Gravity seminar - Leo Stein Seminar

Linear perturbation theory is a powerful tool for studying black holes (BHs). Spherically symmetric (Schwarzschild) BHs are straightforward to study because the high degree of symmetry leads to separation of the field equations. However, generic rotating (Kerr) BHs do not have enough symmetry for the metric equations to separate. Researchers have relied on the Teukolsky formalism to solve for curvature perturbations in Kerr, but this leads to a very complicated metric reconstruction procedure. In this talk, I will discuss separating the metric perturbation equations in a special limit of Kerr named near-horizon extremal Kerr (NHEK), which has more symmetry than Kerr. I will (i) give an overview of the geometry of NHEK, (ii) demonstrate the method of highest/lowest weight to build symmetry-adapted basis functions, (iii) explain why the equations separate, and (iv) present an application: solving for deformations to NHEK due to "stringy" interactions. After showing the metric deformation solutions arising from these stringy interaction [dynamical Chern-Simons (dCS) and Einstein-dilaton-Gauss-Bonnet (EdGB) theories], I will present some physical implications: corrections to orbits, horizon areas, and horizon entropies. The increased horizon entropy is a signature of the additional microscopic degrees of freedom that become available as the black hole shrinks towards a new length scale.