1. Jiří Kovář, Petr Slaný, Vladimír Karas, Zdeněk Stuchlík Claudio Cremaschini and John Miller Claudio Cremaschini and John Miller Institute of Physics Silesian University in Opava Czech Republic Charged tori near compact objects Astronomical Institute Czech Academy of Sciences Prague International School for Advanced Studies, SISSA and INFN, Trieste, Italy

2. Beginning of the story Halo orbits existence and basic properties Kovář, Stuchlík and Karas, 2008, Class. Quantum Gravity Kovář, Kopáček, Karas and Stuchlík, 2010, Class. Quantum Gravity Kopáček, Karas, Kovář and Stuchlík, 2010, The Astrophysical Journal

3. Effective potential and halo orbits Neutron star

4. The crazy idea CHARGED OFF-EQUATORIAL TORI Polish donut Czech double donutCzech triple donut test particles approximation (very low densities) kinetic theory (low densities) MHD (high densitites)

5. our toy model - test non-conductive charged fluid - no selfconsistence (for now) - axial symmetry and azimuthal motion basic GRMHD equations Basic equations

6. pressure equations integrability condition Pressure equations – general case non-integrable integrable

7. Geometry Electric field Pressure equations Pressure equations in RN spacetime

8. Equation of state Angular momentum distribution Charge distribution Density equation Boundary conditions Equation of state – density equations

9. Pressure and density profiles Positively charged torus

10. Correction function and charge density Positively charged torus

11. Pressure and density profiles Negatively charged torus

12. Correction function and charge density Negatively charged torus

13. Total charge Total mass Mass and charge of tori

14. 1.We have built a GR toy model of charged thick dielectric torus rotating in gravitational and electromagnetic fields 2.We have tested it and presented it on the background of charged Reissner- Nordström black hole, considering physically relevant (astrophysically unsuitable) parameters of the fluid 3.We are going to test it in more astrophysically relevant cases (dipole magnetic field, reasonable parameters of the fluid, …) 1.We are going to include the electrostatic correction interaction into the equation of state 2.We are going to construct the off-equatorial charged tori (for now, realizing it in the Newtonian way – talk by Petr Slaný) Kovář, Slaný, Stuchlík, Karas, Cremaschini, Miller, 2011, Physical Review D Summary

15. Acknowledgement Claudio Vladimir John Zdenek Petr Trieste 2011 – Mignon hotel my dish