Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-22T11:16:06.444Z Has data issue: false hasContentIssue false

Singularities and Scalar Fields: Matter Theory and General Relativity

Published online by Cambridge University Press:  01 April 2022

James Mattingly*
Affiliation:
Indiana University
*
Send requests for reprints to the author, Department of History and Philosophy of Science, 130 Goodbody Hall, Indiana University, Bloomington, IN 47405; email: [email protected].

Abstract

Philosophers of physics should be more attentive to the role energy conditions play in General Relativity. I review the changing status of energy conditions for quantum fields—presently there are no singularity theorems for semiclassical General Relativity. So we must reevaluate how we understand the relationship between General Relativity, Quantum Field Theory, and singularities. Moreover, on our present understanding of what it is to be a physically reasonable field, the standard energy conditions are violated classically. Thus the singularity theorems are unavailable for classical General Relativity. Our understanding of singularities in General Relativity turns on delicate issues of what it is to be a matter field—issues distinct from the content of the theory.

Type
Quantum Gravity
Copyright
Copyright © Philosophy of Science Association 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Belot, Gordon, Earman, John, and Ruetsche, Laura (1999), “The Hawking Information Loss Paradox: The Anatomy of a Controversy”, The British Journal for the Philosophy of Science 50:189229.CrossRefGoogle Scholar
Bergmann, Otto and Leipnik, Roy (1957), “Space-Time Structure of a Static Spherically Symmetric Scalar Field”, Physical Review 107:11571161.CrossRefGoogle Scholar
Earman, John (1995), Bangs, Crunches, Whimpers, and Shrieks. Oxford: Oxford University Press.Google Scholar
Ellis, Homer (1973), “Ether flow through a drainhole: A particle model in general relativity”, Journal of Mathematical Physics 14:104118.CrossRefGoogle Scholar
Epstein, H., Glaser, V., and Jaffe, A. (1965), “Nonpositivity of the Energy Density in Quantized Field Theories”, Nuovo Cimento 36:10161022.CrossRefGoogle Scholar
Flanagan, Éanna and Wald, Robert (1996), “Does back reaction enforce the averaged null energy condition in semiclassical gravity?”, Physical Review D 54, 62336283.Google ScholarPubMed
Ford, L. and Roman, Thomas (1995), “Averaged energy conditions and quantum inequalities”, Physical Review D 51:42774286.Google ScholarPubMed
Hawking, Stephen (1975), “Particle Creation by Black Holes”, Communications in Mathematical Physics 43:199220.CrossRefGoogle Scholar
Hawking, Stephen and Ellis, George (1973), The Large Scale Structure of Space-time. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Hawking, Stephen and Penrose, Roger (1970), “The singularities of gravitational collapse and cosmology”, Proceedings of the Royal Society of London A314:529548.Google Scholar
Klinkhammer, Gunnar (1991), “Averaged energy conditions for free scalar fields in flat spacetime”, Physical Review D 43:25422548.Google ScholarPubMed
Misner, Charles (1969), “Absolute Zero of Time”, Physical Review 186:13281333.10.1103/PhysRev.186.1328CrossRefGoogle Scholar
Parker, Leonard and Fulling, S.A. (1973), “Quantized Matter Fields and the Avoidance of Singularities in General Relativity”, Physical Review D 7:23572374.Google Scholar
Penrose, Roger (1965), “Gravitational Collapse and Space-time Singularities”, Physical Review Letters 14:5759.CrossRefGoogle Scholar
Penrose, Roger (1968), “Structure of Spacetime”, in DeWitt, C. and Wheeler, J. (eds.), Battelle Rencontres: 1967 Lectures in Mathematics and Physics. New York: W.A. Benjamin, Inc.Google Scholar
Roman, Thomas (1986a), “Quantum stress-energy tensors and the weak energy condition”, Physical Review D 33:35263533.Google Scholar
Roman, Thomas (1986b), “On the ‘averaged weak energy condition’ and Penrose's singularity theorem”, Physical Review D 37:546548.Google Scholar
Rose, B. (1986), “Construction of matter models which violate the strong energy condition and may avoid the initial singularity”, Classical and Quantum Gravity 3:975995.CrossRefGoogle Scholar
Rose, B. (1987), “A matter model violating the strong energy condition—the influence of temperature”, Classical and Quantum Gravity 4:10191030.10.1088/0264-9381/4/4/032CrossRefGoogle Scholar
Tipler, Frank (1977), “Energy conditions and spacetime singularities”, Physical Review D 17:25212528.Google Scholar
Visser, Matt (1995), Lorentzian Wormholes: From Einstein to Hawking. Woodbury, NY: AIP Press.Google Scholar
Visser, Matt and Barceló, Carlos (2000), “Energy Conditions and Their Cosmological Implications”, plenary talk delivered at Cosmo99, Trieste, Sept/Oct 1999. Preprint available at http://xxx.lanl.gov/abs/gr-qc/0001099.Google Scholar
Wald, Robert (1984), General Relativity. Chicago: University of Chicago Press.CrossRefGoogle Scholar
Wald, Robert (1994), Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics. Chicago: University of Chicago Press.Google Scholar
Yurtsever, Ulvi (1995a), “Averaged null energy condition and difference inequalities in quantum field theory”, Physical Review D 51:57975805.Google Scholar
Yurtsever, Ulvi (1995b), “Remarks on the averaged null energy condition in quantum field theory”, Physical Review D 52: R564R568.Google Scholar
Zel'dovitch, Ya (1961), Zh. Eksp. Teor. Fiz. 41: 1609 [Sov. Phys. JETP 14: 1143 (1962)]. Cited in Klinkhammer 1991.Google Scholar