Plan of talk - filePoster Presentation at XXVI GA IAU, 14-25 August, 2006, JD02-16 Presenter:...
Transcript of Plan of talk - filePoster Presentation at XXVI GA IAU, 14-25 August, 2006, JD02-16 Presenter:...
Poster Presentation at XXVI GA IAU, 14-25 August, 2006, JD02-16
Presenter: Bobomurat Ahmedov, Uzbekistan AS, Tashkent
E-mail: [email protected]
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