Comment on the exterior solutions and their geometry in scalar-tensor theories of gravity

Details Comment on the exterior solutions and their geometry in scalar-tensor theories of gravity Comment on the exterior solutions and their geometry in scalar-tensor theories of gravity

1998-09-02

arxiv.org/abs/gr-qc/9809010v2

Prog.Theor.Phys.101:73-90,1999

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages, 3 figures, Submitted to Progress of Theoretical Physics

Scientific paper

10.1143/PTP.101.73

We study series of the stationary solutions with asymptotic flatness properties in the Einstein-Maxwell-free scalar system because they are locally equivalent with the exterior solutions in some class of the scalar-tensor theories of gravity. First, we classify spherical exterior solutions into two types of the solutions, an apparently black hole type solution and an apparently worm hole type solution. The solutions contain three parameters, and we clarify their physical significance. Second, we reduce the field equations for the axisymmetric exterior solutions. We find that the reduced equations are partially the same as the Ernst equations. As simple examples, we derive new series of the static, axisymmetric exterior solutions, which correspond to Voorhees's solutions. We then show a non-trivial relation between the spherical exterior solutions and our new solutions. Finally, since null geodesics have conformally invariant properties, we study the local geometry of the exterior solutions by using the optical scalar equations and find some anomalous behaviors of the null geodesics.

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