1. Pavel Bakala Martin Blaschke, Martin Urbanec, Gabriel Török and Eva Šrámková Institute of Physics, Faculty of Philosophy and Science, Silesian University in Opava, Czech Republic Compact Star Dipole Magnetic Field on the Background of Hartle-Thorne Spacetime Geometry preliminary results

2. Compact Star Dipole Magnetic Field on the Background of Hartle-Thorne Spacetime Geometry  Hartle-Thorne spacetime geometry  Maxwell equations for the electromagnetic field of slowly rotating compact neutron stars  Magnetic field of aligned dipole character  Perturbative expansion of a fourpotential of the field  Static observers at infinity  Local Keplerian orbiting observers  Conclusions Aims and Scope

3.  Exact solution of Einstein equations describing spacetime in the vicinity of a perfect fluid, stationary and axially symmetric and slowly rotating star  Parameters of the solution:  Mass M  Specific angular momentum j  Dimensionless quadrupole moment q Hartle-Thorne Spacetime Geometry  Coefficients of metric with accuracy up to the quadratic terms

4.  Aligned magnetic dipole fourpotential  Maxwell equation  Fields in ZAMO frame Magnetic field lines frozen into the surface of star Magnetic field lines frozen into the surface of star Maxwell equations on the Hartle-Thorne background

5.  Linear approximation (in terms j) of the Hartle-Thorne metric  Magnetic component of the fourpotential  Electric component of fourpotential induced by rotation and frame dragging  Perturbation expansion First Step: Magnetic Dipole on the Background of the Lense-Thirring Spacetime Geometry

6.  Completed perturbation expansion  Maxwell equations Solution on the Hartle-Thorne Spacetime Background

7.  Maxwell equations of perturbations term: hierarchy and depencies  Final perturbation expansion  New perturbation terms of azimuthal component The solution on the Hartle-Thorne Spacetime Background

8. Electromagnetic Field of Realistic Neutron Stars  Model neutron stars  Local magnetic field on the surface B=1000T  Boost from ZAMO frame to an arbitrary rotating frame (Martin Urbanec, Prague Synergy 2013 talk)

9. Electric Field for Static Observers at Infinity

10. Magnetic Field for Static Observers at Infinity

11. Electric Field for Keplerian Local Observers Magnetic Field for Keplerian Local Observers

12.  Perturbation expansion for the dipole field with an arbitrary declination on the Hartle-Thorne spacetime geometry background.  Analysis of charged matter orbital motion in such field. Conclusions Plans:

13. Thank you for your attention.