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This review summarizes the current status of the energy conditions in general relativity and quantum field theory.
Beiträge zur Einsteinschen Gravitationstheorie
L. Flamm · 1916
Earlier work this paper cites.
On gauss’ theorem and the concept of mass in general relativity
E. T. Whittaker · 1935
Earlier work this paper cites.
The Particle Problem in the General Theory of Relativity
A. Einstein and N. Rosen · 1935
Earlier work this paper cites.
On the current and the density of the electric charge, the energy, the linear momentum and the angular momentum of arbitrary fields
F. J. Belinfante · 1940
Earlier work this paper cites.
Sur le tenseur d’impulsion-énergie
L. J. H. C. Rosenfeld · 1940
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An example of a new type of cosmological solutions of einstein’s field equations of gravitation
K. Gödel · 1949
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Relativistic cosmology. 1
A. Raychaudhuri · 1955
Earlier work this paper cites.
Republication of: On the physical significance of the Riemann tensor [mr0088370]
F. A. E. Pirani · 1956
Earlier work this paper cites.
Necessity of singularities in the solution of the field equations of general relativity
A. Komar · 1956
Earlier work this paper cites.
Contributions to the relativistic mechanics of continuous media
J. Ehlers · 1961
Earlier work this paper cites.
Bemerkungen zur unitäräquivalenz von lorentzinvarianten feldern
H. Reeh and S. Schlieder · 1961
Earlier work this paper cites.
The equation of state at ultra high densities and its relativistic limitations
Ya. B. Zel’dovich · 1962
Earlier work this paper cites.
Gravitational collapse and space-time singularities
R. Penrose · 1965
Earlier work this paper cites.
Nonpositivity of energy density in Quantized field theories
H. Epstein, V. Glaser, and A. Jaffe · 1965
Earlier work this paper cites.
The Occurrence of singularities in cosmology
S. Hawking · 1966
Earlier work this paper cites.
The occurrence of singularities in cosmology. iii. causality and singularities
S. W. Hawking · 1967
Earlier work this paper cites.
Topology in general relativity
R. P. Geroch · 1967
Earlier work this paper cites.
Vacuum stress between conducting plates: An Image solution
L. S. Brown and G. J. Maclay · 1969
Earlier work this paper cites.
The Singularities of gravitational collapse and cosmology
S. W. Hawking and R. Penrose · 1970
Earlier work this paper cites.
Gravitation and cosmology: principles and applications of the general theory of relativity
S. Weinberg · 1972
Earlier work this paper cites.
Black holes in general relativity
S. W. Hawking · 1972
Earlier work this paper cites.
Gravitation
C. W. Misner, K. S. Thorne, and J. A. Wheeler · 1973
Earlier work this paper cites.
The large scale structure of space-time
S. W. Hawking and G. F. R. Ellis · 1973
Earlier work this paper cites.
Quantized matter fields and the avoidance of singularities in general relativity
L. Parker and S. A. Fulling · 1973
Earlier work this paper cites.
The four laws of black hole mechanics
J. M. Bardeen, B. Carter, and S. W. Hawking · 1973
Earlier work this paper cites.
Exact solutions of einstein-conformal scalar equations
J. D. Bekenstein · 1974
Earlier work this paper cites.
Particle creation by black holes
S. W. Hawking · 1976
Earlier work this paper cites.
Singularities and Causality Violation
F. J. Tipler · 1977
Earlier work this paper cites.
Quantum Coherence Effects and the Second Law of Thermodynamics
L. H. Ford · 1978
Earlier work this paper cites.
Energy conditions and spacetime singularities
F. J. Tipler · 1978
Earlier work this paper cites.
General relativity and conjugate ordinary differential equations
F. J. Tipler · 1978
Earlier work this paper cites.
The vacuum stress tensor for automorphic fields on some flat space-times
R. Banach and J. S. Dowker · 1979
Earlier work this paper cites.
Boundary Effects in Quantum Field Theory
D. Deutsch and P. Candelas · 1979
Earlier work this paper cites.
Line integration of ricci curvature and conjugate points in lorentzian and riemannian manifolds
C. Chicone and P. Ehrlich · 1980
Earlier work this paper cites.
Semi-Riemannian geometry With Applications to Relativity
B. O’Neill · 1983
Earlier work this paper cites.
Asymptotic behavior of homogeneous cosmological models in the presence of a positive cosmological constant
R. M. Wald · 1983
Earlier work this paper cites.
General relativity
R. M. Wald · 1984
Earlier work this paper cites.
