Static black holes with axial symmetry in asymptotically AdS_{4} spacetime
Abstract
The known static electrovacuum black holes in a globally AdS_{4} background have an event horizon which is geometrically a round sphere. In this work we argue that the situation is different in models with matter fields possessing an explicit dependence on the azimuthal angle φ , which, however, does not manifest at the level of the energymomentum tensor. As a result, the full solutions are axially symmetric only, possessing a single (timelike) Killing vector field. Explicit examples of such static black holes are constructed in Einstein(complex) scalar field and EinsteinYangMills theories. The basic properties of these solutions are discussed, looking for generic features. For example, we notice that the horizon has an oblate spheroidal shape for solutions with a scalar field and a prolate one for black holes with YangMills fields. The deviation from sphericity of the horizon geometry manifests itself in the holographic stress tensor. Finally, based on the results obtained in the probe limit, we conjecture the existence in EinsteinMaxwell theory of static black holes with axial symmetry only.
 Publication:

Physical Review D
 Pub Date:
 February 2016
 DOI:
 10.1103/PhysRevD.93.044037
 arXiv:
 arXiv:1510.08935
 Bibcode:
 2016PhRvD..93d4037K
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 21 pages, 12 figures