**1. Background:**

Lense-Thirring precession is the rotation undergone by the spin of a particle located in the gravitational field of a massive spinning body. In terms of asymptotically inertial coordinates $(t,\vec x)$ in a four-dimensional space-time, and if we denote by $\vec J$ the angular momentum of the source, the angular velocity of precession of a particle at position $\vec x$ is

$$\vec\Omega = \frac{1}{r^3}\left(-\vec J+3\frac{(\vec J\cdot\vec x)\vec x}{r^2}\right)$$

where $r\equiv\sqrt{\vec x\cdot\vec x}$ and the dot denotes the scalar product of spatial vectors. We use units such that $G=c=1$. (For the derivation of this formula, see e.g. Misner-Thorne-Wheeler, section 40.7.)

**2. My question:**

The dependence of the angular velocity $\vec\Omega$ on the source's angular momentum $\vec J$ and on the spatial position $\vec x$ is exactly the same as that of the electric field generated by an electric dipole. Under such an identification, $\vec\Omega$ is identified with the electric field while $\vec J$ is identified with the dipole moment. My question is the following: is there an *intuitive *explanation for why the precessional angular velocity *has* to be of the same form as the field sourced by a dipole?

Just to make things clear: I'm not looking for a mathematical proof that the above formula for $\vec\Omega$ is correct. Instead, I'd like to find an intuitive (but nevertheless rigorous) argument that makes the above result obvious. Indeed, the standard derivation of the formula for $\vec\Omega$ relies on some relatively advanced mathematical tools, but the result is so simple and pretty that I suspect there's a deeper reason for the apparent coincidence with the formula from electrostatics. (Of course, my expectation may be wrong.)