Conformastatic spacetimes

Conformastatic spacetimes refer to a special class of static solutions to Einstein's equation in general relativity. == Introduction == The line element for the conformastatic class of solutions in Weyl's canonical coordinates reads ( 1 ) d s 2 = − e 2 Ψ ( ρ , ϕ , z ) d t 2 + e − 2 Ψ ( ρ , ϕ , z ) ( d ρ 2 + d z 2 + ρ 2 d ϕ 2 ) , {\displaystyle (1)\qquad ds^{2}=-e^{2\Psi (\rho ,\phi ,z)}dt^{2}+e^{-2\Psi (\rho ,\phi ,z)}{\Big (}d\rho ^{2}+dz^{2}+\rho ^{2}d\phi ^{2}{\Big )}\;,} as a solution to the field equation ( 2 ) R a b − 1 2 R g a b = 8 π T a b .

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