# 重力磁性

## 背景

This approximate reformulation of gravitation as described by general relativity in the weak field limit makes an apparent field appear in a frame of reference different from that of a freely moving inertial body. This apparent field may be described by two components that act respectively like the electric and magnetic fields of electromagnetism, and by analogy these are called the gravitoelectric and gravitomagnetic fields, since these arise in the same way around a mass that a moving electric charge is the source of electric and magnetic fields. The main consequence of the gravitomagnetic field, or velocity-dependent acceleration, is that a moving object near a rotating massive object will experience acceleration not predicted by a purely Newtonian (gravitoelectric) gravity field. More subtle predictions, such as induced rotation of a falling object and precession of a spinning object are among the last basic predictions of general relativity to be directly tested.

## 數學形式

$\nabla \cdot \mathbf{E} = -4 \pi G \rho \$
$\nabla \cdot \left( \frac{1}{2} \mathbf{B} \right) = 0 \$
$\nabla \times \mathbf{E} = -\frac{1}{c} \frac{\partial \left( \frac{1}{2} \mathbf{B} \right)} {\partial t} \$
$\nabla \times \left( \frac{1}{2} \mathbf{B} \right) = \frac{1}{c} \left( -4 \pi G \mathbf{J} + \frac{\partial \mathbf{E}} {\partial t} \right) = \frac{1}{c} \left( -4 \pi G \rho \mathbf{v}_{\rho} + \frac{\partial \mathbf{E}} {\partial t} \right) \$