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Black holes with a conformally coupled scalar field

  • Cristián Martínez
Conference paper

We consider gravity in presence of a cosmological constant in arbitrary spacetime dimensions with a conformally coupled scalar field and a self-interacting potential. The energy-momentum tensor is traceless when the constant appearing in front of the non-minimal coupling term and the power of the self-interacting potential are properly chosen. First, configurations with a constant scalar field are studied. In the general case, the spacetime is required to be an Einstein space. However, for a special value of the scalar field this condition can be relaxed and it is enough that the spacetime has a constant scalar curvature fixed by the cosmological constant. In this case the cosmological constant and the self-interacting coupling constant are related. The second part is devoted to searching black holes dressed with a conformally coupled scalar field in dimensions greater than four. Since the existence of a no-go theorem discarding static and asymptotically flat black holes in higher dimensions, we introduce a cosmological constant and a self-interacting potential in the action. Using a standard static ansatz for the metric, which includes both spherically symmetric as topological black holes, and a scalar field depending only on the radial coordinate, it is shown that there are no higher-dimensional counterparts of the known black holes in three and four dimensions.

Keywords

Black Hole Cosmological Constant Event Horizon Black Hole Solution Constant Scalar Curvature 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York 2009

Authors and Affiliations

  1. 1.Centro de Estudios Científicos (CECS)Centro de Ingeniería de la Innovación del CECS (CIN)Chile

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