MG15 - Talk detail

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We study the horizon geometry of Kerr black holes (BHs) with scalar synchronised hair, a family of solutions of the Einstein-Klein-Gordon system that continuously connects to vacuum Kerr BHs. We identify the region in parameter space wherein a global isometric embedding in Euclidean 3-space is possible for the horizon geometry of the hairy BHs. For the Kerr case, such embedding is possible if and only if the horizon dimensionless spin, j_H, the sphericity, s, and the horizon linear velocity, v_H, are smaller than critical values, j_H^(S), s^(S), v_H^(S), respectively. For the hairy BHs, we find that j_H < j^(S) is a sufficient, but not necessary, condition for being embeddable; v_H > v_H^(S) is a necessary, but not sufficient, condition for being embeddable; whereas s < s^(S) is a necessary and sufficient condition for being embeddable. Thus the latter quantity provides the most faithful diagnosis for the existence of an embedding in Euclidean 3-space within the whole family of solutions.

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