A class of exact solutions of Einstein's field equations
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Abstract: (APS)
The work of Weyl on the gravitational field occasioned by an axially symmetric distribution of matter and charge is generalized to the case in which g44 and φ for an electrostatic field are functionally related, with or without spatial symmetry. It is shown that the most general electrostatic field in which g44 and φ are related by an equation of the form g44=12(φ+c)2 can be represented by a line element of the form (ds)2=−e−w[(dx1)2+(dx2)2+(dx3)2]+ew(dt)2. Certain of the field equations are then identically satisfied while the remaining ones reduce to a single equation for w. The substitution w=−2log(1+v) transforms this into Laplace's equation for v, so that the solution can be expressed in terms of harmonic function.References(1)
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