A pulsar model from an oscillating black hole
- 49 Downloads
The first part of this paper examines conditions in accord with Einstein's criterion of regularity on the field solutions everywhere that would correspond to the existence of a black hole star, following from solutions of his (nonvacuum) field equations. ‘Black hole’ is defined here as a star whose matter is so condensed as to correspond to a complete family of spatially closed geodesics. The condition imposed is that the angular momentum of a test body in each of the closed geodesics is a constant of the motion. The second part of the paper examines the implications in the problem of the condensed star of a generalized (factorized) version of the metrical field equations, discovered earlier by the author. It is found that in general relativity stars should naturally pulsate, and in its succeeding cycles the gravitational radius of the star is attenuated by a factor exp(−0.349T), where T is the pulsation period. Conditions are discussed for the possibility that the (relatively) regular emissions of radiation from a pulsar may be dynamically rooted in a (smaller) part of the pulsation cycle when the star is out of the black hole state (less dense → open geodesics)—when radiation would be emitted to the outside world—and the (greater) part of the cycle when it is in the black hole state (more dense → closed geodesics)—when radiation would not be emitted.
KeywordsBlack Hole General Relativity Angular Momentum Field Equation Pulsation Period
Unable to display preview. Download preview PDF.
- 1.R. Adler, M. Bazin, and M. Schiffer,Introduction to General Relativity (McGraw-Hill, 1975), Second edition, chapter 6, 7.Google Scholar
- 2.A. Einstein, “Autobiographical Notes,” inAlbert Einstein-Philosopher-Scientist, P. A. Schilpp, ed. (Library of Living Philosophers, 1949), p. 81.Google Scholar
- 3.A. Einstein and N. Rosen,Phys. Rev. 48, 73 (1935).Google Scholar
- 4.S. W. Hawking and G. F. R. Ellis,The Large Scale Structure of Space-Time (Cambridge, 1973), p. 365.Google Scholar
- 5.C. Lanczos,The Variational Principles of Mechanics (Toronto, 1966), Third edition.Google Scholar
- 6.M. Sachs, “On the Nature of Light and the Problem of Matter,” inContemporary Research in the Foundations and Philosophy of Quantum Theory, C. A. Hooker, ed. (Reidel, 1973), p. 346.Google Scholar
- 7.(a)M. Sachs,Ann. Inst. H. Poincaré 28, 399 (1978);Eighth Int. Conference on General Relativity and Gravitation (Waterloo, 1977), p. 309;Google Scholar
- 7.(b)M. Sachs,Int. Jour. Theoret. Phys. 14, 115 (1975).Google Scholar
- 8.M. Sachs,Nuovo Cimento 47, 759 (1967);Nuovo Cimento 55B, 199 (1968).Google Scholar
- 9.M. Sachs,Nuovo Cimento 66B, 137 (1970).Google Scholar
- 10.P. A. M. Dirac,General Theory of Relativity (Wiley, 1975), p. 32.Google Scholar