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Advances in High Energy Physics
Volume 2013, Article ID 367029, 7 pages
Research Article

Regular Solutions in Vacuum Brans-Dicke Theory Compared to Vacuum Einstein Theory

1Ya.B. Zel'dovich International Center for Astrophysics, BSPU, Ufa 450000, Russia
2Department of Mathematics, University of North Bengal, Siliguri 734013, India
3Department of Mathematics, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy

Received 28 June 2013; Accepted 24 August 2013

Academic Editor: Gongnan Xie

Copyright © 2013 Alina Khaybullina et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We will confront some static spherically symmetric vacuum Brans-Dicke solutions in the Jordan and Einstein Frames with the Robertson parameters. While the regular solution in the vacuum Einstein theory is just the Schwarzschild black hole, the same in the Jordan frame Brans-Dicke theory is shown to represent not a black hole but a traversable wormhole. But, in this case, the valid range of becomes too narrow to yield the observed weak field Robertson parameters at the positive mass mouth. The corresponding solution in the Einstein frame also provides a regular wormhole, and it yields the correct parametric values but only up to “one and half order.” We argue that a second-order contribution can in principle distinguish between the signatures of the regular wormhole and the singular Buchdahl solution in the Einstein frame. Thus, at the level of regular solutions, Brans-Dicke theory in each frame predicts effects very different from those of Einstein's theory. To our knowledge, these theoretical distinctions seem not to have received adequate attention so far.