Is the method of images applicable to gravity? It is well known that the method of images is a useful tool for solving electrostatics problems. I was wondering why this technique is not applied when considering newtonian gravity?
Obviously there is no "negative mass" to correspond to a negative charge in electromagnetism, but surely could the unphysical nature of negative mass be ignored and considered a mathematical trick to solve a given problem?
The classic example for the method of images is the point charge near an infinite conducting plane, is there a way to apply a similar method to calculate the gravitational field between a point mass and an infinite thin plane?
Some preliminary research online has resulted in no resources on this idea so any references for/against this would be great.
 A: While rare, there are a few uses of the method of images to gravitational problems. As lurscher says, the problem is finding equipotential surfaces. In most problems, such a surface doesn't exist, and hence the scare use of the method of images in GR.
One class of problems for which it does applies are the so-called Dirichlet problems. Suppose one was interested in solving for the metric in some region, with specified boundary conditions on the boundary surface. This is not usually what is done--usually the entire spacetime is solved for. For the case of Dirichlet boundary conditions (requiring the metric to approach some specified value on the boundary surface), image charges can be useful. In this case the image charges could correspond to image black holes, for example.
However, this is somewhat of an exotic problem, and I've only seen perhaps one or two examples where image charges have been used.
A: The method of images works on the electrostatic case because the axis of symmetry of the mirror charges induces an equipotential line that is equivalent to the infinite conductor surface. In gravitational physics, there are no known instances of a physical surface that is at the same potential in the gravitational field.
