Ernst equation, Fay identities and variational formulas on hyperelliptic curves

Details Ernst equation, Fay identities and variational formulas on hyperelliptic curves Ernst equation, Fay identities and variational formulas on hyperelliptic curves

2004-01-29

arxiv.org/abs/math-ph/0401055v1

Math. Res. Lett., Vol. 9, 1-20 (2002)

Physics

Mathematical Physics

Scientific paper

We present a unified approach to theta-functional solutions of the stationary
axisymmetric Einstein equations in vacuum. Using Fay's trisecant identity and
variational formulas on hyperelliptic Riemann surfaces, we establish formulas
for the metric functions, the Ernst potential and their derivatives.

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