Searching for nonminimally coupled scalar hairs.pdfVIP

US-FT/4-96 Searching for non-minimally coupled scalar hairs Alberto Saa∗ Departamento de F´ısica de Part´ıculas Universidade de Santiago de Compostela 6 9 15706 Santiago de Compostela, Spain 9 1 (February 4, 2008) b e F 9 2 Abstract 1 v 1 In this work we study the asymptotically flat, static, and spherically sym- 6 0 2 metric black-hole solutions of the theory described by the action 0 6 9 S = dnx√−g 1 − ξφ2 R − gµν ∂ φ∂ φ , / µ ν c q - r with n 3 and arbitrary ξ . We demonstrate the absence of scalar hairs for g : n−2 v ξ 0. For ξ ξc = 4(n−1) , we show that there is no scalar hair obeying i X |φ(r)| 1/√ξ or |φ(r)| 1/√ξ . For 0 ξ ξ , we prove the absence of r c a √ξ or 1 2 ξc scalar hairs such that |φ(r)| 1/ ξ φ (r) ξ (ξc −ξ) . 97.60.Lf, 04.70.Bw Typeset using REVT X E 1 The Bekenstein black-hole solution [1] for Einstein gravity conformally coupled to a scalar