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Pavel Bakala Martin Blaschke , Martin Urbanec , Gabriel Török and Eva Šrámková

Compact Star Dipole Magnetic Field on the Background o f Hartle -Thorne Spacetime Geometry preliminary results. Pavel Bakala Martin Blaschke , Martin Urbanec , Gabriel Török and Eva Šrámková.

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Pavel Bakala Martin Blaschke , Martin Urbanec , Gabriel Török and Eva Šrámková

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

  2. Compact Star Dipole Magnetic Field on the Background of Hartle-Thorne Spacetime Geometry AimsandScope • Hartle-Thornespacetime 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

  3. Hartle-Thorne Spacetime Geometry • Exactsolutionof Einstein equationsdescribingspacetime in thevicinityof a perfect fluid, stationaryandaxiallysymmetricandslowlyrotatingstar • Parametersofthe solution: • MassM • Specificangularmomentumj • Dimensionlessquadrupole moment q • Coefficients of metric with accuracy up to the quadratic terms

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

  5. First Step: Magnetic Dipole on the Background of the Lense-ThirringSpacetime Geometry • 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

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

  7. The solution on the Hartle-Thorne Spacetime Background • Maxwell equations ofperturbations term: hierarchyand depencies • Final perturbation expansion • New perturbation terms ofazimuthalcomponent

  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. Conclusions Plans: • 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.

  13. Thankyouforyourattention.

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