SAM Lectures on Extremal Black Holes in d = 4 Extended Supergravity

Abstract

We report on recent results in the study of extremal black hole attractors in N = 2, d = 4 ungauged Maxwell-Einstein supergravities.For homogeneous symmetric scalar manifolds, the three general classes of attractor solutions with non-vanishing Bekenstein-Hawking entropy are discussed. They correspond to three (inequivalent) classes of orbits of the charge vector, which sits in the relevant symplectic representation R V of the U -duality group. Other than the 1 2 -BPS one, there are two other distinct non-BPS classes of charge orbits, one of which has vanishing central charge.The complete classification of the U -duality orbits, as well as of the moduli spaces of non-BPS attractors (spanned by the scalars which are not stabilized at the black hole event horizon), is also reviewed.Finally, we consider the analogous classification for N 3-extended, d = 4 ungauged supergravities, in which also the 1 N -BPS attractors yield a related moduli space.arXiv:0905.3739v1 [hep-th]

Global structure of five-dimensional fuzzballs

“…There has also been extensive work on extremal non-BPS solutions (see, for example, [117,118,119,120,121,105,90,106,107,122,123,124,108,109]) and our analysis of the Smarr formula is valid for any stationary solution. It would be interesting to investigate the more detailed analysis to these more general solutions and examine the role of the Chern-Simons interaction for such non-BPS solutions.…”

Black holes in supergravity and integrability

“…The study and construction of black hole solutions in supergravity has a long history [1][2][3][4][5].…”

Extremal black attractors in 8D maximal supergravity

“…They also have (p þ 1)-form gauge fields A pþ1 A ½ 1 ... pþ1 in addition to the graviton G , the usual 1-form gauge fields A , scalars f I g and their supersymmetric partners c , . These central charges Z p and gauge fields A pþ1 play, like in the case of 4D black holes [11][12][13], a crucial role in dealing with static, asymptotically flat, and spherically symmetric extremal black p-brane solutions living in higher dimensions. In this regard, and following the first original works [14][15][16][17][18][19] and subsequent ones led by S. Ferrara and collaborators [20,21] and references therein, growing attention has been devoted to the study of the black hole solutions in various dimensions and their attractor mechanism taking into account p-branes carrying nontrivial magnetic p à and electric charges q à of the (p þ 2)-form gauge field strengths F à pþ2 and their magnetic dualsF DÀpÀ2jà [22][23][24][25][26][27][28][29][30][31][32].…”