# 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

$\nabla \cdot \mathbf{E}_\text{g} = -4 \pi G \rho_\text{g} \$ $\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}$
$\nabla \cdot \mathbf{B}_\text{g} = 0 \$ $\nabla \cdot \mathbf{B} = 0 \$
$\nabla \times \mathbf{E}_\text{g} = -\frac{\partial \mathbf{B}_\text{g} } {\partial t} \$ $\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B} } {\partial t} \$
$\nabla \times \mathbf{B}_\text{g} = -\frac{4 \pi G}{c^2} \mathbf{J}_\text{g} + \frac{1}{c^2} \frac{\partial \mathbf{E}_\text{g}} {\partial t}$ $\nabla \times \mathbf{B} = \frac{1}{\epsilon_0 c^2} \mathbf{J} + \frac{1}{c^2} \frac{\partial \mathbf{E}} {\partial t}$

### 勞侖茲力

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

### 坡印廷向量

$\mathcal{S}_\text{g} = -\frac{c^2}{4 \pi G} \mathbf{E}_\text{g} \times 4 \mathbf{B}_\text{g}$ $\mathcal{S} = c^2 \varepsilon_0 \mathbf{E} \times \mathbf{B}$

## 參考文獻

1. ^ R. Penrose. Gravitational collapse: The role of general relativity. Rivista de Nuovo Cimento. 1969,. Numero Speciale 1: 252–276. Bibcode:1969NCimR...1..252P.
2. ^ R.K. Williams. Extracting x rays, Ύ rays, and relativistic ee+ pairs from supermassive Kerr black holes using the Penrose mechanism. Physical Review. 1995, 51 (10): 5387–5427. Bibcode:1995PhRvD..51.5387W. doi:10.1103/PhysRevD.51.5387.
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. arXiv:gr-qc/9912027. Bibcode:2001LNP...562...83M.
5. ^ S.J. Clark, R.W. Tucker. Gauge symmetry and gravito-electromagnetism. Classical and Quantum Gravity. 2000, 17 (19): 4125–4157. arXiv:gr-qc/0003115. Bibcode:2000CQGra..17.4125C. doi:10.1088/0264-9381/17/19/311.
6. ^ B. Mashhoon. Gravitoelectromagnetism: A Brief Review. 2008. arXiv:gr-qc/0311030. Bibcode:2003gr.qc....11030M.