Kerr black holes with scalar hair

Kerr black holes with scalar hair Φ lev ole Angular Momentum Mass Strangeness Charge Gravitational and Baryons Leptons electromagnetic waves Scalar waves [and I* Φ? 111 Φ? '0 !' Javil' Φ? Φ? I-B) I bv »! Mass Charge Angular Momentum Figurative representation of a black hole in action All details of the infalling matter are washed out The final configuration is believed to be uniquely determined by mass, electric charge, and angular momentum Figure C Herdeiro 31 Departamento de Física da Universidade de Aveiro, Portugal PHYSICS TODAY / JANUARY 1971 Downloaded 24 Nov 2012 to 136.159.235.223 Redistribution subject to AIP license or copyright; see http://www.physicstoday.org/about_us/terms New Frontiers in Dynamical Gravity, Cambridge, 24 March 2014 based on arXiv:1403:2757 with E Radu Slide 1/16 R Price, i s " P log t This disappearance of the dipole takes place according to the same kind of law as the fadeout of perturbations of the quadruoole and higher moments of the mass distribution The collapse leads to a black hole endowed with mass and charge and angular momentum but, so far as we can now judge, no other adjustable parameters: "a black hole has no hair." Make one black hole out of matter; the possibility of measuring baryon number, and therefore this quantity can not be well defined for a collapsed object Similarly, strangeness is no longer conserved The “no-hair” idea Angular momentum 36 The third property of a black hole is angular momentum When it is nonzero, the geometry becomes more complicated One deals with the Kerr solution2 to the field equations instead of the Schwarzschild solution There are two interesting surfaces associated with the Kerr geometry, the "surface of in- process can be so arranged tha emerging fragment has more ene infinity than the original particle The extra energy is effectivel tracted from the rotational ener the black hole If a particle ca through the ergosphere and escap some of the energy and angula mentum of the black hole, it is als that a particle that is captured c crease the energy and angular mentum of the black hole Capt possible when the particle pass sufficiently close to the black hole critical impact is smaller for a c PHYSICS TODAY / JANUARY 1971 Downloaded 24 Nov 2012 to 136.159.235.223 Redistribution subject to AIP license or copyright; see http://www.physicstoday.org/about_us/terms Ruffini, Wheeler (1971) Misner, Thorne, Wheeler (1973) Original idea: collapse leads to equilibrium black holes uniquely determined by M,J,Q asymptotically measured quantities subject to a Gauss law and no other independent characteristics (hair) Motivated by uniqueness theorems e.g: Israel 1967, 1968; Carter 1970; Hawking 1972; Robinson 1975, 1977; and many others Overview: “Four decades of black hole uniqueness theorems” D Robinson (2004, 2009) Slide 2/16 Hairy black hole solutions exist (D=4, asymptotically flat): Early example: Einstein-Yang-Mills theory Bizón 1990; Kunzle and Masood-ul-Alam, 1990; Volkov and Galtsov, 1990 Other examples were obtained in: Einstein-Skyrme, Einstein-Yang-MillsDilaton, Einstein-Yang-Mills-Higgs, Einstein-non-Abelian-Proca, etc Review