This course will examine supersymmetric "black-hole-like" solutions of supergravity in various dimensions. 

 

We will start by constructing the simplest charged black-hole geometries, and will show how supersymmetry greatly simplifies  the solutions, and the "BPS equations" that govern them.   We will then use supersymmetry to construct multi-centered BPS black-hole solutions.  We will study the near-horizon geometry and the tidal forces experienced by geodesic probes. 

 

To construct gravitational solitons, we will dissect one of the original "no go" theorems in five-dimensional gravity and show how Chern-Simons interactions and magnetic fluxes threading non-trivial spatial topology provides a way around the standard dogma that there are "no solitions without horizons."  In five dimensions, supersymmetry reduces the "BPS equations" to a linear "electromagnetic problem" and we will use this to construct large families of supersymmetric solitons in five-dimensional supergravity. We discuss the regularity and moduli spaces of such solutions.

 

If there is sufficient time, we will survey an even richer classes of six-dimensional microstate geometries and discuss the tidal forces on geodesic probes.  We will see that, unlike their black-hole counterparts, microstate geometries generate large tidal forces well before the probe reaches the horizon scale. This has very important implications for how infalling matter is “scrambled” by the black hole.