Spherically symmetric, static spacetimes in a tensor-vector-scalar theory

Details Spherically symmetric, static spacetimes in a tensor-vector-scalar theory Spherically symmetric, static spacetimes in a tensor-vector-scalar theory

Aug 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006aipc..848..720g&link_type=abstract

RECENT ADVANCES IN ASTRONOMY AND ASTROPHYSICS: 7th International Conference of the Hellenic Astronomical Society. AIP Conferenc

Astronomy and Astrophysics

Astrophysics

Dark Matter, Black Holes, Exact Solutions

Scientific paper

Recently, a relativistic gravitation theory has been proposed by Bekenstein that gives the Modified Newtonian Dynamics (or MOND) in the weak acceleration regime. The theory is based on three dynamic gravitational fields and succeeds in explaining a large part of extragalactic and gravitational lensing phenomenology without invoking dark matter. In this work we consider the strong gravity regime of TeVeS. We study spherically symmetric, static and vacuum spacetimes relevant for a non-rotating black hole or the exterior of a star. Two branches of solutions are identified: in the first the vector field is aligned with the time direction while in the second the vector field has a non-vanishing radial component. We show that in the first branch of solutions the β and γ PPN coefficients in TeVeS are identical to these of general relativity (GR) while in the second the β PPN coefficient differs from unity violating observational determinations of it (for the choice of the free function F of the theory made in Bekenstein's paper). For the first branch of solutions, we derive analytic expressions for the physical metric and discuss their implications. Applying these solutions to the case of black holes, it is shown that they violate causality (since they allow for superluminal propagation of metric, vector and scalar waves) in the vicinity of the event horizon and/or that they are characterized by negative energy density carried by the fields.

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