Poster Presentation at XXVI GA IAU, 14-25 August, 2006, JD02-16

Presenter: Bobomurat Ahmedov, Uzbekistan AS, Tashkent

E-mail: ahmedov@astrin.uzsci.net

External Electromagnetic Fields of Slowly Rotating Relativistic

Magnetized NUT Stars

Co-author: Avas Khugaev

Plan of talk

• Basic assumptions and approach• Electromagnetic Fields of Slowly Rotating

Axial Symmetric Magnetized NUT Star• Conclusion

gR

GRRBBconstBR

12200

2

10)/( ∝=

⇒=

200

2

)/( RRconstR

Ω=Ω

⇒=Ω

GR effects are important for compact objects

Immense difficulty of simultaneously solving the Maxwell eqs and the highly nonlinear Einstein eqs

5.0~)21(,5~2,10~ 22 rcGMkm

rcGMRkmR g −=

αβαβαβ

αβαβαβ κ

)()(

,21

Gem TTT

TRgR

+=

=−

αβ

αβ

νβμαβμν

π JF

Fe

4

,0

;

,

=

=

APPROACH

EMF are considered in a given background geometry

Slow rotation approximation: comparing the neglected terms with the lower order one gives ratios

R3Ω2/GM < 10%even for fastest rotating stars (PSR J1748-2446ad & PSR 1937+214)

Rα β - gα β R/2 = κ Tα β

Tα β = Tα β(matter) + Tα β

(em) ¼ Tα β(matter)

ρ(em) c2 ¼ B2/8π ) ρ(em) ¼ 103 g/cm3 if B s 1012 G

ρ(em) ¿ ρ(matter) ¼ 1014 g/cm3 consequently Tα β(em) ¿ Tα β

(matter)

),1( gg Bvc

Emdtvdm ×+= r

rGMEg 2−=

])(3[23r

rrJJcGBg

⋅−=

METRIC OF SLOWLY ROTATING NUT STAR

ZAMO OBSERVER:

ω(r) ´ 2aM/r3

20

rBr μ

=

Monopolar configuration for MF

04

sin3

)( 300

,ˆˆ

, =−−− θμ

θωμθ

θ ctgr

lr

rNEE rr

0)(sin)(sin ,ˆ

,ˆ2 =+ θ

θθθ ENrEr r

r

⎥⎦⎤

⎢⎣⎡ +⎟

⎠⎞

⎜⎝⎛−⎟

⎠⎞

⎜⎝⎛−

Ω=

Mr

rM

rMl

MrRrEr

2ln211

2cos),( 2

002

0ˆ μθωμμθ

⎭⎬⎫

⎩⎨⎧

⎟⎠⎞

⎜⎝⎛ ++−= θθωμθθ ctg

rM

Mrl

MNrE 21

2sin

2),( 0ˆ

DIPOLAR MAGNETIC FIELD

.sin]11ln[43

,cos)]1(2[ln43

22

2

23

θμ

θμ

θ ++=

++−=

NN

Mr

rMNB

rM

rMN

MBr

CONCLUSIONE/M Fields of Rotating Magnetized NUT stars in General Relativity:GR Effects Resulting from Dragging of Inertial Frames Monopolar Part and NUT parameter are Very Important for EF For MF only mass of star plays a role

3/2 raM=ωRcGM 2/

l