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KERR SUPERSPINARS AS AN ALTERNATIVE TO BLACK HOLES Zdeněk Stuchlík Institute of Physics, Faculty of Philosophy and Science, Silesian university in Opava RAGtime Opava , 1 4 . 9 .2011 Coauthors: Stanislav Hledík, Jan Schee and Gabriel T ö r ö k.
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KERR SUPERSPINARS AS AN ALTERNATIVE TO BLACK HOLES Zdeněk Stuchlík Institute of Physics, Faculty of Philosophy and Science, Silesian university in Opava RAGtime Opava, 14.9.2011 Coauthors: Stanislav Hledík, Jan Schee and Gabriel Török
Chapter 1: Keplerian accretion discs orbiting Kerr superspinars • Chapter 2: Evolution of superspinars due to Keplerian accretion discs • Chapter 3:Near-extreme Kerr superspinars as sources of extremely high energy particles • Chapter 4: Epicyclic oscillations of Keplerian discs around superspinars • Chapter 5: Appearances of Keplerian discs orbiting Kerr superspinars • comparison to the Kerr black hole cases • Chapter 6: Profiled lines of thin Keplerian rings in the vicinity of superspinar.
Kerr geometry The line element in Boyer-Linquist coordinates where is
Kerr geometry • Black hole ... • Naked singularity … • Superspinar ... The hypothetical surface is at Rs=0.1M .
String theory behind superspinars • Hořava et.al. – interior solution of the Godel type matched to the external Kerr solution • Time machine removed by the internal solution • Exact model constructed for 4+1 SUSY black hole solution • Defects- no limits – even supermassive superspinars possible in early universe, in agreement with cosmic censor Superspinar - Naked Singularity geometry with RS= 0.1 M . Properties of the boundary assumed similar to those of the Horizon – non-radiating, absorbing.
Chapter 1 Keplerian accretion discs orbiting Kerr superspinars [Stuchlík 1980]
Geodesic structureof KNS circular orbit (Keplerian) Specific energy and specific angular momentum of circular geodesics Parameter Angular velocity with respect to static observers at infinity
Energy efficiency of accretion There is jump in for in BH and NS side.
Efficiency of Keplerian discs a: (0,1) <=>(1.66,6.53)identical spectra(Takahashi&Harada,CQG,2010)
Chapter 2 Evolution of superspinars due to Keplerian accretion discs [Stuchlik 1981, Stuchlík & Hledík 2010]
Evolution of Kerr superspinars and black holes • Accretion rate: • dm/dt ~ 10^(-8) M/year (BH) • dm/dt ~ 10^(-9) M/year (KS) • Conversion due to counterrotating disc by almost three order faster than by corrotating discs • Energy radiated during conversion: • DErad = Dmc(a) – DM(a) • Corotating discs: DErad / Mi ~ 2.5 Counterrotating discs: DErad / Mi ~ 10^(-2) • Inversion of BH spin: DErad / Mi ~ 0.5
Chapter 3 Near extreme Kerr superspinars as an source of extremely high energy particles [Stuchlik 2011]
Circular orbits at r =1 No fine tuning necessary
Chapter 4 Epicyclic oscillations of Keplerian discs around superspinars [Torok& Stuchlík 2005]
Epicyclic frequencies Black holes:
Epicyclic frequencies Black hole Naked singularity
Loci of marginally stable orbits and extrema points of epicyclic frequencies
Loci of marginally stable orbits and extrema points of epicyclic frequencies
Discoseismology, trapped oscillations,… Axisymmetric modes: NS BH (after Kato, Fukue & Mineshige; Wagoner et al.) Nonaxisymmetric modes… NS BH
Orbital frequencies in discs orbiting Kerr superspinars (summary) • Behaviour of orbital epicyclic frequencies very different from black holes • Existence of three radii giving the same frequency ratio (but with different frequencies) • Strong resonance radius at r = a^2 where the radial and vertical epicyclic frequencies coincide • Possible instabilities
Chapter 5 Appearance of Keplerian discs orbiting Kerr superspinars [Stuchlík & Schee 2010]
Optical effects in the field of KS (KNS) • Null geodesic – Integration of Carter equations • Radial and latitudinal motion • Light escape cones of LNRF and GF • Silhouette of BH, KNS and KS • Appearance of Keplerian discs • Captured and trapped photons
Radial and latitudinal motion where we have introduced impact parameters
Latitudinal motion Turning points are determined by the condition The extrema of the function are determined by At the maxima of function , there is