by Bizón 1994; Volkov and Gal’tsov (1999) Slide 3/16 Hairy black hole solutions exist (D=4, asymptotically flat): Early example: Einstein-Yang-Mills theory Bizón 1990; Kunzle and Masood-ul-Alam, 1990; Volkov and Galtsov, 1990 Other examples were obtained in: Einstein-Skyrme, Einstein-Yang-MillsDilaton, Einstein-Yang-Mills-Higgs, Einstein-non-Abelian-Proca, etc Review by Bizón 1994; Volkov and Gal’tsov (1999) Picture of hairy black holes as bound states of BHs with gravitating solitons Ashtekar, Corichi and Sudarsky (2001) Slide 3/16 Hairy black hole solutions exist (D=4, asymptotically flat): Early example: Einstein-Yang-Mills theory Bizón 1990; Kunzle and Masood-ul-Alam, 1990; Volkov and Galtsov, 1990 Other examples were obtained in: Einstein-Skyrme, Einstein-Yang-MillsDilaton, Einstein-Yang-Mills-Higgs, Einstein-non-Abelian-Proca, etc Review by Bizón 1994; Volkov and Gal’tsov (1999) Picture of hairy black holes as bound states of BHs with gravitating solitons Ashtekar, Corichi and Sudarsky (2001) .but, apparently, no bound state of boson stars with (hairless) BHs Slide 3/16 Boson stars: Kaup (1968); Ruffini and Bonazzola (1969) Review: Liebling and Palenzuela (2012) Einstein-KleinGordon theory: S= 16πG � √ � ab ∗ ∗ d x −g R − g ∂a Φ ∂b Φ − µ Φ Φ � Slide 4/16 Boson stars: Kaup (1968); Ruffini and Bonazzola (1969) Review: Liebling and Palenzuela (2012) Einstein-KleinGordon theory: Rotating boson stars: S= 16πG ds = −e 2F0 (r,θ) dt + e Yoshida and Eriguchi (1997) Schunck and Mielke (1998) � � √ ab ∗ ∗ d x −g R − g ∂a Φ ∂b Φ − µ Φ Φ 2F1 (r,θ) � 2 dr + r dθ � � + e2F2 (r,θ) r2 sin2 θ (dϕ − W (r, θ)dt) Φ = φ(r, θ)ei(mϕ−wt) Three input parameters: (w,m,n) Slide 4/16 Boson stars: Kaup (1968); Ruffini and Bonazzola (1969) Review: Liebling and Palenzuela (2012) Einstein-KleinGordon theory: Rotating boson stars: S= 16πG ds = −e 2F0 (r,θ) dt + e Yoshida and Eriguchi (1997) Schunck and Mielke (1998) � � √ ab ∗ ∗ d x −g R − g ∂a Φ ∂b Φ − µ Φ Φ 2F1 (r,θ) � 2 dr + r dθ � � + e2F2 (r,θ) r2 sin2 θ (dϕ − W (r, θ)dt) Φ = φ(r, θ)ei(mϕ−wt) Three input parameters: (w,m,n) Solutions preserved by a single helicoidal Killing vector field: ∂ w ∂ + ∂t m ∂ϕ Slide 4/16 Boson stars phase space (nodeless): m=1 Mµ 0.5 0.6 0.7 0.8 0.9 w/(mµ) Slide 5/16 Boson stars phase space (nodeless): m=1 Mµ Mµ 0.5 0.5 m=1 0.6 0.7 0.8 w/(mµ) 0.9 0 0.5 Jµ 1.5 Slide 5/16 Hairy black holes phase space Mµ m=10 m=1 m=4 Mµ m=3 m=2 0 0.25 0.5 1H/µ 0.5 m=1 0.6 0.7 0.8 0.75w/(mµ) 0.9 1 Slide 12/16 Hairy black holes phase space Mµ m=10 m=1 Boson Stars (q=1) q=0.97 m=4 q=0.85 q=1 Mµ extremal HBHs m=3 m=2 0.5 q=0 m=1 Kerr black holes 0 0.25 0.5 1H/µ 0.6 0.7 0.8 0.75w/(mµ) 0.9 1 Slide 12/16 Hairy black holes phase space m=1 Boson Stars (q=1) q=0.97 extremal HBHs q=0.85 Mµ q=1 mQ q≡ J 0.5 q=0 Kerr black holes 0.6 0.7 0.8 0.9 w/(mµ) Mµ m=10 m=4 m=3 m=2 0 0.25 0.5 1H/µ m=1 0.75 Slide 12/16 Hairy black holes phase space m=1 Boson Stars (q=1) q=0.97 extremal HBHs q=0.85 Mµ q=1 0.5 mQ q≡ J m=2 m=1 q=0 0.25 0.6 Kerr black holes 0.5 0.75 0.7 0.8 0.9 w/(mµ) Mµ m=10 m=4 m=3 m=2 0 0.25 0.5 1H/µ m=1 0.75 Slide 12/16 Hairy black holes phase space Boson Stars (q=1) Kerr limit (q=0) Mµ 0.5 m=1 0 0.5 Jµ 