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R - TCPA Foundation

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D.S., P. Fiziev, The Spectrum of Electromagnetic Jets from Kerr Black Holes and Naked SingularitiesBoundary conditions1. Stability condition: ω I>0 ( ω = ω R+ iω I).2. On the angular equation: polynomial condition – we use singular solutions!E s=−1, m=−a 2 −2 a m±2 a 2 a m − − N 1=02 N 1=03. On the radial equation: the “black hole” boundary conditions.a) On r +: only incoming wave – sets the choice between R 1(r) and R 2(r).b) On infinity: only outgoing in ∞ wave.¿On infinity the solution is a linear combination from ingoing and outgoing waves:R=C R C R . In order to have only outgoing wave, we need to set lim =0.r ∞ R Using the direction of steepest descent and =∣∣e iarg ,r=∣r∣e iargrwe get:Rarg r=3/2−arg And then: C =lim =0r ∞ R will give us the spectrum for ω.July 5­9, 'GR19 ­Mexico City 2010'R

D.S., P. Fiziev, The Spectrum of Electromagnetic Jets from Kerr Black Holes and Naked SingularitiesThe spectrum (s=­1, M=1/2):At a=0, we find a set of complex frequencies:Jets: D.S., Fiziev P. (2010) QNM: Fiziev P., D.S. (2010)arXiv:1002.0480 [astro­ph.HE]arXiv:1005.5375 [cs.NA]Fiziev P P, D.S., 2009 arxiv: astro­ph:HE/0902.2408, BAJ 10, 2009,Fiziev P P, D.S., 2009 arxiv: astro­ph:HE/0902.2411, BAJ 10, 2009July 5­9, 'GR19 ­Mexico City 2010'

D.S., P. Fiziev, The Spectrum of Electromagnetic Jets from Kerr Black Holes and Naked SingularitiesWhen we add rotation (a>0, n=0,1):aMaM+R 0, m≈R ± 1, mI + 0, m ≪ I 1, m± a=M=1/2Our numerical results are best fit by the formula: n=0,1 ,m=−mi N b 2 −1¿, N =0,1Fiziev P. P., Class. Quant. Grav.27:135001, 2010arXiv:0908,.4234 [gr­qc]July 5­9, 'GR19 ­Mexico City 2010'b=M /a­ bifurcation parameterΩ +=a/2Mr +­ angularvelocity of the horizon

D.S., P. Fiziev, The Spectrum of Electromagnetic Jets from Kerr Black Holes and Naked SingularitiesThe modes with n>1:m=0 m=-1July 5­9, 'GR19 ­Mexico City 2010'

D.S., P. Fiziev, The Spectrum of Electromagnetic Jets from Kerr Black Holes and Naked Singularities●The relation E( ω)and collimation inthe angular solutionsOur results so far:●For a=0, aM, complexspectra ω ndifferent from the QNM case●Analytical formula fitting the first twomodes (n=0,1) ω n=0,1(a)●●Qualitative change of the behaviour ofω n=0,1(a) at the bifurcation point a=M.(transition from black hole to nakedsingularity)Highly non­trivial relation ω n(a) for allmodesJuly 5­9, 'GR19 ­Mexico City 2010'

Conclusion:We obtain specific spectrum of EM jets from black holes and nakedsingularities that can be compared with the existing observational data.Credit: NASA/Swift/Mary Pat Hrybyk­Keith and John Jones.For more information:http://tcpa.uni­sofia.bg/researchThank you for your attention!

D.S., P. Fiziev, The Spectrum of Electromagnetic Jets from Kerr Black Holes and Naked SingularitiesAcknowledgmentsThis talk was supported by the Foundation ”Theoretical andComputational Physics and Astrophysics”, by the BulgarianNational Scientific Found under contracts DO­1­872, DO­1­895,DO­02­136, and Sofia University Scientific Fund, contract185/26.04.2010.July 5­9, 'GR19 ­Mexico City 2010'

D.S., P. Fiziev, The Spectrum of Electromagnetic Jets from Kerr Black Holes and Naked SingularitiesThe polynomial condition:QNM:s=-2P. Fiziev, Classes of Exact Solutions to the TeukolskyMaster Equation Class. Quant. Grav.27:135001, 2010,arXiv:0908.4234P. Fiziev, Novel relations and new properties of confluentHeun's functions and their derivatives of arbitrary order,arXiv:0904.0245v1 [math­ph], J.Phys. A: Math. Theor.43 (2010). 035203July 5­9, 'GR19 ­Mexico City 2010'