Artículos científicos
Cómo citar
González, G. A. (2001). Soluciones de las ecuaciones de Einstein mediante el procedimiento de Papapetrou. Revista Integración, Temas De matemáticas, 19(2), 58–67. Recuperado a partir de https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/739
Resumen
Se presenta un procedimiento, debido a Papapetrou, mediante el cual se pueden generar soluciones de las ecuaciones de Einstein en el vacío para espacio-tiempos estacionarios axialmente simétricos partiendo de soluciones de Weyl correspondientes a espacio-tiempos estáticos axial-mente simétricos. Con el fin de ilustrar el procedimiento, se presentan tres ejemplos específicos, obtenidos tomando soluciones simples de Weyl conocidas en la literatura como las soluciones de Chazy-Curzon, Zipoy-Voorhees y Bonnor-Sackfield; sin embargo, las soluciones obtenidas no son asintóticamente planas, lo cual hace que su interpretación física en términos de campos gravitacionales producidos por distribuciones finitas de materia no sea muy clara.
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Referencias
[1] Kramer, D., Stephani, H., Herlt, E. and McCallum, M.Exact Solutions ofEinstein’s Field Equations. (Cambridge University Press, 1980).
[2] Belinsky, V. A. and Zakharov, V. E. “Integration of the Einstein Equations bymeans of the Inverse Scattering Technique and Construction of Exact SolitonSolutions”.Zh. Eksp. Teor. Fis.75, 1955 (1978). [Sov. Phys. JETP48, 985(1978).]
[3] Belinsky, V. A. and Zakharov, V. E. “Stationary Gravitational Solitons withAxial Symmetry”.Zh. Eksp. Teor. Fis.77, 3 (1979). [Sov. Phys. JETP50,1 (1979).]
[4] Chaudhuri, S. and Das, K. C.Two-soliton Solutions of Axially SymmetricMetrics. Gen. Rel. Grav. 29, 75 (1997).
[5] Letelier, P. S. “Cylindrically Symmetric Solitary Wave Solutions to the Ein-stein Equations”.J. Math. Phys.25, 2675 (1984).
[6] Letelier, P. S. “Static and Stationary Multiple Soliton Solutions to the EinsteinEquations”.J. Math. Phys.26, 467 (1985).
[7] Letelier, P. S. “Soliton Solutions to the Vacuum Einstein Equations Obtainedfrom a Nondiagonal Seed Solution”.J. Math. Phys.27, 564 (1986).
[8] Letelier, P. S.On Soliton Solutions to the Vacuum Einstein Equations Obtainedfrom a General Seed Solution. Class. Quantum Grav. 6, 875 (1989).
[9] Letelier, P. S. and Oliveira, S. R. “Exact Selfgraviting Disks and Rings: aSolitonic Approach”.J. Math. Phys.28, 165 (1987).
[10] McCrea, J. D. “Static Axially Symmetric Gravitational Fields with Shell Sources”.J. Phys.A9, 697 (1976).[11] Weyl, H.Zur Gravitationstheorie. Ann. Physik 54, 117 (1917).
[12] Weyl, H.Bemerkung ̈Uber die Axialsymmetrischen L ̈osungen der Einstein-schen Gravitationsgleichungen. Ann. Physik 59, 185 (1919).
[13] Zipoy, D. M. “Topology of Some Spheroidal Metrics”.J. Math. Phys. 7, 1137(1966).
[14] Voorhees, B. H. “Static Axially Symmetric Gravitational Fields”.Phys. Rev.D2, 2119 (1970).
[15] Bonnor, W. B. and Sackfield, A. “The Interpretation of Some Spheroidal Met-rics”.Comm. Math. Phys.8, 338 (1968).
[16] Chazy, J. “Sur le Champ de Gravitation de Deux Masses Fixes dans la Th ́eoriede la Relativit ́e”.Bull. Soc. Math. France.52, 17 (1924).
[17] Curzon, H. E. J. “Cylindrical Solutions of Einstein’s Gravitation Equations”.Proc. London Math. Soc.23, 477 (1924).
