Abstract
The energy conditions of general relativity are satisfied by all experimentally detected fields. We discuss their interpretation and application to charged spheres. It is found that they prevent the existence of naked singularities, and demand that the effective gravitational mass be everywhere non-negative. We focus on the emergence of limiting configurations-sources of the Reissner-Nordström field that have vanishing effective mass everywhere within the sphere. These configurations have a number of interesting features. Among them we find that, near the center, the limiting form of the equation of state isρ+3p=0. Notably this is the only equation of state consistent with the existence of zero-point electromagnetic field, and it has been considered in different contexts, in discussions of cosmic strings and in derivations of (3+1) properties of matter from (4+1) geometry. The consistency of these configurations with the Einstein-Maxwell equations is shown by means of explicit examples. These configurations can be interpreted as due to selfinteracting gravitational effects of the zero-point electromagnetic field.
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References
Gautreau, R. (1985).Phys. Rev. D1, 1860.
Tiwari, R. N., Rao, J.R., and Kanakamedala, R. R. (1984).Phys. Rev. D30, 489.
Bonnor, B. W., and Cooperstock, F. I. (1989).Phys. Lett. A139, 442.
Hawking, S. W., and Ellis, G. F. R. (1973).The Large Scale Structure of Space-Time (Cambridge University Press, Cambridge).
Barrow, J. D. (1988).Nucl. Phys. B296, 697.
Kolb, E. (1989).Astrophys. J. 344, 543.
Vilenkin, A. (1984).Phys. Rev. Lett. 53, 1056.
Gott, J. R., and Rees, M. J. (1987).Mon. Not. R. Astron. Soc. 227, 453.
Davidson, A., and Owen, D. (1985).Phys. Lett. B155, 247.
Ponce de Leon, J., and Wesson, P.S. (1993). “Exact solutions and the effective equation of state in Kaluza-Klein theory”,J. Math. Phys. (to appear).
Cooperstock, F. I., and De La Cruz, V. (1978).Gen. Rel. Grav.,9, 835.
Herrera, L., and Ponce de Leon, J. (1985).J. Math. Phys. 26, 2302.
Tolman, Richard C. (1930).Phys. Rev. 35, 875.
Ponce de Leon, J. (1987).J. Math. Phys. 28, 410.
Ponce de Leon, J. (1988).J. Math. Phys. 29, 197.
Ponce de Leon, J. (1988).Phys. Rev. D37, 309.
Shvartsman, F. (1971).Sov. Phys. JETP 33, 475.
Ponce de Leon, J. (1987).Gen. Rel. Grav. 19, 797.
Adler, R. J. (1974).J. Math. Phys. 15, 727.
Wesson, P. S. (1991).Astrophys. J. 378, 466.
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Ponce de Leon, J. Limiting configurations allowed by the energy conditions. Gen Relat Gravit 25, 1123–1137 (1993). https://doi.org/10.1007/BF00763756
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DOI: https://doi.org/10.1007/BF00763756