Spinors and space-time: Volume 2, Spinor and twistor methods in space-time geometry
R. Penrose and W. Rindler · 1984
Earlier work this paper cites.
The Casimir Effect
G. Plunien, B. Muller, and W. Greiner · 1986
Earlier work this paper cites.
Curvature, causality and completeness in space-times with causally complete spacelike slices
G. J. Galloway · 1986
Earlier work this paper cites.
Quantum Stress Energy Tensors and the Weak Energy Condition
T. A. Roman · 1986
Earlier work this paper cites.
Relativity, thermodynamics, and cosmology
R. C. Tolman · 1987
Earlier work this paper cites.
Geodesic focusing, energy conditions and singularities
A. Borde · 1987
Earlier work this paper cites.
The existence of singularities in general relativity despite isolated failures of geodesic focusing
A. Borde · 1987
Earlier work this paper cites.
On the ’Averaged Weak Energy Condition’ and Penrose’s Singularity Theorem
T. A. Roman · 1988
Earlier work this paper cites.
Wormholes, Time Machines, and the Weak Energy Condition
M. S. Morris, K. S. Thorne, and U. Yurtsever · 1988
Earlier work this paper cites.
The splitting theorem for space-times with strong energy condition
J.-H. Eschenburg · 1988
Earlier work this paper cites.
The lorentzian splitting theorem without the completeness assumption
G. J. Galloway · 1989
Earlier work this paper cites.
Does quantum field theory enforce the averaged weak energy condition?
U. Yurtsever · 1990
Earlier work this paper cites.
General proof of the averaged null energy condition for a massless scalar field in two-dimensional curved space-time
R. M. Wald and U. Yurtsever · 1991
Earlier work this paper cites.
The Uncertainty Relation Between Energy and Time in Non-relativistic Quantum Mechanics
L. Mandelstam and Ig. Tamm · 1991
Earlier work this paper cites.
Averaged energy conditions for free scalar fields in flat space-times
G. Klinkhammer · 1991
Earlier work this paper cites.
Closed timelike curves produced by pairs of moving cosmic strings: Exact solutions
J. R. Gott, III · 1991
Earlier work this paper cites.
Averaged-null-energy condition for electromagnetism in minkowski spacetime
A. Folacci · 1992
Earlier work this paper cites.
Chronology protection conjecture
S. W. Hawking · 1992
Earlier work this paper cites.
A positive mass theorem based on the focusing and retardation of null geodesics
R. Penrose, R. D. Sorkin, and E. Woolgar · 1993
Earlier work this paper cites.
Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics
R. M. Wald · 1994
Earlier work this paper cites.
The Warp drive: Hyperfast travel within general relativity
M. Alcubierre · 1994
Earlier work this paper cites.
Averaged energy conditions and quantum inequalities
L. H. Ford and T. A. Roman · 1995
Earlier work this paper cites.
Black Holes & Time Warps: Einstein’s Outrageous Legacy (Commonwealth Fund Book Program)
K. Thorne · 1995
Earlier work this paper cites.
Feynman Lectures on Gravitation
R. P. Feynman, F. B. Morinigo, and W. G. Wagner · 1995
Earlier work this paper cites.
General relativistic scalar-field models and asymptotic flatness
P. Hübner · 1995
Earlier work this paper cites.
Averaged energy conditions and quantum inequalities
L. H. Ford and T. A. Roman · 1995
Earlier work this paper cites.
Scale anomalies imply violation of the averaged null energy condition
M. Visser · 1995
Earlier work this paper cites.
Topological censorship
J. L. Friedman, K. Schleich, and D. M. Witt · 1995
Earlier work this paper cites.
Lorentzian wormholes: From einstein to hawking. 412 p
M. Visser · 1996
Earlier work this paper cites.
Does back reaction enforce the averaged null energy condition in semiclassical gravity?
É. É. Flanagan and R. M. Wald · 1996
Cited alongside, same era.
Stars and Relativity
Ya. B. Zel’dovich and I. D. Novikov · 1996
Cited alongside, same era.
The microlocal spectrum condition and wick polynomials of free fields on curved spacetimes
R. Brunetti, K. Fredenhagen, and M. Köhler · 1996
Cited alongside, same era.
Averaged energy conditions and evaporating black holes
L. H. Ford and T. A. Roman · 1996
Cited alongside, same era.
Warp drive and causality
A. E. Everett · 1996
Cited alongside, same era.
Quantum field theory constrains traversable wormhole geometries
L. H. Ford and T. A. Roman · 1996
Cited alongside, same era.
