Hairy black holes in scalar tensor theories E Babichev and CC - PowerPoint PPT Presentation

Introduction: basic facts about scalar-tensor theories Scalar-tensor black holes and the no hair paradigm Building higher order scalar-tensor black holes Hairy black hole Conclusions Hairy black holes in scalar tensor theories E Babichev and CC gr-qc/1312.3204 CC, T Kolyvaris, E Papantonopoulos and M Tsoukalas gr-qc/1404.1024 C. Charmousis and D Iossifidis gr-qc/1501.05167 E Babichev CC and M Hassaine gr-qc/1503.02545 LPT Orsay, CNRS Gravitation and scalar fields: LUTH C. Charmousis Hairy black holes in scalar tensor theories

Introduction: basic facts about scalar-tensor theories Scalar-tensor black holes and the no hair paradigm Building higher order scalar-tensor black holes Hairy black hole Conclusions Introduction: basic facts about scalar-tensor theories 1 Scalar-tensor black holes and the no hair paradigm 2 Conformal secondary hair? Building higher order scalar-tensor black holes 3 An integrability theorem Example solutions Hairy black hole 4 Conclusions 5 C. Charmousis Hairy black holes in scalar tensor theories

Introduction: basic facts about scalar-tensor theories Scalar-tensor black holes and the no hair paradigm Building higher order scalar-tensor black holes Hairy black hole Conclusions Scalar-tensor theories are the simplest modification of gravity with one additional degree of freedom Admit a uniqueness theorem due to Horndeski 1973. contain or are limits of other modified gravity theories. f ( R ), massive gravity etc. Are there non trivial black hole solutions in Horndeski theory? No hair paradigm C. Charmousis Hairy black holes in scalar tensor theories

Introduction: basic facts about scalar-tensor theories Scalar-tensor black holes and the no hair paradigm Building higher order scalar-tensor black holes Hairy black hole Conclusions What is the most general scalar-tensor theory with second order field equations [ Horndeski 1973 ] , [ Deffayet et.al. ] ? Horndeski has shown that the most general action with this property is � d 4 x √− g ( L 2 + L 3 + L 4 + L 5 ) = S H L 2 = K ( φ, X ) , L 3 = − G 3 ( φ, X ) � φ, ( � φ ) 2 − ( ∇ µ ∇ ν φ ) 2 � � L 4 = G 4 ( φ, X ) R + G 4 X , L 5 = G 5 ( φ, X ) G µν ∇ µ ∇ ν φ − G 5 X ( � φ ) 3 − 3 � φ ( ∇ µ ∇ ν φ ) 2 + 2( ∇ µ ∇ ν φ ) 3 � � 6 the G i are free functions of φ and X ≡ − 1 2 ∇ µ φ ∇ µ φ and G iX ≡ ∂ G i /∂ X . In fact same action as covariant Galileons [ Deffayet, Esposito-Farese, Vikman ] C. Charmousis Hairy black holes in scalar tensor theories

Introduction: basic facts about scalar-tensor theories Scalar-tensor black holes and the no hair paradigm Building higher order scalar-tensor black holes Hairy black hole Conclusions Horndeski theory includes, R , f ( R ) theories, Brans Dicke theory with arbitrary potential Scalar-tensor interaction terms: G µν ∇ µ φ ∇ ν φ , P µρνσ ∇ µ ∇ ν φ ∇ ρ φ ∇ σ φ , V ( φ )ˆ G (Fab 4) higher order Galileons : � φ ( ∇ φ ) 2 ( DGP ) , ( ∇ φ ) 4 (ghost condensate) Higher order terms originate form KK reduction of Lovelock theory ( [ Van arXiv:1102.0487 [gr-qc] ] , [ CC, Goutéraux and Kiritsis ] ) Acoleyen et.al. Gallileons in flat spacetime have Gallilean symmetry [ Nicolis et.al.: arXiv:0811.2197 [hep-th] ] Horndeski theories appear at "decoupling limit" of DGP and massive gravity theories What about black holes in scalar-tensor theories? C. Charmousis Hairy black holes in scalar tensor theories

Introduction: basic facts about scalar-tensor theories Scalar-tensor black holes and the no hair paradigm Building higher order scalar-tensor black holes Hairy black hole Conclusions Horndeski theory includes, R , f ( R ) theories, Brans Dicke theory with arbitrary potential Scalar-tensor interaction terms: G µν ∇ µ φ ∇ ν φ , P µρνσ ∇ µ ∇ ν φ ∇ ρ φ ∇ σ φ , V ( φ )ˆ G (Fab 4) higher order Galileons : � φ ( ∇ φ ) 2 ( DGP ) , ( ∇ φ ) 4 (ghost condensate) Higher order terms originate form KK reduction of Lovelock theory ( [ Van arXiv:1102.0487 [gr-qc] ] , [ CC, Goutéraux and Kiritsis ] ) Acoleyen et.al. Gallileons in flat spacetime have Gallilean symmetry [ Nicolis et.al.: arXiv:0811.2197 [hep-th] ] Horndeski theories appear at "decoupling limit" of DGP and massive gravity theories What about black holes in scalar-tensor theories? C. Charmousis Hairy black holes in scalar tensor theories

