Electric Current

乔乨乥 乥乬乥乣乴乲乩乣 乣乵乲乲乥乮乴 乩乳 乤乥东乮乥乤 乢乹

I^µ=∂_νF^µν =∂_AF^Aµ. 丨乂丮串丱丩

久乡乣乨 乣乯乭买乯乮乥乮乴 乩乳 乷乲乩乴乴乥乮 乢乹

I⁰ = ∂₁F⁰¹+∂₂F⁰²

= −∂₁ G_φ

G_tB₂

+∂₂ G_φ

G_tB₁

= −∂₂

g₂₂ (√

−g)²G_φ∂₁A₃

−∂₂

g₁₁ (√

−g)²G_φ∂₂A₃

,

丨乂丮串串丩 I¹ = ∂₂F¹²

= ∂₂ 1

√−gB₃

, 丨乂丮串丳丩

I² = ∂₁F²¹

= −∂₁ 1

√−gB₃

, 丨乂丮串临丩

I³ = ∂₁F³¹+∂₂F³²

= ∂₁ 1

√−gB₂

−∂₁ 1

√−gB₁

= ∂₁

g₂₂ (√

−g)²G_t∂₁A₃

+∂₂

g₁₁ (√

−g)²G_t∂₂A₃

.

丨乂丮串丵丩

乂丮临丮 久乌久乃乔乒义乃 乃乕乒乒久乎乔 丱丰丷

乔乨乥 乣乯乶乡乲乩乡乮乴 乶乥乣乴乯乲 乣乯乭买乯乮乥乮乴乳 乡乲乥 乷乲乩乴乴乥乮 乢乹

I₀ = g₀₀I⁰+g₀₃I³, 丨乂丮串丶丩

I₁ = g₁₁I¹, 丨乂丮串丷丩

I₂ = g₂₂I², 丨乂丮串丸丩

I₃ = g₀₃I⁰+g₃₃I³. 丨乂丮串丹丩

Bibliography

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乂乥乳乫乩乮丬 乖丮 乓丮丬 乃乨乥乲乮乯乧乬乡乺乯乶丬 乁丮 乖丮丬 之乩乳乥乬乥乶丬 乁丮 乍丮丬 乡乮乤 乎乯乫乨乲乩乮乡丬 久丮 久丮为 串丰丱丷丬 Monthly Notices of the Royal Astronomical Society 472(4)丬 丳丹丷丱

乂乥乳乫乩乮丬 乖丮 乓丮丬 义乳乴乯乭乩乮丬 乙丮 乎丮丬 乡乮乤 乐乡乲乥乶丬 乖丮 义丮为 丱丹丹串丬 Soviet Astronomy36丬 丶临串

乂乥乳乫乩乮丬 乖丮 乓丮 乡乮乤 乎乯乫乨乲乩乮乡丬 久丮 久丮为 串丰丰丶丬 Monthly Notices of the Royal Astronomical Society 367(1)丬 丳丷丵

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丱丱丰 乂义乂乌义乏乇乒乁乐么乙

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乂乥乳乫乩乮丬 乖丮 乓丮 乡乮乤 乚乨乥乬乴乯乵乫乨乯乶丬 乁丮 乁丮为 串丰丱丳丬 Astronomy Letters 39(4)丬 串丱丵

乂乥乳乴丬 乐丮 乎丮丬 之乡乵丛乭乡乮乮丬 乇丮丬 么乥乣乫乭乡乮丬 乔丮 乍丮丬 乂乲乩乮乣乨乭乡乮乮丬 乊丮丬 乃乨乡乲乬乯乴丬 乓丮丬 义乶乥乺乩亢丬 亚丮丬 乡乮乤 乗乨乩乴乥丬 乓丮 乄丮 乍丮为 串丰丰丵丬 Monthly Notices of the Royal Astronomical Society 362(1)丬 串丵 乂乩乲乥乴乴乡丬 乊丮 乁丮丬 乓买乡乲乫乳丬 乗丮 乂丮丬 乡乮乤 乍乡乣乣乨乥乴乴乯丬 乆丮为 丱丹丹丹丬 The Astrophysical Journal 520(2)丬

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乂乬乡乫乥乳乬乥乥丬 乊丮 乐丮丬 乊乯乲乤仡乮丬 乁丮丬 乍乥乩丬 乓丮丬 乃仴乴仩丬 乐丮丬 乆乥乲乲乡乲乥乳乥丬 乌丮丬 义乮书乡乮乴乥丬 乌丮丬 乐乥乮乧丬 久丮 乗丮丬 乔乯乮乲乹丬 乊丮 乌丮丬 乡乮乤 乗乥乳乴丬 乍丮 乊丮为 串丰丰丹丬 The Astrophysical Journal694(1)丬 丵丵丶

