Abstract
This report will attempt to describe briefly a new technique in cosmological theory, and some applications, interpretations, and conjectures that can utilize it. The technique is the use of the Arnowitt, Deser, and Misnerl (ADM) Hamiltonian methods for formulating and solving the Einstein equations for homogeneous cosmological models.2 Among the applications are a simplified and more detailed presentation3 of the Mix-Master Universe.4 This is a closed universe in which it is possible5 for light rays to travel completely around the universe in certain epochs near the initial singularity. Some numerical examples of the evolution of these models have been given by Okerson.6 As another application, these techniques have allowed Ryan7’8 to give a concise description of a closed expanding universe model which has rotation as well as shear, but does not employ a cosmological constant. This Hamiltonian technique also leads to models of quantized geometry2 which should be useful as a testing ground for many ideas concerning the full quantum theory of curved space-time. The main application developed so far is a study of quantum effects on the initial singularity in closed universes which I have pursued in collaboration with Dr. Kenneth Jacobs and Professor Harold Zapolsky.9
Supported in part by NSF Grant GP8560 and NASA Grant NSG-21-002-010.
Invited talk given June 3, 1969, at the. Relativity Conference in the Midwest, Cincinnati, Ohio.
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References
Arnowitt, R., Deser, S., and Misner, C. W., Chapt. 7 in Gravitation: an introduction to current research,edited by L. Witten (Wiley, N.Y. 1962), referred to subsequently as ADM.
Misner, C. W., “Quantum Cosmology. I.” (submitted to the Physical Review).
Misner, C. W., paper in preparation (will be submitted to Proc. Roy. Soc., London).
Misner, C. W., Phys. Rev. Letters 22, 1071 (1969).
Chitre, D., unpublished Ph.D. Thesis research, University of Maryland.
Okerson, D. J., unpublished B.S. Thesis, Princeton University, 1969.
Misner, C. W. and Ryan, M., paper in preparation (for submission to Phys. Rev. Letters).
Ryan, M., unpublished Ph.D. Thesis research, University of Maryland.
Jacobs, K., Misner, C. W. and Zapolsky, H., “Quantum Cosmology. II.” paper in preparation, referred to subsequently as JMZ.
Misner, C. W., “Gravitational Collapse,” in Astrophysics and General Relativity, 1968 Brandeis Summer Institute, edited by M. Chretien, S. Deser, and J. Goldstein (Gordon and Breach, Deser, and J. 1969 ), Vol. 1, pp 198–201.
Misner, C. W., “The Absolute Zero of Time,” submitted to Physical Review.
Belinski, V. A. and Khalatnikov, I. M., to be published. I thank Professor K. S. Thorne for making this preprint available to me in an English translation by Dr. A. Pogo.
Misner, C. W., “The Absolute Zero of Time,” an unsuccessful essay submitted for the 1969 gravity essay competition (Gravity Research Foundation, New Boston, N.H.).
Isaacson, R. A., Phys. Rev. 166, 1263, 1272 (1968).
Misner, C. W., Ap. J. 151, 431 (1968)
Schelkunoff, S. A., Electromagnetic Waves ( Van Nostrand, N.Y., 1943 ), pp. 393–4.
Komar, A., “The Quantization Program for General Relativity,” these proceedings (Relativity Conference in the Midwest, Cincinnati, Ohio, 2–6 June 1969 ).
DeWitt, B. S., Phys. Rev. 160, 1113 (1967).
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Misner, C.W. (1970). Classical and Quantum Dynamics of a Closed Universe. In: Carmeli, M., Fickler, S.I., Witten, L. (eds) Relativity. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-0721-1_5
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