On the Jebsen-Birkhoff Theorem in a Born-Infeld Type Theory of Gravity
Author(s)
Tiago de Oliveira Rosa1,
Maria Emilia Xavier Guimarães2,
Rocco Pascale Neto2,
Joaquim Lopes Neto3
Affiliation(s)
1 Instituto Federal Goiano, Campus Urutaí, Rodovia Geraldo Silva Nascimento, Urutaí, Brazil. 2 Instituto de Física, Universidade Federal Fluminense, Niterói, Brazil. 3 Instituto de Física, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil.
1 Instituto Federal Goiano, Campus Urutaí, Rodovia Geraldo Silva Nascimento, Urutaí, Brazil. 2 Instituto de Física, Universidade Federal Fluminense, Niterói, Brazil. 3 Instituto de Física, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil.
ABSTRACT
In this paper we work with a special theory of gravity|the Novello-Di Lorenci-Luciane (hereby called NDL theory) which extends the Feynman-Deser standard theoretical-fi eld approach to General Relativity. In the so-called NDL theory, matter interacts universally with gravity in accordance with the Weak Equivalence Principle, while gravitons have a nonlinear self-interaction. Our main aim in this work is to show that, though the NDL theory does not admit a Schwarzschild solution, the Jebsen-Birkhoff theorem is still valid in this framework.
In this paper we work with a special theory of gravity|the Novello-Di Lorenci-Luciane (hereby called NDL theory) which extends the Feynman-Deser standard theoretical-fi eld approach to General Relativity. In the so-called NDL theory, matter interacts universally with gravity in accordance with the Weak Equivalence Principle, while gravitons have a nonlinear self-interaction. Our main aim in this work is to show that, though the NDL theory does not admit a Schwarzschild solution, the Jebsen-Birkhoff theorem is still valid in this framework.
Cite this paper
Rosa, T. , Guimarães, M. , Neto, R. and Neto, J. (2019) On the Jebsen-Birkhoff Theorem in a Born-Infeld Type Theory of Gravity. Journal of High Energy Physics, Gravitation and Cosmology, 5, 1051-1056. doi: 10.4236/jhepgc.2019.54057.
Rosa, T. , Guimarães, M. , Neto, R. and Neto, J. (2019) On the Jebsen-Birkhoff Theorem in a Born-Infeld Type Theory of Gravity. Journal of High Energy Physics, Gravitation and Cosmology, 5, 1051-1056. doi: 10.4236/jhepgc.2019.54057.
References
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https://doi.org/10.1016/0550-3213(85)90506-1 [3] Corda, C. (2009) Interferometric Detection of Gravitational Waves: The De nitive Test for General Relativity. International Journal of Modern Physics D, 18, 2275-2282. arXiv:0905.2505[gr-qc]
https://doi.org/10.1142/S0218271809015904 [4] Novello, M., De Lorenci, V.A., de Freitas, L.R. and Aguiar, O.D. (1999) The Velocity of Gravitational Waves. Physics Letters A, 254, 245-250.
https://doi.org/10.1016/S0375-9601(99)00080-8 [5] Novello, M. and De Lorenci, V.A. (1997) Do Gravitational Waves Travel at Light Velocity? Annals of Physics, 254, 83 [6] Corlin, A. (1934) A New Hard Component of the Cosmic Ultra- Radiation. Nature, 133, 63.
https://doi.org/10.1038/133063a0 [7] Comelli, D. (2004) Born-Infeld-Type Gravity. Physical Review D, 72, Article ID: 064018.
https://doi.org/10.1103/PhysRevD.72.064018 [8] Feynman, R. (1995) Lectures on Gravitation. Addison-Wesley, Boston. [9] Deser, S. (1970) Self-Interaction and Gauge Invariance. General Relativity and Gravitation, 1, 9-18.
https://doi.org/10.1007/BF00759198 [10] Wohlfarth, M.N.R. (2004) Gravity a la Born-Infeld. Classical and Quantum Gravity, 21, 5297.