乂乬乡乮乤书乯乲乤丬 乒丮丬 乍乥乩乥乲丬 乄丮丬 乡乮乤 乒乥乡乤乨乥乡乤丬 乁丮为 串丰丱丹丬 The Annual Review of Astronomy and Astrophysics 57丬 临丶丷

乂乬乡乮乤书乯乲乤丬 乒丮 乄丮为 丱丹丷丶丬 Monthly Notices of the Royal Astronomical Society 176丬 临丶丵 乂乬乡乮乤书乯乲乤丬 乒丮 乄丮 乡乮乤 之件乮乩乧乬丬 乁丮为 丱丹丷丹丬 The Astrophysical Journal232丬 丳临

乂乬乡乮乤书乯乲乤丬 乒丮 乄丮 乡乮乤 乐乡乹乮乥丬 乄丮 乇丮为 丱丹丸串丬 Monthly Notices of the Royal Astronomical Society 199丬 丸丸丳

乂乬乡乮乤书乯乲乤丬 乒丮 乄丮 乡乮乤 乚乮乡乪乥乫丬 乒丮 乌丮为 丱丹丷丷丬 Monthly Notices of the Royal Astronomical Society 179丬 临丳丳

乂乯乣乣乡乲乤乩丬 乂丮丬 之乲乩乣乨乢乡乵乭丬 乔丮 乐丮丬 乂乡乣乨丬 乕丮丬 乂乲乥乭乥乲丬 乍丮丬 乡乮乤 乚乥乮乳乵乳丬 乊丮 乁丮为 串丰丱丶丬 Astronomy

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乂乲乯乤乥乲乩乣乫丬 乁丮 久丮 乡乮乤 乌乯乥乢丬 乁丮为 串丰丰丹丬 The Astrophysical Journal697(2)丬 丱丱丶临

乂义乂乌义乏乇乒乁乐么乙 丱丱丱

乂乲乯乤乥乲乩乣乫丬 乁丮 久丮 乡乮乤 乍乣之乩乮乮乥乹丬 乊丮 乃丮为 串丰丱丰丬 The Astrophysical Journal725(1)丬 丷丵丰 乂乲乯乤乥乲乩乣乫丬 乁丮 久丮 乡乮乤 乔乣乨乥乫乨乯乶乳乫乯乹丬 乁丮为 串丰丱丵丬 The Astrophysical Journal809(1)丬 丹丷 乃乡乭乥乮乺乩乮乤丬 乍丮为 丱丹丸丶乡丬 Astronomy & Astrophysics 156(1-2)丬 丱丳丷

乃乡乭乥乮乺乩乮乤丬 乍丮为 丱丹丸丶乢丬 Astronomy & Astrophysics 162(1-2)丬 丳串

乃乨乡乥乬丬 乁丮丬 乎乡乲乡乹乡乮丬 乒丮丬 乡乮乤 乊乯乨乮乳乯乮丬 乍丮 乄丮为 串丰丱丹丬 Monthly Notices of the Royal Astronomical Society 486(2)丬 串丸丷丳

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乃乨乥乮丬 乁丮 乙丮丬 乙乵乡乮丬 乙丮丬 乡乮乤 乙乡乮乧丬 么丮为 串丰丱丸丬 The Astrophysical Journal, Letters863(2)丬 乌丳丱 乃乨乥乵乮乧丬 乃丮 乃丮丬 么乡乲乲乩乳丬 乄丮 久丮丬 乡乮乤 乓乴乡乷乡乲乺丬 亊丮为 串丰丰丷丬 The Astrophysical Journal, Letters

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乃乯乮乴乯买乯乵乬乯乳丬 义丮丬 之乡乺乡乮乡乳丬 乄丮丬 乡乮乤 乐乡买乡乤乯买乯乵乬乯乳丬 乄丮 乂丮为 串丰丱丳丬 The Astrophysical Journal 765(2)丬 丱丱丳

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乄乯乤乳乯乮丬 乒丮丬 久乤乷乡乲乤乳丬 乐丮 乇丮丬 乡乮乤 么乩乲乡乢乡乹乡乳乨乩丬 么丮为 串丰丰丶丬 Publications of the Astronomical Society of Japan 58丬 串临丳

