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Main article: Wormhole
Einstein collaborated with others to produce a model of a wormhole. His motivation was to model elementary particles with charge as a solution of gravitational field equations, HP Pavilion dv7-1243cl Battery in line with the program outlined in the paper “Do Gravitational Fields play an Important Role in the Constitution of the Elementary Particles?”. These solutions cut and pasted Schwarzschild black holes to make a bridge between two patches.
If one end of a wormhole was positively charged, HP Pavilion dv7-1245ca Battery the other end would be negatively charged. These properties led Einstein to believe that pairs of particles and antiparticles could be described in this way.
Main article: Einstein–Cartan theoryHP Pavilion dv7-1245dx Battery
In order to incorporate spinning point particles into general relativity, the affine connection needed to be generalized to include an antisymmetric part, called the torsion. This modification was made by Einstein and Cartan in the 1920s.
Equations of motionHP Pavilion dv7-1245ef Battery
Main article: Einstein–Infeld–Hoffmann equations
The theory of general relativity has a fundamental law – the Einstein equations which describe how space curves, the geodesic equation which describes how particles move may be derived from the Einstein equations. HP Pavilion dv7-1245eo Battery
Since the equations of general relativity are non-linear, a lump of energy made out of pure gravitational fields, like a black hole, would move on a trajectory which is determined by the Einstein equations themselves, HP Pavilion dv7-1247cl Batterynot by a new law. So Einstein proposed that the path of a singular solution, like a black hole, would be determined to be a geodesic from general relativity itself.
This was established by Einstein, Infeld, and Hoffmann for pointlike objects without angular momentum, and by Roy Kerr for spinning objects.HP Pavilion dv7-1249ef Battery