Quantum Energy Inequalities for the Non-Minimally Coupled Scalar Field
C. J. Fewster and L. W. Osterbrink · 2008
Later among the works it cites.
Absolute quantum energy inequalities in curved spacetime
C. J. Fewster and C. J. Smith · 2008
Later among the works it cites.
Relative entropy and the bekenstein bound
H. Casini · 2008
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Rigidity of marginally trapped surfaces and the topology of black holes
G. J. Galloway · 2008
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The Cauchy Problem in General Relativity
H. Ringström · 2009
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General Relativity and the Einstein Equations
Y. Choquet-Bruhat · 2009
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On the Attraction Between Two Perfectly Conducting Plates
H. B. G. Casimir · 1997
Cited alongside, same era.
Restrictions on negative energy density in flat spacetime
L. H. Ford and T. A. Roman · 1997
Cited alongside, same era.
Quantum inequalities in two-dimensional minkowski spacetime
É. É. Flanagan · 1997
Cited alongside, same era.
Self-consistent wormhole solutions of semiclassical gravity
D. Hochberg, A. Popov, and S. V. Sushkov · 1997
Cited alongside, same era.
A Superluminal subway: The Krasnikov tube
A. E. Everett and T. A. Roman · 1997
Cited alongside, same era.
The Unphysical nature of ’warp drive’
M. J. Pfenning and L. H. Ford · 1997
Cited alongside, same era.
H. Bostelmann and C. J. Fewster · 2009
Later among the works it cites.
Null energy conditions in quantum field theory
C. J. Fewster and T. A. Roman · 2009
Later among the works it cites.
Quantum Interest in (3+1) dimensional Minkowski space
G. Abreu and M. Visser · 2009
Later among the works it cites.
Proving the Achronal Averaged Null Energy Condition from the Generalized Second Law
A. C. Wall · 2010
Later among the works it cites.
Probability distributions of smeared quantum stress tensors
C. J. Fewster, L. H. Ford, and T. A. Roman · 2010
Later among the works it cites.
Averaged null energy condition violation in a conformally flat spacetime
D. Urban and K. D. Olum · 2010
Later among the works it cites.
Singularity theorems from weakened energy conditions
C. J. Fewster and G. J. Galloway · 2011
Later among the works it cites.
Faster than light?
R. Geroch · 2011
Later among the works it cites.
Lectures on quantum energy inequalities
C. J. Fewster · 2012
Later among the works it cites.
Time travel and warp drives: a scientific guide to shortcuts through time and space
A. Everett and T. Roman · 2012
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Local quantum physics: Fields, particles, algebras
R. Haag · 2012
Later among the works it cites.
Probability distributions for quantum stress tensors in four dimensions
C. J. Fewster, L. H. Ford, and T. A. Roman · 2012
Later among the works it cites.
Revisiting cosmic no-hair theorem for inflationary settings
A. Maleknejad and M. M. Sheikh-Jabbari · 2012
Later among the works it cites.
If vacuum energy can be negative, why is mass always positive? uses of the subdominant trace energy condition
J. D. Bekenstein · 2013
Later among the works it cites.
Quantum Energy Inequality for the Massive Ising Model
H. Bostelmann, D. Cadamuro, and C. J. Fewster · 2013
Later among the works it cites.
Negative Energy Seen By Accelerated Observers
L. H. Ford and T. A. Roman · 2013
Later among the works it cites.
Trapped Surfaces
J. M. M. Senovilla · 2013
Later among the works it cites.
No superluminal propagation for classical relativistic and relativistic quantum fields
J. Earman · 2014
Later among the works it cites.
Electromagnetism, local covariance, the aharonov–bohm effect and gauss’ law
K. Sanders, C. Dappiaggi, and T.-P. Hack · 2014
Later among the works it cites.
The null energy condition and its violation
V. A. Rubakov · 2014
Later among the works it cites.
Quantum inequality for a scalar field with a background potential
E.-A. Kontou and K. D. Olum · 2014
Later among the works it cites.
Quantum inequality in spacetimes with small curvature
E.-A. Kontou and K. D. Olum · 2015
Later among the works it cites.
Proof of the averaged null energy condition in a classical curved spacetime using a null-projected quantum inequality
E.-A. Kontou and K. D. Olum · 2015
Later among the works it cites.
Derivation of the Null Energy Condition
M. Parikh and J. P. van der Schaar · 2015
Later among the works it cites.
