Contents

Table 11.3. Solutions with proper homothety groups H4 on V4, described using the conventions of Table 11.2Metric Tab Homothety Reference(s)(13.51)≡(22.7), cp. (13.53) V (13.52) Godfrey (1972)(13.72) E 2t∂t + y∂y + z∂z Koutras (1992b)(13.73) E 2r∂r + y∂y + z∂z Koutras (1992b)(13.76) E (1 − k 2 )v∂v + t∂t + y∂y − k 2 φ∂φ McIntosh (1979)(13.87) F r∂r + s(φ∂φ + t∂t) Hermann (1983)(14.28b) F (13.52) Hsu and Wainwright (1986)(14.30) F t∂t +2qx∂x +(1− 3q)y∂y +(1− q)z∂z Hewitt (1991b)(14.31) F 3∂t +6x∂x +4y∂y +2z∂z Hewitt et al. (2001)(14.33) F t∂t +(1− p2)y∂y +(1− p3)z∂z Hsu and Wainwright (1986)(14.41) F 5t∂t +4y∂y +2z∂z Hsu and Wainwright (1986)(14.42) F t∂t +(1+q − s)y∂y +(1− q − s)z∂z Rosquist and Jantzen (1985)(15.17), k =0,H = const u q /r R 4u∂u +2(q +1)r∂r +(1− q)x 1 ∂ x 1 Koutras (1992b)(20.32) with Ω = log ρ V (φ − 2t)∂φ + t∂t +4(ρ∂ρ + z∂z) Steele (1991)(20.32) with Ω = z V 3∂φ − t∂t +4(ρ∂ρ + z∂z) Steele (1991)(22.27a), a =0,β = χ, F ∂ρ +4q(γ − 1)(φ∂φ + z∂z) Debever and Kamran (1982)α =4(γ − 1)(qρ + r) + ((2γ − 4)q +2b)t∂t(24.40), H = ln(ζ ¯ζ), ζ = x +iy V x∂x + y∂y + u∂u +(v − 2u)∂v Steele (1991)(28.16), cp. (13.64) V r∂r + u∂u McIntosh (1976b)(33.30) F x∂x + y∂y − u∂u, y =Imζ Koutras (1992b)