Black holes inN=8supergravity from SO(4,4) hidden symmetries

Abstract

We detail the construction of the most general asymptotically flat, stationary, rotating, non-extremal, dyonic black hole of the four-dimensional N = 2 supergravity coupled to 3 vector multiplets that describes the ST U model. It generates through Udualities the most general asymptotically flat, stationary black hole of N = 8 supergravity. We develop the solution generating technique based on SO(4, 4)/SL(2, R) 4 coset model symmetries, with an emphasis on the 4-fold permutation symmetry of the gauge fields. We indicate how previously known non-extremal and extremal solutions of the ST U model are recovered as limiting cases. Several properties of the general black hole solution are discussed, including its thermodynamics, the quadratic mass formula, the Bogomolny-Prasad-Sommerfield limit, the slow and fast extremal rotating limits, its properties in regards to the Kerr/conformal field theory correspondence, its Killing tensors and the separability of geodesic motion and probe scalars.

Black holes with intrinsic spin

“…A more ambitious strategy for making a connection between 4D black holes and microscopic considerations is inspired by the remarkable separability of scalar field equations noticed in the background of rotating "four charge" black holes [17] (and now extended to the "fifth" charge [13,14]). It reads off general conformal weights that apply beyond the dilute gas limit [18], at least for some purposes.…”

“…with a canonical normalization referred to as level k. The states in the CFT can then be taken of the form 14) where operators with integral U(1) quantum number F…”

“…These constructions employed the solution generating techniques, by acting with a subset of O(4,4) transformations on a neutral (Kerr or Schwarzschild) black hole, reduced on time-like Killing vector to three dimensions. Only recently did a remarkable tour de force by Chow and Compère lead to a construction of the most general black hole solutions in the STU model [13,14]. While employing the same solutions generating techniques, the missing parameter way obtained by acting with symmetry transformations on a neutral Taub-NUT solution.…”

Wave equation for the Wu black hole

“…The angular equation, 16) has four regular singularities as a 2 , b 2 , 1 g 2 , ∞ and it can be solved in terms of the general Heun's functions [36][37][38].…”

“…The literature with the separability analysis of the wave equations and the subtracted geometry of the asymptotically flat solutions [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] is much richer and complete than the number of studies on the asymptotically anti-de Sitter (AdS) spacetimes, including the recent most general solution for the maximally supersymmetric ungauged supergravity [16][17][18]. The remarkable structure of separability seen in these works has also been found in some gauged supergravity solutions [19][20][21][22][23][24][25][26].…”