Averaged null energy condition and quantum inequalities in curved spacetime
E.-A. Kontou · 2015
Later among the works it cites.
Holographic proof of the averaged null energy condition
W. R. Kelly and A. C. Wall · 2015
Later among the works it cites.
The 1965 Penrose singularity theorem
J. M. M. Senovilla and D. Garfinkle · 2015
Later among the works it cites.
Republication of: Contributions to einstein’s theory of gravitation
L. Flamm · 2015
Later among the works it cites.
Entanglement equilibrium and the einstein equation
T. Jacobson · 2016
Later among the works it cites.
Negative energy densities in integrable quantum field theories at one-particle level
H. Bostelmann and D. Cadamuro · 2016
Later among the works it cites.
Proof of the Quantum Null Energy Condition
R. Bousso, Z. Fisher, J. Koeller, S. Leichenauer, and A. C. Wall · 2016
Later among the works it cites.
Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition
T. Faulkner, R. G. Leigh, O. Parrikar, and H. Wang · 2016
Later among the works it cites.
Proof of the cosmic no-hair conjecture in the 𝕋 3 \mathbb{T}^{3} -gowdy symmetric einstein–vlasov setting
H. Andréasson and H. Ringström · 2016
Later among the works it cites.
Versatile method for renormalized stress-energy computation in black-hole spacetimes
A. Levi and A. Ori · 2016
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A primer on energy conditions
E. Curiel · 2017
Later among the works it cites.
Lower bound on the energy density in classical and quantum field theories
A. C. Wall · 2017
Later among the works it cites.
Wormholes, warp drives and energy conditions
F. S. N. Lobo · 2017
Later among the works it cites.
Classical and Semi-classical Energy Conditions
P. Martín-Moruno and M. Visser · 2017
Later among the works it cites.
Quantum Energy Inequalities
C. J. Fewster · 2017
Later among the works it cites.
Local Versus Global Temperature Under a Positive Curvature Condition
K. Sanders · 2017
Later among the works it cites.
Hawking’s area theorem with a weaker energy condition
M. Lesourd · 2017
Later among the works it cites.
Renormalized stress-energy tensor of an evaporating spinning black hole
A. Levi, E. Eilon, A. Ori, and M. van de Meent · 2017
Later among the works it cites.
Recovering the QNEC from the ANEC
F. Ceyhan and T. Faulkner · 2018
Later among the works it cites.
Energy conditions in arbitrary dimensions
H. Maeda and C. Martinez · 2018
Later among the works it cites.
A singularity theorem for Einstein–Klein–Gordon theory
P. J. Brown, C. J. Fewster, and E.-A. Kontou · 2018
Later among the works it cites.
The proca field in curved spacetimes and its zero mass limit
M. Schambach and K. Sanders · 2018
Later among the works it cites.
On the global “two-sided” characteristic cauchy problem for linear wave equations on manifolds
U. Lupo · 2018
Later among the works it cites.
Quantum energy inequalities in premetric electrodynamics
C. J. Fewster, C. Pfeifer, and D. Siemssen · 2018
Later among the works it cites.
The Smeared Null Energy Condition
B. Freivogel and D. Krommydas · 2018
Later among the works it cites.
Quantum strong energy inequalities
C. J. Fewster and E.-A. Kontou · 2019
Later among the works it cites.
Light Rays, Singularities, and All That
E. Witten · 2019
Later among the works it cites.
Spacetime and geometry
S. M. Carroll · 2019
Later among the works it cites.
Upper and Lower Bounds on the Integrated Null Energy in Gravity
S. Leichenauer and A. Levine · 2019
Later among the works it cites.
Probability distributions for the stress tensor in conformal field theories
C. J. Fewster and S. Hollands · 2019
Later among the works it cites.
Achronal averaged null energy condition, weak cosmic censorship, and AdS/CFT duality
A. Ishibashi, K. Maeda, and E. Mefford · 2019
Later among the works it cites.
Self-consistent description of a spherically-symmetric gravitational collapse
D. R. Terno · 2019
Later among the works it cites.
Analysis of quantum effects inside spherical charged black holes
A. Lanir, A. Ori, N. Zilberman, O. Sela, A. Maline, and A. Levi · 2019
Later among the works it cites.
Entropy Distribution of Localised States
R. Longo · 2020
Closest in time.
A new derivation of singularity theorems with weakened energy hypotheses
C. J. Fewster and E.-A. Kontou · 2020
Closest in time.
In preparation
C. J. Fewster and E.-A. Kontou, 2020 · 2020
Closest in time.