Exact Results in Quantum Theory

I will review recent progress in our understanding of near-extremal black holes. Starting from classical gravity, I will show that in AdS spacetimes and in higher dimensions these black holes are extremely sensitive to sources located arbitrarily far away, which can generate large curvature near the horizon. While this effect is absent for four-dimensional asymptotically flat black holes, an analogous enhancement of curvature appears once higher-curvature corrections to the Einstein–Maxwell theory are included. Remarkably, since these corrections arise from electron loops, the resulting effect is unexpectedly large.Finally, I will show that sufficiently close to extremality new very light modes appear, describing fluctuations of the near-horizon region. Because of their small mass, these modes cannot be neglected and they significantly modify black hole thermodynamics and Hawking evaporation.