Quantum strong energy inequalities

Fewster, Christopher J.; Kontou, Eleni-Alexandra

doi:10.1103/physrevd.99.045001

Cited by 20 publications

(43 citation statements)

References 40 publications

(78 reference statements)

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“…In the timelike case the relevant QEI is the quantum strong energy inequality (QSEI) bounding the weighted renormalized effective energy density T µν U µ U ν − T/(n − 2), the quantity appearing in the SEC. Such a QSEI was derived by the authors in a recent publication [17] for the non-minimally coupled scalar field.…”

Section: Resultsmentioning

confidence: 99%

A new derivation of singularity theorems with weakened energy hypotheses

Fewster

Kontou

2020

Class. Quantum Grav.

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The original singularity theorems of Penrose and Hawking were proved for matter obeying the Null Energy Condition or Strong Energy Condition respectively. Various authors have proved versions of these results under weakened hypotheses, by considering the Riccati inequality obtained from Raychaudhuri's equation. Here, we give a different derivation that avoids the Raychaudhuri equation but instead makes use of index form methods. We show how our results improve over existing methods and how they can be applied to hypotheses inspired by Quantum Energy Inequalities. In this last case, we make quantitative estimates of the initial conditions required for our singularity theorems to apply.

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Section: Resultsmentioning

confidence: 99%

A new derivation of singularity theorems with weakened energy hypotheses

Fewster

Kontou

2020

Class. Quantum Grav.

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“…We should note however, that the only nontrivial quantum field appearing in the bound is the Wick square :Φ 2 : which enables us to show that the QEI derived is nontrivial (see Ref. 16 for more details).…”

Section: Strong Quantum Energy Inequalitymentioning

confidence: 97%

Classical and quantum strong energy inequalities and the Hawking singularity theorem

Brown¹,

Fewster²,

Kontou³

2019

Preprint

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Hawking's singularity theorem concerns matter obeying the strong energy condition (SEC), which means that all observers experience a non-negative effective energy density (EED). The SEC ensures the timelike convergence property. However, for both classical and quantum fields, violations of the SEC can be observed even in the simplest of cases, like the Klein-Gordon field. Therefore there is a need to develop theorems with weaker restrictions, namely energy conditions averaged over an entire geodesic and weighted local averages of energy densities such as quantum energy inequalities (QEIs). We present lower bounds of the EED for both classical and quantum scalar fields allowing nonzero mass and nonminimal coupling to the scalar curvature. In the quantum case these bounds take the form of a set of state-dependent QEIs valid for the class of Hadamard states. We also discuss how these lower bounds are applied to prove Hawking-type singularity theorems asserting that, along with sufficient initial contraction, the spacetime is future timelike geodesically incomplete.

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“…Following Ref. [4] and [32] we define a small sampling domain. A small sampling domain Σ is defined to be an open subset of (M, g) that (i) is contained in a globally hyperbolic convex normal neighbourhood of M , (ii) may be covered by a single hyperbolic coordinate chart {x µ }, which requires that ∂/∂x 0 is future pointing and timelike and that there exists a constant c > 0 such that…”

Section: A a General Quantum Null Energy Inequalitymentioning

confidence: 99%

The double smeared null energy condition

Fliss¹,

Freivogel²,

Kontou³

2021

Preprint

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The null energy condition (NEC), an important assumption of the Penrose singularity theorem, is violated by quantum fields. The natural generalization of the NEC in quantum field theory, the renormalized null energy averaged over a finite null segment, is known to be unbounded from below.Here, we propose an alternative, the double smeared null energy condition (DSNEC), stating that the null energy smeared over two null directions has a finite lower bound. We rigorously derive DSNEC from general worldvolume bounds for free quantum fields in Minkowski spacetime. Our method allows for future systematic inclusion of curvature corrections. As a further application of the techniques we develop, we prove additional lower bounds on the expectation values of various operators such as conserved higher spin currents. DSNEC provides a natural starting point for proving singularity theorems in semi-classical gravity.

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Quantum strong energy inequalities

Cited by 20 publications

References 40 publications

A new derivation of singularity theorems with weakened energy hypotheses

A new derivation of singularity theorems with weakened energy hypotheses

Classical and quantum strong energy inequalities and the Hawking singularity theorem

The double smeared null energy condition

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