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Motion of Inertial Observers Through Negative Energy
General Relativity and Quantum Cosmology · Submitted 31 Mar 1993
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim It seems likely that, in general, these types of negative energy fluxes are not constrained by inequalities on the magnitude and duration of the flux.
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The abstract, sentence by sentence
Recent research has indicated that negative energy fluxes due to quantum coherence effects obey uncertainty principle-type inequalities of the form $|\Delta E|\,{\Delta \tau} \lprox 1\,$. Here $|\Delta E|$ is the magnitude of the negative energy which is transmitted on a timescale $\Delta \tau$. Our main focus in this paper is on negative energy fluxes which are produced by the motion of observers through static negative energy regions. We find that although a quantum inequality appears to be satisfied for radially moving geodesic observers in two and four-dimensional black hole spacetimes, an observer orbiting close to a black hole will see a constant negative energy flux. In addition, we show that inertial observers moving slowly through the Casimir vacuum can achieve arbitrarily large violations of the inequality. It seems likely that, in general, these types of negative energy fluxes are not constrained by inequalities on the magnitude and duration of the flux. We construct a model of a non-gravitational stress-energy detector, which is rapidly switched on and off, and discuss the strengths and weaknesses of such a detector.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Recent research has indicated that negative energy fluxes due to quantum coherence effects obey uncertainty principle-type inequalities of the form $|\Delta E|\,{\Delta \tau} \lprox 1\,$. | background 1.00 | 0.04 | 0.03 | hedged possibility 0.99 |
| s1 | Here $|\Delta E|$ is the magnitude of the negative energy which is transmitted on a timescale $\Delta \tau$. | background 1.00 | 0.09 | 0.02 | asserted 0.92 |
| s2 | Our main focus in this paper is on negative energy fluxes which are produced by the motion of observers through static negative energy regions. | contribution 0.91 | 0.23 | 0.05 | asserted 0.94 |
| s3 | We find that although a quantum inequality appears to be satisfied for radially moving geodesic observers in two and four-dimensional black hole spacetimes, an observer orbiting close to a black hole will see a constant negative energy flux. | result 1.00 | 0.95 | 0.18 | asserted 0.89 |
| s4 | In addition, we show that inertial observers moving slowly through the Casimir vacuum can achieve arbitrarily large violations of the inequality. | result 1.00 | 0.93 | 0.13 | asserted 1.00 |
| s5 | It seems likely that, in general, these types of negative energy fluxes are not constrained by inequalities on the magnitude and duration of the flux. | interpretation 0.98 | 0.42 | 0.80 | hedged possibility 1.00 |
| s6 | We construct a model of a non-gravitational stress-energy detector, which is rapidly switched on and off, and discuss the strengths and weaknesses of such a detector. | method 0.85 | 0.92 | 0.02 | asserted 0.96 |
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The paper
Original abstract
Recent research has indicated that negative energy fluxes due to quantum coherence effects obey uncertainty principle-type inequalities of the form $|\Delta E|\,{\Delta \tau} \lprox 1\,$. Here $|\Delta E|$ is the magnitude of the negative energy which is transmitted on a timescale $\Delta \tau$. Our main focus in this paper is on negative energy fluxes which are produced by the motion of observers through static negative energy regions. We find that although a quantum inequality appears to be satisfied for radially moving geodesic observers in two and four-dimensional black hole spacetimes, an observer orbiting close to a black hole will see a constant negative energy flux. In addition, we show that inertial observers moving slowly through the Casimir vacuum can achieve arbitrarily large violations of the inequality. It seems likely that, in general, these types of negative energy fluxes are not constrained by inequalities on the magnitude and duration of the flux. We construct a model of a non-gravitational stress-energy detector, which is rapidly switched on and off, and discuss the strengths and weaknesses of such a detector.
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References
How the literature uses it
10 arXiv papers cite this in 14 sentences
Papers citing it · 7 sentences without a confident label
Uses its method or tool 3 papers
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Now, the energy density measured by the freely falling observer can be calculated as [ref] , [equation] by using the proper velocity and the energy-momentum tensor.
The effective Tolman temperature in curved spacetimes · Free-fall frame · 0.98
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Knowing the stress-energy tensor, we can construct the local observables, energy density and flux, following reference [ref] .
Black hole kinematics: the "in"-vacuum energy density and flux for different observers · Energy density and Fluxes · 1.00
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If we fill the spacetime by a suitable congruence of radially freely falling observers with four-velocity $u^a$, then we can construct [ref] two useful scalar quantities, at any event in spacetime, by the following definition: [equation] Here $n^a$ is the normal in the radial direction (such that $u_an^a=0$), $𝒰$ is the energy density and $ℱ$ is the flux at that event as measured by a freely falling observer.
A quantum peek inside the black hole event horizon · Introduction, Motivation and Summary of Results · 0.90
Cites it as background 3 papers
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These quantities have been studied in the literature (for example see [ref] and Appendix D of [ref] ) for the case of either an asymptotic observer who perceives the standard Hawking flux or for a radial in-faller from infinity and that too in the Unruh vacuum construction.
Black hole kinematics: the "in"-vacuum energy density and flux for different observers · Summary and Discussion · 0.87
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It may possible to violate the null energy condition with exotic forms of matter [ref] , non-minimal coupling [ref] , or quantum gravity effects [ref] , though these approaches often face challenges that we will not explore further here.
Towards the Raychaudhuri Equation Beyond General Relativity · Introduction · 0.80
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We have also been assuming that the matter content of the background, bubble interior, and bubble wall obeys the NEC; it is possible to consider cosmological models based on violations of the NEC, either through quantum gravity effects [ref] , NEC-violating matter fields (see e.g. [ref] for some common models), or non-minimal coupling [ref] .
Consistent Cosmic Bubble Embeddings · Discussion · 0.96
Discussion
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