prove that ANEC is obeyed by a minimally-coupled, free quantum scalar field on any achronal null geodesic surrounded by a tubular neighborhood whose curvature is produced by a classical source.

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“…Although the present contribution is largely conceptual in scope, the ideas which led up to it have found concrete applications in providing the a priori bounds already mentioned [24,40], and in proving the averaged null energy condition for the free scalar field along null geodesics with suitable Minkowskian neighbourhoods [21]. Moreover, the local physical equivalence property and the new abstract field algebras are of independent interest.…”

Section: Introductionmentioning

confidence: 99%

Quantum energy inequalities and local covariance II: categorical formulation

Fewster

2007

Gen Relativ Gravit

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We formulate Quantum Energy Inequalities (QEIs) in the framework of locally covariant quantum field theory developed by Brunetti, Fredenhagen and Verch, which is based on notions taken from category theory. This leads to a new viewpoint on the QEIs, and also to the identification of a new structural property of locally covariant quantum field theory, which we call Local Physical Equivalence. Covariant formulations of the numerical range and spectrum of locally covariant fields are given and investigated, and a new algebra of fields is identified, in which fields are treated independently of their realisation on particular spacetimes and manifestly covariant versions of the functional calculus may be formulated.

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Averaged null energy condition in spacetimes with boundaries

Cited by 39 publications

References 34 publications

Versatile Method for Renormalized Stress-Energy Computation in Black-Hole Spacetimes

Versatile Method for Renormalized Stress-Energy Computation in Black-Hole Spacetimes

Averaged null energy condition in a classical curved background

Quantum energy inequalities and local covariance II: categorical formulation

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