Geometry and Thermodynamics of Black Holes in Magnetic Fields ...

Magnetised Black Holes in STU Supergravity• We can magnetise black holes in supergravities too. Currentlywe (Cvetič, Gibbons, Saleem, CNP) are looking in the fourdimensionalSTU model (N = 2 supergravity coupled to 3vector multiplets). Now have four independent U(1) gaugefields, so four charges and four magnetic fields. We no use theO(4, 4) symmetry of the associated KK reduced 3-dimensionalsigma model to generate the magnetised solutions.• As well as magnetising electric black holes, it is also nowof interest to magnetise magnetically-charged black holes.Consider static black holes for simplicity. The metric isds 2 = H ds 2 3 + H−1 sin 2 θ (dφ − ωdt) 2 ,(ds 2 3 = −r(2 − 2m)dt2 + R 1 r 2 r 3 r 4 dθ 2 + R )1r 2 r 3 r 4r(r − 2m) dr2ω =4∑i=1[− p iB i+ p iB 1 B 2 B 3 B 4 [r i + (r − 2m) cos 2 ]θ]r,2r i 8B i r iH 2 1 ∏ 4 (=(1 + 1r 1 r 2 r 3 r2 B ip i cos θ) 2 + B2 i r 1r 2 r 3 r 44 i=1ri2r i = r + 2m sinh 2 δ i , p i = 2m sinh δ i cosh δ i .,]sin 2 θ ,