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 R s =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 R S = 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 structure of KNS circular orbit (Keplerian) Specific energy and specific angular momentum of circular geodesics Angular velocity with respect to static observers at infinity Parameter

10. 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:  E rad =  m c (a) –  M(a) Corotating discs:  E rad / M i ~ 2.5 Counterrotating discs:  E rad / M i ~ 10^(-2) Inversion of BH spin:  E rad / M i ~ 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 holeNaked singularity

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

37. Epicyclic frequencies (BH)

39. Epicyclic frequencies (NS)

41. Resonant radii (NS)

42. Discoseismology, trapped oscillations,… Axisymmetric modes: BH (after Kato, Fukue & Mineshige; Wagoner et al.) NS 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 functionare determined by At the maxima of function, there is

50. Latitudinal motion

51. Radial motion The reality conditions and lead to the restrictions on the impact parameter where is

52. Radial motion Defining functions - determine extrema of surface - determine where is fulfilled

53. Radial motion

55. Light escape cones (LEC) Locally Non-Rotating Frame (LNRF) tetrad,, where is

56. Light escape cones (LEC) Geodetic Frame (GF) tetrad (r-th and  -th component same as for LNRF) where is

57. Light escape cones (LEC) We construct LEC of source frame (LNRF, GF) for fixed (r 0,  0 ) in the following procedure

64. The silhouette of superspinar The superspinar silhouette is determined by photons that reach its surface and finish their travel there, contrary to the case of the rim of a black hole silhouette that corresponds to photon trajectories spiralling near the unstable spherical photon orbit around the black hole many times before they reach the observer. The spiralling photons concentrated around unstable spherical photon orbits will create an additional arc characterizing the superspinar (or a Kerr naked singularity) The shape of the superspinar silhouette (arc) is the boundary of the no-turning point region in  plane of the observer.

65. a=1.001 a=2.0 a=6.0  0 =85 o

66. a=1.001 a=2.0 a=6.0  0 =60 o

67. KBH, KNS and KS a/  0 0.998 60 o 1.001KNS1.001KS 85 o

68. Appearance of Keplerian discs Direct image – photons do not cross the equatorial plane. InDirect image – photons cross the equatorial plane once. Transfer function method for the emitted light is used. Integration of null geodesics - deformation of isoradial curves - frequency shift factor - lensing effect

69. Keplerian discs

70. Frequency shift factors for accretion Keplerian discs Frequency shift is defined as which in particular case of source on circular geodesic reads

74. Appearance of Keplerian discs Direct Images The representative rotational parameters are a: 0.9981, 1.0001, 1.001, 1.01, 1.1, 1.5, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0 The inclination of the observer:  0 =85 o Inner edge of the disk: r MS =r MS (a) Outer edge of the disk: r=20M

75. a=0.9981 rms=1.24M

76. a=1.0001 rms=0.94M

77. a=1.001 rms=0.87M

78. a=1.01 rms=0.76M

79. a=1.1 rms=0.67M

80. a=1.5 rms=0.88M

81. a=2.0 rms=1.26M

82. a=3.0 rms=2.17M

83. a=4.0 rms=3.17M

84. a=5.0 rms=4.25M

85. a=6.0 rms=5.39M

86. a=7.0 rms=6.65M

87. Appearance of Keplerian discs InDirect Images The representative rotational parameters are a: 0.9981, 1.0001, 1.001, 1.01, 1.1, 1.5, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0 The inclination of the observer:  0 =85 o Inner edge of the disk: r MS =r MS (a) Outer edge of the disk: r=20M

88. a=0.9981 rms=1.24M

89. a=1.0001 rms=0.94M

90. a=1.001 rms=0.87M

91. a=1.01 rms=0.76M

92. a=1.1 rms=0.67M

93. a=1.5 rms=0.88M

94. a=2.0 rms=1.26M

95. a=3.0 rms=2.17M

96. a=4.0 rms=3.17M

97. a=5.0 rms=4.25M

98. a=6.0 rms=5.39M

99. a=7.0 rms=6.65M

100. Appearance of Keplerian discs Direct Images The representative rotational parameters are a: 0.9981, 1.0001, 1.001, 1.01, 1.1, 1.5, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0 The inclination of the observer:  0 =30 o Inner edge of the disk: r MS =r MS (a) Outer edge of the disk: r=20M

101. a=0.9981 rms=1.24M

102. a=1.0001 rms=0.94M

103. a=1.001 rms=0.87M

104. a=1.01 rms=0.76M

105. a=1.1 rms=0.67M

106. a=1.5 rms=0.88M

107. a=2.0 rms=1.26M

108. a=3.0 rms=2.17M

109. a=4.0 rms=3.17M

110. a=5.0 rms=4.25M

111. a=6.0 rms=5.39M

112. a=7.0 rms=6.65M

113. Appearance of Keplerian discs InDirect Images The representative rotational parameters are a: 0.9981, 1.0001, 1.001, 1.01, 1.1, 1.5, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0 The inclination of the observer:  0 =30 o Inner edge of the disk: r MS =r MS (a) Outer edge of the disk: r=20M

114. a=0.9981 rms=1.24M

115. a=1.0001 rms=0.94M

116. a=1.001 rms=0.87M

117. a=1.01 rms=0.76M

118. a=1.1 rms=0.67M

119. a=1.5 rms=0.88M

120. a=2.0 rms=1.26M

121. a=3.0 rms=2.17M

122. a=4.0 rms=3.17M

123. a=5.0 rms=4.25M

124. Captured and trapped photons

127. Chapter 6 Profiled lines of thin Keplerian rings in the vicinity of Kerr superspinars. [Stuchlík & Schee 2011]

128. Profiled lines The flux of radiation from monochromatic and isotropic source reads where is The resulting formula takes form

129. Profiled lines

132. The end… and the beginning… The work must go on. Thank you for your attention