1.5 Slide 13/16 Hairy black holes phase space Boson Stars (q=1) Kerr limit (q=0) Mµ 0.5 m=1 0 0.5 Jµ 1.5 - Can violate Kerr bound Slide 13/16 Hairy black holes phase space Boson Stars (q=1) Kerr limit (q=0) Mµ 0.5 m=1 0 0.5 Jµ 1.5 - Can violate Kerr bound - Non-uniqueness (different solutions for same M,J); but degeneracy raised with q Slide 13/16 Hairy black holes phase space Boson Stars (q=1) Kerr limit (q=0) Mµ Kerr BHs AH//µ2 0.5 m=1 0 HBHs 0.1 Jµ 0.5 Jµ 2 0.2 0.3 1.5 - Entropically favoured; Slide 13/16 Hairy black holes are more star-like Geroch-Hansen quadrupole moment: Geroch (1970); Hansen (1974); Pappas and Apostolatos (2012) 150 reduced quadrupole 1H/µ=0.99 1H/µ=0.9875 100 q=0 1H/µ=0.98 q=0.3 q=0.7 50 q=0.9 q=0.98 q=1 m=1 0.75 1.25 J/M 1.5 1.75 quadrupole reduced quadrupole = −J /M Slide 14/16 Hairy black holes are more star-like Geroch-Hansen quadrupole moment: Geroch (1970); Hansen (1974); Pappas and Apostolatos (2012) 150 reduced quadrupole 1H/µ=0.99 1H/µ=0.9875 100 q=0 1H/µ=0.98 q=0.3 q=0.7 50 q=0.9 q=0.98 q=1 m=1 0.75 1.25 J/M 1.5 1.75 quadrupole reduced quadrupole = −J /M Similar considerable deviations occur for the orbital frequency at the ISCO Slide 14/16 Final remarks: Hairy black holes interpolate between Kerr and boson stars Two viewpoints: Slide 15/16 Final remarks: Hairy black holes interpolate between Kerr and boson stars Two viewpoints: Boson stars: one can add a BH for spinning configurations Kerr black holes: branching towards a new family of solutions due to superradiant instability Slide 15/16 Final remarks: Hairy black holes interpolate between Kerr and boson stars Two viewpoints: Boson stars: one can add a BH for spinning configurations Kerr black holes: branching towards a new family of solutions due to superradiant instability General mechanism? A (hairless) BH which is afflicted by the superradiant instability of a given field must allow a hairy generalization with that field E.g in AdS, the first BH example with a single KVF Dias, Horowitz and Santos (2011) Slide 15/16 Final remarks: Hairy black holes interpolate between Kerr and boson stars Two viewpoints: Boson stars: one can add a BH for spinning configurations Kerr black holes: branching towards a new family of solutions due to superradiant instability General mechanism? A (hairless) BH which is afflicted by the superradiant instability of a given field must allow a hairy generalization with that field E.g in AdS, the first BH example with a single KVF Dias, Horowitz and Santos (2011) Stability ? Slide 15/16 Thank you for your attention! Slide 16/16 ... constant scalar energy density C H., Radu, 2014 (to appear) Slide 6/16 Black holes with scalar hair? (no other fields) Various no (scalar) hair theorems: Chase 1970 Bekenstein 1972, 1975, ; (scalar- tensor... time dependence: no hairy black hole in spherically symmetric case Pena and Sudarsky (1997) Slide 7/16 Black holes with scalar hair? (no other fields) Various no (scalar) hair theorems: Chase... Sotiriou and Faraoni 2011 Slide 7/16 Black holes with scalar hair? (no other fields) Various no (scalar) hair theorems: Chase 1970 Bekenstein 1972, 1975, ; (scalar- tensor theories): Hawking 1972