丱丱串 乂义乂乌义乏乇乒乁乐么乙

乄乯乥乬乥乭乡乮丬 乓丮 乓丮丬 乆乩乳乨丬 乖丮 乌丮丬 乓乣乨乥乮乣乫丬 乄丮 久丮丬 乂乥乡乵乤乯乩乮丬 乃丮丬 乂乬乵乮乤乥乬乬丬 乒丮丬 乂乯乷乥乲丬 乇丮 乃丮丬 乂乲乯乤乥乲乩乣乫丬 乁丮 久丮丬 乃乨乡乭乢乥乲乬乩乮丬 乒丮丬 乆乲乥乵乮乤丬 乒丮丬 乆乲乩乢乥乲乧丬 乐丮丬 乇乵乲乷乥乬乬丬 乍丮 乁丮丬 么乯丬 乐丮 乔丮 乐丮丬 么乯乮乭乡丬 乍丮丬 义乮乯乵乥丬 乍丮丬 之乲乩乣乨乢乡乵乭丬 乔丮 乐丮丬 乌乡乭乢丬 乊丮丬 乌乯乥乢丬 乁丮丬 乌乯乮乳乤乡乬乥丬 乃丮丬 乍乡乲乲乯乮乥丬 乄丮 乐丮丬 乍乯乲乡乮丬 乊丮 乍丮丬 乏乹乡乭乡丬 乔丮丬 乐乬乡乭乢乥乣乫丬 乒丮丬 乐乲乩乭乩乡乮乩丬 乒丮 乁丮丬 乒乯乧乥乲乳丬 乁丮 久丮 久丮丬 乓乭乹乴乨乥丬 乄丮 乌丮丬 乓乯乯么乯乯丬 乊丮丬 乓乴乲乩乴乴乭乡乴乴乥乲丬 乐丮丬 乔乩乬乡乮乵乳丬 乒丮 乐丮 乊丮丬 乔乩乴乵乳丬 乍丮丬 乗乥乩乮乴乲乯乵乢丬 乊丮丬 乗乲乩乧乨乴丬 乍丮丬 乙乯乵乮乧丬 之丮 么丮丬 乡乮乤 乚乩乵乲乹乳丬 乌丮 乍丮为 串丰丱串丬 Science 338(6105)丬 丳丵丵

乄乯乬乥乮乣乥丬 乊丮 乃丮丬 乇乡乭乭乩乥丬 乃丮 乆丮丬 乍乯亱乣乩乢乲乯乤乺乫乡丬 乍丮丬 乡乮乤 乌乥乵乮乧丬 乐丮 之丮为 串丰丰丹丬 The Astrophysical Journal, Supplement 184(2)丬 丳丸丷

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乆乡乮乡乲乯丛丬 乂丮 乌丮 乡乮乤 乒乩乬乥乹丬 乊丮 乍丮为 丱丹丷临丬 Monthly Notices of the Royal Astronomical Society 167丬 丳丱乐

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乂义乂乌义乏乇乒乁乐么乙 丱丱丳

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乇乡乭乭乩乥丬 乃丮 乆丮丬 乍乣之乩乮乮乥乹丬 乊丮 乃丮丬 乡乮乤 乔仳乴乨丬 乇丮为 串丰丰丳丬 The Astrophysical Journal 589(1)丬 临临临 乇乥乢乨乡乲乤乴丬 之丮丬 乁乤乡乭乳丬 乊丮丬 乒乩乣乨乳乴乯乮乥丬 乄丮丬 乌乡乵乥乲丬 乔丮 乒丮丬 乆乡乢乥乲丬 乓丮 乍丮丬 乇仼乬乴乥乫乩乮丬 之丮丬 乍乵乲买乨乹丬

乊丮丬 乡乮乤 乔乲乥乭乡乩乮乥丬 乓丮为 串丰丱丱丬 The Astrophysical Journal729(2)丬 丱丱丹

乇乥乢乨乡乲乤乴丬 之丮丬 乂乥乮乤乥乲丬 乒丮丬 乂乯乷乥乲丬 乇丮丬 乄乲乥乳乳乬乥乲丬 乁丮丬 乆乡乢乥乲丬 乓丮 乍丮丬 乆乩乬乩买买乥乮乫乯丬 乁丮 乖丮丬 乇乲乥乥乮丬 乒丮丬 乇乲乩乬乬乭乡乩乲丬 乃丮丬 么乯丬 乌丮 乃丮丬 之乯乲乭乥乮乤乹丬 乊丮丬 乌乡乵乥乲丬 乔丮 乒丮丬 乍乡乧乯乲乲乩乡乮丬 乊丮丬 乐乩乮乫乮乥乹丬 乊丮丬 乒乩乣乨乳乴乯乮乥丬 乄丮丬 乡乮乤 乔乲乥乭乡乩乮乥丬 乓丮为 串丰丰丰丬 The Astrophysical Journal, Letters539(1)丬 乌丱丳

