On the Jebsen-Birkhoff Theorem in a Born-Infeld Type Theory of Gravity


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.

Share and Cite:

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.

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.


[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.
[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]
[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.
[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.
[7] Comelli, D. (2004) Born-Infeld-Type Gravity. Physical Review D, 72, Article ID: 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.
[10] Wohlfarth, M.N.R. (2004) Gravity a la Born-Infeld. Classical and Quantum Gravity, 21, 5297.
[11] Feigenbaum, J.A., Freund, P.G.O. and Pigli, M. (2004) Gravitational Analogues of Nonlinear Born Electrodynamics. Physical Review D, 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.
[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.

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.