[18] Demia ́nski, M. and Newmann, E. T. “A Combined Kerr-NUT Solution of theEinstein Field Equations”.Bull. Acad. Polon. Sci. Ser. Math. Astron. Phys.14, 653 (1966).
[19] Newmann, E., Tamburino, L. and Unti, T. “Empty-Space Generalization ofthe Schwarzschild Metric”.J. Math. Phys.4, 915 (1963).
[20] Reina, C. and Treves, A. ”Axisymmetric Gravitational Fields”.Gen. Rel.Grav.7, 817 (1976).
[21] Boyer, R. H. and Lindquist, R. W. “Maximal Analytic Extension of the KerrMetric”.J. Math. Phys. 8, 265 (1967).
[2] Belinsky, V. A. and Zakharov, V. E. “Integration of the Einstein Equations bymeans of the Inverse Scattering Technique and Construction of Exact SolitonSolutions”.Zh. Eksp. Teor. Fis.75, 1955 (1978). [Sov. Phys. JETP48, 985(1978).]
[3] Belinsky, V. A. and Zakharov, V. E. “Stationary Gravitational Solitons withAxial Symmetry”.Zh. Eksp. Teor. Fis.77, 3 (1979). [Sov. Phys. JETP50,1 (1979).]
[4] Chaudhuri, S. and Das, K. C.Two-soliton Solutions of Axially SymmetricMetrics. Gen. Rel. Grav. 29, 75 (1997).
[5] Letelier, P. S. “Cylindrically Symmetric Solitary Wave Solutions to the Ein-stein Equations”.J. Math. Phys.25, 2675 (1984).
[6] Letelier, P. S. “Static and Stationary Multiple Soliton Solutions to the EinsteinEquations”.J. Math. Phys.26, 467 (1985).
[7] Letelier, P. S. “Soliton Solutions to the Vacuum Einstein Equations Obtainedfrom a Nondiagonal Seed Solution”.J. Math. Phys.27, 564 (1986).
[8] Letelier, P. S.On Soliton Solutions to the Vacuum Einstein Equations Obtainedfrom a General Seed Solution. Class. Quantum Grav. 6, 875 (1989).
[9] Letelier, P. S. and Oliveira, S. R. “Exact Selfgraviting Disks and Rings: aSolitonic Approach”.J. Math. Phys.28, 165 (1987).
[10] McCrea, J. D. “Static Axially Symmetric Gravitational Fields with Shell Sources”.J. Phys.A9, 697 (1976).[11] Weyl, H.Zur Gravitationstheorie. Ann. Physik 54, 117 (1917).
[12] Weyl, H.Bemerkung ̈Uber die Axialsymmetrischen L ̈osungen der Einstein-schen Gravitationsgleichungen. Ann. Physik 59, 185 (1919).
[13] Zipoy, D. M. “Topology of Some Spheroidal Metrics”.J. Math. Phys. 7, 1137(1966).
[14] Voorhees, B. H. “Static Axially Symmetric Gravitational Fields”.Phys. Rev.D2, 2119 (1970).
[15] Bonnor, W. B. and Sackfield, A. “The Interpretation of Some Spheroidal Met-rics”.Comm. Math. Phys.8, 338 (1968).
[16] Chazy, J. “Sur le Champ de Gravitation de Deux Masses Fixes dans la Th ́eoriede la Relativit ́e”.Bull. Soc. Math. France.52, 17 (1924).
[17] Curzon, H. E. J. “Cylindrical Solutions of Einstein’s Gravitation Equations”.Proc. London Math. Soc.23, 477 (1924).
[18] Demia ́nski, M. and Newmann, E. T. “A Combined Kerr-NUT Solution of theEinstein Field Equations”.Bull. Acad. Polon. Sci. Ser. Math. Astron. Phys.14, 653 (1966).
[19] Newmann, E., Tamburino, L. and Unti, T. “Empty-Space Generalization ofthe Schwarzschild Metric”.J. Math. Phys.4, 915 (1963).
[20] Reina, C. and Treves, A. ”Axisymmetric Gravitational Fields”.Gen. Rel.Grav.7, 817 (1976).
[21] Boyer, R. H. and Lindquist, R. W. “Maximal Analytic Extension of the KerrMetric”.J. Math. Phys. 8, 265 (1967).