Abstract
The present article deals with solutions for a minimally coupled scalar field propagating in a static plane symmetric spacetime. The considered metric describes the curvature outside a massive infinity plate and exhibits an intrinsic naked singularity (a singular plane) that makes the accessible universe finite in extension. This solution can be interpreted as describing the spacetime of static domain walls. In this context, a first solution is given in terms of zero order Bessel functions of the first and second kind and presents a stationary pattern which is interpreted as a result of the reflection of the scalar waves at the singular plane. This is an evidence, at least for the massless scalar field, of an old interpretation given by Amundsen and Grøn regarding the behaviour of test particles near the singularity. A second solution is obtained in the limit of a weak gravitational field which is valid only far from the singularity. In this limit, it was possible to find out an analytic solution for the scalar field in terms of the Kummer and Tricomi confluent hypergeometric functions.
Similar content being viewed by others
References
M.B. Green, J.H. Schwarz, E. Witten, Superstring Theory (Cambridge University Press, Cambridge, England, 1987)
A.H. Guth, Inflationary universe: A possible solution to the horizon and flatness problems. Phys. Rev. D. 23, 347 (1981)
K.A. Olive, Inflation. Phys. Rep. 190, 307 (1990)
S. Perlmutter et al., Measurements of Omega and Lambda from 42 high-redshift supernovae. Astron. J. 517, 565 (1999)
A.G. Riess et al., Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J. 116, 1009–1038 (1998)
A.H. Taub, Empty space-times admitting a three parameter group of motions. Ann. Math. 53, 472 (1951)
J. Novotný, J. Horský, On the plane gravitational condensor with the positive gravitational constant,. Czech. J. Phys. B 24, 718–723 (1974)
T. Singh, A plane symmetric solution of Einstein’s field equations of general relativity containing zero-rest-mass scalar fields. Gen. Relativ. Gravit. 5, 657–662 (1974)
C. Vuille, Exact solutions for the massless plane symmetric scalar field in general relativity, with cosmological constant. Gen. Relativ. Gravit. 39, 621–632 (2007)
F. Rohrlich, The Principle of equivalence. Ann. Phys. 22, 169–191 (1963)
J. Horský, The gravitational field of planes in general relativity. Czech. J. Phys. B. 18, 569–583 (1968)
P.A. Amundsen, Ø. Grn, General static plane-symmetric solutions of the Einstein-Maxwell equations,. Phys. Rev. D. 27, 1731–1739 (1983)
P. Jones et al., The general relativistic infinite plane,. Am. J. Phys. 76, 73–78 (2008)
M. Abramowitz, A. Irene, eds, Handbook of Mathematical Functions (Dover, New York, 1965), p. 364
N.D. Birrell, P.C.W. Davies, Quantum Fields in Curved Space (Cambridge University Press, Cambridge, England, 1982), p. 87
Acknowledgments
JC would like to thank to FAPEMIG for financial support. MESA would like to thank the Brazilian agency FAPESP for financial support (grant 13/26258-4).F.A. Barone would like to thank to CNPq financial support (grant: 311514/2015-4, 484736/2012-4).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Celestino, J., Alves, M.E.S. & Barone, F.A. Propagation of Scalar Fields in a Plane Symmetric Spacetime. Braz J Phys 46, 784–792 (2016). https://doi.org/10.1007/s13538-016-0458-8
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13538-016-0458-8