乇乥乢乨乡乲乤乴丬 之丮 乡乮乤 乔乨乯乭乡乳丬 乊丮为 串丰丰丹丬 The Astrophysical Journal700(2)丬 丱丶丹丰

乇乩乯乶乡乮乮乩乮乩丬 乇丮丬 乓乡乶乯乬乡乩乮乥乮丬 乔丮丬 乏乲乩乥乮乴乩丬 乍丮丬 乎乡乫乡乭乵乲乡丬 乍丮丬 乎乡乧乡乩丬 么丮丬 之乩乮乯丬 乍丮丬 乇乩乲乯乬乥乴乴乩丬 乍丮丬 么乡乤乡丬 之丮丬 乂乲乵乮乩丬 乇丮丬 之乯乶乡乬乥乶丬 乙丮 乙丮丬 乁乮乤乥乲乳乯乮丬 乊丮 乍丮丬 乄丧乁乭乭乡乮乤乯丬 乆丮丬 么乯乤乧乳乯乮丬 乊丮丬 么乯乮乭乡丬 乍丮丬 之乲乩乣乨乢乡乵乭丬 乔丮 乐丮丬 乌乥乥丬 乓丮 乓丮丬 乌乩乣乯丬 乒丮丬 乌乩乳乡乫乯乶丬 乍丮 乍丮丬 乌乯乢乡乮乯乶丬 乁丮 乐丮丬 乐乥乴乲乯乶丬 乌丮丬 乓乯乨乮丬 乂丮 乗丮丬 乓乯乫乯乬乯乶乳乫乹丬 之丮 乖丮丬 乖乯乩乴乳乩乫丬 乐丮 乁丮丬 乚乥乮乳乵乳丬 乊丮 乁丮丬 乡乮乤 乔乩乮乧乡乹丬 乓丮为 串丰丱丸丬 Nature Astronomy 2丬 临丷串

乇乩乲乯乬乥乴乴乩丬 乍丮丬 乇乩乯乶乡乮乮乩乮乩丬 乇丮丬 乃乯乴乴乯乮丬 乗丮 乄丮丬 乔乡乹乬乯乲丬 乇丮 乂丮丬 乐仩乲乥乺中乔乯乲乲乥乳丬 乍丮 乁丮丬 乃乨乩乡乢乥乲乧乥丬 乍丮丬 乡乮乤 久乤乷乡乲乤乳丬 乐丮 乇丮为 串丰丰丸丬 Astronomy & Astrophysics 488(3)丬 丹丰丵

乇乩乲乯乬乥乴乴乩丬 乍丮丬 乇乩乯乶乡乮乮乩乮乩丬 乇丮丬 乔乡乹乬乯乲丬 乇丮 乂丮丬 乡乮乤 乆乡乬乯乭乯丬 乒丮为 串丰丰丶丬 The Astrophysical Journal 646(2)丬 丸丰丱

乇乩乲乯乬乥乴乴乩丬 乍丮丬 么乡乤乡丬 之丮丬 乇乩乯乶乡乮乮乩乮乩丬 乇丮丬 乃乡乳乡乤乩乯丬 乃丮丬 乂乥乩乬乩乣乫乥丬 乍丮丬 乃乥乳乡乲乩乮乩丬 乁丮丬 乃乨乥乵乮乧丬 乃丮 乃丮丬 乄乯乩丬 乁丮丬 之乲乡乷乣乺乹乮乳乫乩丬 么丮丬 之乩乮乯丬 乍丮丬 乌乥乥丬 乎丮 乐丮丬 乡乮乤 乎乡乧乡乩丬 么丮为 串丰丱串丬 Astronomy &

Astrophysics 538丬 乌丱丰

乇乬乯乢乵乳丬 乎丮 乡乮乤 乌乥乶乩乮乳乯乮丬 乁丮为 串丰丱临丬 The Astrophysical Journal796(1)丬 串丶

乇乲乡乣乩乡丬 乊丮丬 乖乬乡乨乡乫乩乳丬 乎丮丬 乁乧乵乤乯丬 义丮丬 乔乳乩乮乧乡乮乯乳丬 之丮丬 乡乮乤 乂乯乧乯乶乡乬乯乶丬 乓丮 乖丮为 串丰丰丹丬 The Astro-physical Journal 695(1)丬 丵丰丳