Fetching the paper…
Reading the bibliography…
The original singularity theorems of Penrose and Hawking were proved for matter obeying the Null Energy Condition or Strong Energy Condition respectively.
Witten, E.: Light Rays, Singularities, and All That (2019) · 1901
Earlier work this paper cites.
Event Horizon Telescope Collaboration, et al.: First M87 Event Horizon Telescope Results. IV. Imaging the Central Supermassive Black Hole · 1906
Earlier work this paper cites.
Nuovo Cim
Epstein, H., Glaser, V., Jaffe, A.: Nonpositivity of energy density in Quantized field theories · 1965
Earlier work this paper cites.
Phys. Rev. Lett
Penrose, R.: Gravitational collapse and space-time singularities · 1965
Earlier work this paper cites.
Astrophys. J
Penzias, A.A., Wilson, R.W.: A Measurement of Excess Antenna Temperature at 4080 Mc/s · 1965
Earlier work this paper cites.
Proc. Roy. Soc. Lond
Hawking, S.W.: The Occurrence of singularities in cosmology · 1966
Earlier work this paper cites.
Astrophys. J
Hawking, S.W., Ellis, G.F.R.: The Cosmic Black-Body Radiation and the Existence of Singularities in Our Universe · 1968
Earlier work this paper cites.
Proc. Roy. Soc. London Ser. A
Hawking, S.W., Penrose, R.: The singularities of gravitational collapse and cosmology · 1970
Earlier work this paper cites.
Nature (London)
Bolton, C.T.: Identification of Cygnus X-1 with HDE 226868 · 1972
Earlier work this paper cites.
Nature (London)
Webster, B.L., Murdin, P.: Cygnus X-1-a Spectroscopic Binary with a Heavy Companion? · 1972
Earlier work this paper cites.
Cambridge University Press, London-New York (1973)
Hawking, S.W., Ellis, G.F.R.: The large scale structure of space-time · 1973
Earlier work this paper cites.
W. H. Freeman, San Francisco (1973)
Misner, C.W., Thorne, K., Wheeler, J.: Gravitation · 1973
Earlier work this paper cites.
Proc. Roy. Soc. Lond
Ford, L.H.: Quantum Coherence Effects and the Second Law of Thermodynamics · 1978
Earlier work this paper cites.
Phys. Rev
Tipler, F.J.: Energy conditions and spacetime singularities · 1978
Earlier work this paper cites.
J. Differential Equations
Tipler, F.J.: General relativity and conjugate ordinary differential equations · 1978
Earlier work this paper cites.
Manuscripta Math
Chicone, C., Ehrlich, P.: Line integration of Ricci curvature and conjugate points in Lorentzian and Riemannian manifolds · 1980
Cited alongside, same era.
Manuscripta Math
Galloway, G.J.: Some results on the occurrence of compact minimal submanifolds · 1981
Cited alongside, same era.
Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York (1983)
O’Neill, B.: Semi-Riemannian geometry, · 1983
Cited alongside, same era.
University of Chicago Press, Chicago, IL (1984)
Wald, R.M.: General relativity · 1984
Cited alongside, same era.
Math. Proc. Cambridge Philos. Soc
Galloway, G.J.: Curvature, causality and completeness in space-times with causally complete spacelike slices · 1986
Cited alongside, same era.
Class. Quant. Grav
Borde, A.: Geodesic focusing, energy conditions and singularities · 1987
Cited alongside, same era.
Phys. Rev
Fewster, C.J., Osterbrink, L.W.: Averaged energy inequalities for the non-minimally coupled classical scalar field · 2006
Later among the works it cites.
Annales Henri Poincare
Fewster, C.J., Smith, C.J.: Absolute quantum energy inequalities in curved spacetime · 2008
Later among the works it cites.
Phys. Rev
Fewster, C.J., Roman, T.A.: Null energy conditions in quantum field theory · 2009
Later among the works it cites.
In: W. Becker (ed.) Astrophysics and Space Science Library, vol. 357, p. 247 (2009)
Page, D.: Neutron Star Cooling: I · 2009
Later among the works it cites.
Fewster, C.J., Galloway, G.J.: Singularity theorems from weakened energy conditions · 2011
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Phys. Rev
Roman, T.A.: On the ’Averaged Weak Energy Condition’ and Penrose’s Singularity Theorem · 1988
Cited alongside, same era.
Phys. Rev
Wald, R.M., Yurtsever, U.: General proof of the averaged null energy condition for a massless scalar field in two-dimensional curved space-time · 1991
Cited alongside, same era.
Marcel Dekker, Inc., New York (1996)
Beem, J.K., Ehrlich, P.E., Easley, K.L.: Global Lorentzian geometry, · 1996
Cited alongside, same era.
Phys. Rev
Flanagan, E.E., Wald, R.M.: Does back reaction enforce the averaged null energy condition in semiclassical gravity? · 1996
Cited alongside, same era.
Phys. Rev
Fewster, C.J., Eveson, S.P.: Bounds on negative energy densities in flat space-time · 1998
Cited alongside, same era.
Phys. Rev. D (3)
Ford, L.H., Roman, T.A.: The quantum interest conjecture · 1999
Cited alongside, same era.
Kontou, E.A., Olum, K.D.: Proof of the averaged null energy condition in a classical curved spacetime using a null-projected quantum inequality · 2015
Later among the works it cites.
Kontou, E.A., Olum, K.D.: Quantum inequality in spacetimes with small curvature · 2015
Later among the works it cites.
Springer International Publishing, Cham (2017)
Fewster, C.J.: Quantum Energy Inequalities, pp. 215–254 · 2017
Later among the works it cites.
arXiv preprint arXiv:1807.06209 (2018)
Aghanim, N., Akrami, Y., Ashdown, M., Aumont, J., Baccigalupi, C., Ballardini, M., Banday, A., Barreiro, R., Bartolo, N., Basak, S., et al.: Planck 2018 results. VI. Cosmological parameters · 2018
Later among the works it cites.
Gen. Relativity Gravitation
Brown, P.J., Fewster, C.J., Kontou, E.A.: A singularity theorem for Einstein-Klein-Gordon theory · 2018
Later among the works it cites.
Gen. Relativity Gravitation
Lesourd, M.: A remark on the energy conditions for Hawking’s area theorem · 2018
Later among the works it cites.
In preparation
Connor, S.B., Fewster, C.J.: (2019) · 2019
Closest in time.
http://dlmf.nist.gov/, Release 1.0.22 of 2019-03-15
2019
Closest in time.
In preparation
Fewster, C.J., Kontou, E.A.: (2019) · 2019
Closest in time.
Phys. Rev. D
Fewster, C.J., Kontou, E.A.: Quantum strong energy inequalities · 2019
Closest in time.