Hyperbolicity of scalar-tensor theories of gravity

Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology

Scientific paper

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15 pages two-column RevTex; minor corrections: references added, comments added, typos corrected; accepted for publication in

Scientific paper

10.1103/PhysRevD.77.104010

Two first order strongly hyperbolic formulations of scalar-tensor theories of gravity (STT) allowing nonminimal couplings (Jordan frame) are presented along the lines of the 3+1 decomposition of spacetime. One is based on the Bona-Masso formulation while the other one employs a conformal decomposition similar to that of Baumgarte-Shapiro-Shibata-Nakamura. A modified Bona-Masso slicing condition adapted to the scalar-tensor theory is proposed for the analysis. This study confirms that the scalar-tensor theory posses a well posed Cauchy problem even when formulated in the Jordan frame.

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