# 重力電磁性

（重定向自重力磁性

## 背景

 重力磁性—重力磁場H，場源為（總）角動量J。
 電磁現象—磁場B，場源為磁偶極矩m…
 …或者場源可為電流I，產生一樣的場分布。
 流體力學—對於浸於流體中的固體球產生的旋轉流體拖曳，類比於電磁學的磁性，以及重力磁性產生的參考系拖曳。

## 數學形式

### 方程式

${\displaystyle \nabla \cdot \mathbf {E} _{\text{g}}=-4\pi G\rho _{\text{g}}\ }$ ${\displaystyle \nabla \cdot \mathbf {E} ={\frac {\rho }{\epsilon _{0}}}}$
${\displaystyle \nabla \cdot \mathbf {B} _{\text{g}}=0\ }$ ${\displaystyle \nabla \cdot \mathbf {B} =0\ }$
${\displaystyle \nabla \times \mathbf {E} _{\text{g}}=-{\frac {\partial \mathbf {B} _{\text{g}}}{\partial t}}\ }$ ${\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}\ }$
${\displaystyle \nabla \times \mathbf {B} _{\text{g}}=-{\frac {4\pi G}{c^{2}}}\mathbf {J} _{\text{g}}+{\frac {1}{c^{2}}}{\frac {\partial \mathbf {E} _{\text{g}}}{\partial t}}}$ ${\displaystyle \nabla \times \mathbf {B} ={\frac {1}{\epsilon _{0}c^{2}}}\mathbf {J} +{\frac {1}{c^{2}}}{\frac {\partial \mathbf {E} }{\partial t}}}$

### 勞侖茲力

${\displaystyle \mathbf {F_{\text{g}}} =m\left(\mathbf {E} _{\text{g}}\ +\ 4\mathbf {v} \times \mathbf {B} _{\text{g}}\right)}$ ${\displaystyle \mathbf {F_{\text{e}}} =q\left(\mathbf {E} \ +\ \mathbf {v} \times \mathbf {B} \right)}$

### 坡印廷向量

${\displaystyle {\mathcal {S}}_{\text{g}}=-{\frac {c^{2}}{4\pi G}}\mathbf {E} _{\text{g}}\times 4\mathbf {B} _{\text{g}}}$ ${\displaystyle {\mathcal {S}}=c^{2}\varepsilon _{0}\mathbf {E} \times \mathbf {B} }$

## 參考文獻

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3. ^ Gravitation and Inertia, I. Ciufolini and J.A. Wheeler, Princeton Physics Series, 1995, ISBN 0-691-03323-4
4. ^ B. Mashhoon, F. Gronwald, H.I.M. Lichtenegger. Gravitomagnetism and the Clock Effect. Lect.Notes Phys. 1999, 562: 83–108. Bibcode:2001LNP...562...83M. arXiv:gr-qc/9912027.
5. ^ S.J. Clark, R.W. Tucker. Gauge symmetry and gravito-electromagnetism. Classical and Quantum Gravity. 2000, 17 (19): 4125–4157. Bibcode:2000CQGra..17.4125C. arXiv:gr-qc/0003115. doi:10.1088/0264-9381/17/19/311.
6. ^ B. Mashhoon. Gravitoelectromagnetism: A Brief Review. 2008. Bibcode:2003gr.qc....11030M. arXiv:gr-qc/0311030.