The Abraham Zelmanov Journal
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| Title | Behaviour of the EGR persistent vacuum field following the Lichnerowicz matching conditions |
| Author | Patrick Marquet |
| Abstract | Recently, the author has proposed an extension of the General Theory of Relativity | the EGR theory, which allows for a persistent gravity-like eld to exist as a homogeneous energy density background. In this paper, we demonstrate the continuity of this eld with respect to the gravitational eld of a massive body. To achieve this goal, we make use of the Lichnerowicz conjecture which formulates the conditions required to match a hyperbolic 4-metric characterized by a material-energy tensor, with a similar type of vacuum-solution metric. This is herein applied to a spherically symmetric class of the general relativistic solutions compatible with the Schwarzschild exterior metric. The EGR covariant derivatives of the metric are then only radial and time-dependent functions: the radial persistent eld tensor component vanishes on a hypersurface separating the vacuum from the matter state. As a consequence, when this hypersurface is narrowed down to the size of a particle, it follows a non-Riemannian geodesic describing the trajectory of the particle whose mass slightly increased: this e ect can be interpreted as the bare mass carrying its subsequent gravitational eld. |
| Citation | |
| References | 1. Lichnerowicz A. Sur les equations de la gravitation. Bulletin de la Societe Mathematique de France, 1952, tome 80, 237-251. 2. Lichnerowicz A. Sur les equations riemanniennes completement harmoniques. Bulletin de la Societe Mathematique de France, 1944, tome 72, 146-68 (for- mulae 6-1). 3. Hernandez-Pastora J. L., Martin J., and Ruiz E. Admissible Lichnerowicz coor- dinates for the Schwarzschild metric. Cornell University arXiv: gr-qc/0109031. 4. Marquet P. The EGR theory: An extended formulation of General Relativity. The Abraham Zelmanov Journal, 2009, vol. 2, 148-170. 5. Lichnerowicz A. Les Theories Relativistes de la Gravitation et de l'Electro- magnetisme: Relativite Generale et Theories Unitaires. Masson et Cie, Paris, 1955. 6. Lichnerowicz A. L'integration des equations de la gravitation relativiste et le probleme des n corps. Journal de Mathematiques Pures et Appliquees, 1944, tome 23, 37-63. 7. Choquet-Bruhat Y. Maximal submanifolds and manifolds with constant mean extrinsic curvature of a Lorentzian manifold. Annali della Scuola Normale Superiore di Pisa, Classe di Science, 1976, tome 3, no. 3, 373-375. 8. Choquet-Bruhat Y. and Geroch R. Global aspects of the Cauchy problem in General Relativity. Communications in Mathematical Physics, 1969, vol. 14, no. 4, 329-335. 9. Stewart J. M. Numerical relativity. In: Classical General Relativity, Proceed- ings of the Conference on Classical (Non-Quantum) General Relativity, Lon- don, December, 1983, Cambridge University Press, 1984, 231-262. 10. Hawking S. W. and Ellis G. F. R. The Large Scale Structure of Space-Time. Cambridge University Press, 1973. 11. Bruhat Y. The Cauchy problem. In: Gravitation: An Introduction to Current Research, John Wiley & Sons, New York and London, 1962, 130-168. 12. Stephani H., Kramer D., MacCallum M., Hoenselaers C., and Herlt E. Exact Solutions of Einstein's Field Equations. Cambridge University Press, 2002. 13. Straumann N. General Relativity and Relativistic Astrophysics. Springer- Verlag, 1984. 14. Bel L. et Hamoui A. Les conditions de raccordement en relativite generale. Annales de l'Institut Henri Poincare, Section A, Physique theorique, 1967, vol. VII, no. 3, 229-244. 15. Misner C. and Sharp D. Relativistic equations for adiabatic, spherically sym- metric gravitational collapse. Physical Review, 1964, vol. 136, issue 2B, B571-B576. 16. Marquet P. On the physical nature of the wave function: A new approach through the EGR theory. The Abraham Zelmanov Journal, 2009, vol. 2, 195-207. 17. Israel W. Discontinuities in spherically symmetric gravitational elds and shells of radiation. Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, 1958, vol. 248, no. 1254, 404-414. |
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