https://doi.org/10.1088/0264-9381/21/8/001 [11] Feigenbaum, J.A., Freund, P.G.O. and Pigli, M. (2004) Gravitational Analogues of Nonlinear Born Electrodynamics. Physical Review D, 57, 4738.
https://doi.org/10.1103/PhysRevD.57.4738 [12] Novello, M., Bergliaffa, S.E.P. and Hibberd, K.E. (2004) Analysis of the Static and Spherically-Symmetric Solution in NDL Theory of Gravitation. International Journal of Modern Physics D, 13, 527-537.
https://doi.org/10.1142/S0218271804004608 [13] Rosa, T., Guimarães, M. and Neto, J. (2019) On an Exact Cylindrically Symmetric Solution in a Born-Infeld Type Theory of Gravity. Journal of High Energy Physics, Gravitation and Cosmology, 5, 711-718. [14] Faraoni, V. (2010) The Jebsen-Birkhoff Theorem in Alternative Gravities. Physical Review D, 81, Article ID: 044002.
https://doi.org/10.1103/PhysRevD.81.044002
[1] Scherk, J. and Schwarz, J. (1974) Dual Models for Non-Hadrons. Nuclear Physics, Section B, 81, 118-144. [2] Callan, C.G., Friedan, D., Martinec, E.J. and Perry, M.J. (1985) Strings in Background Fields. Nuclear Physics B, 262, 593-609.
https://doi.org/10.1016/0550-3213(85)90506-1 [3] Corda, C. (2009) Interferometric Detection of Gravitational Waves: The De nitive Test for General Relativity. International Journal of Modern Physics D, 18, 2275-2282. arXiv:0905.2505[gr-qc]
https://doi.org/10.1142/S0218271809015904 [4] Novello, M., De Lorenci, V.A., de Freitas, L.R. and Aguiar, O.D. (1999) The Velocity of Gravitational Waves. Physics Letters A, 254, 245-250.
https://doi.org/10.1016/S0375-9601(99)00080-8 [5] Novello, M. and De Lorenci, V.A. (1997) Do Gravitational Waves Travel at Light Velocity? Annals of Physics, 254, 83 [6] Corlin, A. (1934) A New Hard Component of the Cosmic Ultra- Radiation. Nature, 133, 63.
https://doi.org/10.1038/133063a0 [7] Comelli, D. (2004) Born-Infeld-Type Gravity. Physical Review D, 72, Article ID: 064018.
https://doi.org/10.1103/PhysRevD.72.064018 [8] Feynman, R. (1995) Lectures on Gravitation. Addison-Wesley, Boston. [9] Deser, S. (1970) Self-Interaction and Gauge Invariance. General Relativity and Gravitation, 1, 9-18.
https://doi.org/10.1007/BF00759198 [10] Wohlfarth, M.N.R. (2004) Gravity a la Born-Infeld. Classical and Quantum Gravity, 21, 5297.
https://doi.org/10.1088/0264-9381/21/8/001 [11] Feigenbaum, J.A., Freund, P.G.O. and Pigli, M. (2004) Gravitational Analogues of Nonlinear Born Electrodynamics. Physical Review D, 57, 4738.
https://doi.org/10.1103/PhysRevD.57.4738 [12] Novello, M., Bergliaffa, S.E.P. and Hibberd, K.E. (2004) Analysis of the Static and Spherically-Symmetric Solution in NDL Theory of Gravitation. International Journal of Modern Physics D, 13, 527-537.
https://doi.org/10.1142/S0218271804004608 [13] Rosa, T., Guimarães, M. and Neto, J. (2019) On an Exact Cylindrically Symmetric Solution in a Born-Infeld Type Theory of Gravity. Journal of High Energy Physics, Gravitation and Cosmology, 5, 711-718. [14] Faraoni, V. (2010) The Jebsen-Birkhoff Theorem in Alternative Gravities. Physical Review D, 81, Article ID: 044002.
https://doi.org/10.1103/PhysRevD.81.044002