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

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

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

Aligned magnetic dipole fourpotential

Maxwell equation

Fields in ZAMO frame

Magnetic field lines frozen into the surface of star

Maxwell equations on the Hartle-Thorne background

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

Completed perturbation expansion

Maxwell equations

Solution on the Hartle-Thorne Spacetime Background

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

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)

Electric Field for Static Observers at Infinity

Magnetic Field for Static Observers at Infinity

Electric Field for Keplerian Local Observers

Magnetic Field for Keplerian Local Observers

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:

Thank you for your attention.