Introduction: basic facts about scalar-tensor theories Scalar-tensor black holes and the no hair paradigm Building higher order scalar-tensor black holes Hairy black hole Conclusions Horndeski theory includes, R , f ( R ) theories, Brans Dicke theory with arbitrary potential Scalar-tensor interaction terms: G µν ∇ µ φ ∇ ν φ , P µρνσ ∇ µ ∇ ν φ ∇ ρ φ ∇ σ φ , V ( φ )ˆ G (Fab 4) higher order Galileons : � φ ( ∇ φ ) 2 ( DGP ) , ( ∇ φ ) 4 (ghost condensate) Higher order terms originate form KK reduction of Lovelock theory ( [ Van arXiv:1102.0487 [gr-qc] ] , [ CC, Goutéraux and Kiritsis ] ) Acoleyen et.al. Gallileons in flat spacetime have Gallilean symmetry [ Nicolis et.al.: arXiv:0811.2197 [hep-th] ] Horndeski theories appear at "decoupling limit" of DGP and massive gravity theories What about black holes in scalar-tensor theories? C. Charmousis Hairy black holes in scalar tensor theories

Introduction: basic facts about scalar-tensor theories Scalar-tensor black holes and the no hair paradigm Building higher order scalar-tensor black holes Hairy black hole Conclusions Horndeski theory includes, R , f ( R ) theories, Brans Dicke theory with arbitrary potential Scalar-tensor interaction terms: G µν ∇ µ φ ∇ ν φ , P µρνσ ∇ µ ∇ ν φ ∇ ρ φ ∇ σ φ , V ( φ )ˆ G (Fab 4) higher order Galileons : � φ ( ∇ φ ) 2 ( DGP ) , ( ∇ φ ) 4 (ghost condensate) Higher order terms originate form KK reduction of Lovelock theory ( [ Van arXiv:1102.0487 [gr-qc] ] , [ CC, Goutéraux and Kiritsis ] ) Acoleyen et.al. Gallileons in flat spacetime have Gallilean symmetry [ Nicolis et.al.: arXiv:0811.2197 [hep-th] ] Horndeski theories appear at "decoupling limit" of DGP and massive gravity theories What about black holes in scalar-tensor theories? C. Charmousis Hairy black holes in scalar tensor theories

Introduction: basic facts about scalar-tensor theories Scalar-tensor black holes and the no hair paradigm Building higher order scalar-tensor black holes Hairy black hole Conclusions Horndeski theory includes, R , f ( R ) theories, Brans Dicke theory with arbitrary potential Scalar-tensor interaction terms: G µν ∇ µ φ ∇ ν φ , P µρνσ ∇ µ ∇ ν φ ∇ ρ φ ∇ σ φ , V ( φ )ˆ G (Fab 4) higher order Galileons : � φ ( ∇ φ ) 2 ( DGP ) , ( ∇ φ ) 4 (ghost condensate) Higher order terms originate form KK reduction of Lovelock theory ( [ Van arXiv:1102.0487 [gr-qc] ] , [ CC, Goutéraux and Kiritsis ] ) Acoleyen et.al. Gallileons in flat spacetime have Gallilean symmetry [ Nicolis et.al.: arXiv:0811.2197 [hep-th] ] Horndeski theories appear at "decoupling limit" of DGP and massive gravity theories What about black holes in scalar-tensor theories? C. Charmousis Hairy black holes in scalar tensor theories

Introduction: basic facts about scalar-tensor theories Scalar-tensor black holes and the no hair paradigm Building higher order scalar-tensor black holes Hairy black hole Conclusions Horndeski theory includes, R , f ( R ) theories, Brans Dicke theory with arbitrary potential Scalar-tensor interaction terms: G µν ∇ µ φ ∇ ν φ , P µρνσ ∇ µ ∇ ν φ ∇ ρ φ ∇ σ φ , V ( φ )ˆ G (Fab 4) higher order Galileons : � φ ( ∇ φ ) 2 ( DGP ) , ( ∇ φ ) 4 (ghost condensate) Higher order terms originate form KK reduction of Lovelock theory ( [ Van arXiv:1102.0487 [gr-qc] ] , [ CC, Goutéraux and Kiritsis ] ) Acoleyen et.al. Gallileons in flat spacetime have Gallilean symmetry [ Nicolis et.al.: arXiv:0811.2197 [hep-th] ] Horndeski theories appear at "decoupling limit" of DGP and massive gravity theories What about black holes in scalar-tensor theories? C. Charmousis Hairy black holes in scalar tensor theories

Introduction: basic facts about scalar-tensor theories Scalar-tensor black holes and the no hair paradigm Building higher order scalar-tensor black holes Conformal secondary hair? Hairy black hole Conclusions Introduction: basic facts about scalar-tensor theories 1 Scalar-tensor black holes and the no hair paradigm 2 Conformal secondary hair? Building higher order scalar-tensor black holes 3 An integrability theorem Example solutions Hairy black hole 4 Conclusions 5 C. Charmousis Hairy black holes in scalar tensor theories