TY - GEN

T1 - Black holes with a conformally coupled scalar field

AU - Martínez, Cristián

PY - 2009

Y1 - 2009

N2 - 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, configurationswith 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.

AB - 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, configurationswith 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.

UR - http://www.scopus.com/inward/record.url?scp=84892293747&partnerID=8YFLogxK

U2 - 10.1007/978-0-387-87499-9_12

DO - 10.1007/978-0-387-87499-9_12

M3 - Conference contribution

AN - SCOPUS:84892293747

SN - 9780387874982

T3 - Quantum Mechanics of Fundamental Systems: The Quest for Beauty and Simplicity - Claudio Bunster Festschrift

SP - 167

EP - 179

BT - Quantum Mechanics of Fundamental Systems

PB - Springer Science and Business Media, LLC

T2 - 2008 Meeting on Quantum Mechanics of Fundamental Systems: The Quest for Beautyand Simplicity

Y2 - 10 January 2008 through 11 January 2008

ER -