KERR SUPERSPINARS AS AN ALTERNATIVE TO BLACK HOLES Zdeněk Stuchlík

1. 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

4. 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.

5. Kerr geometry The line element in Boyer-Linquist coordinates where is

6. Kerr geometry • Black hole ... • Naked singularity … • Superspinar ... The hypothetical surface is at Rs=0.1M .

7. 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.

8. Chapter 1 Keplerian accretion discs orbiting Kerr superspinars [Stuchlík 1980]

9. 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

10. Keplerian discs

11. Keplerian discs

12. Energy efficiency of accretion There is jump in for in BH and NS side.

13. Efficiency of Keplerian discs a: (0,1) <=>(1.66,6.53)identical spectra(Takahashi&Harada,CQG,2010)

14. Chapter 2 Evolution of superspinars due to Keplerian accretion discs [Stuchlik 1981, Stuchlík & Hledík 2010]

17. (Calvani & Nobili, 1979; Stuchlík 1981)

27. 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

28. Chapter 3 Near extreme Kerr superspinars as an source of extremely high energy particles [Stuchlik 2011]

29. Circular orbits at r =1 No fine tuning necessary

31. Chapter 4 Epicyclic oscillations of Keplerian discs around superspinars [Torok& Stuchlík 2005]

32. Epicyclic frequencies in Kerr geometry

33. Epicyclic frequencies Black holes:

34. Epicyclic frequencies Black hole Naked singularity

35. Loci of marginally stable orbits and extrema points of epicyclic frequencies

36. Loci of marginally stable orbits and extrema points of epicyclic frequencies

37. Epicyclic frequencies (BH)

38. Epicyclic frequencies (BH)

39. Epicyclic frequencies (NS)

40. Epicyclic frequencies (NS)

41. Resonant radii (NS)

42. Discoseismology, trapped oscillations,… Axisymmetric modes: NS BH (after Kato, Fukue & Mineshige; Wagoner et al.) Nonaxisymmetric modes… NS BH

43. Strong resonant radii ( )

44. 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

45. Chapter 5 Appearance of Keplerian discs orbiting Kerr superspinars [Stuchlík & Schee 2010]

46. 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

47. Carter equations of motion for the case m=0 where is

48. Radial and latitudinal motion where we have introduced impact parameters

49. Latitudinal motion Turning points are determined by the condition The extrema of the function are determined by At the maxima of function , there is

50. Latitudinal motion