5.5 Microscopic accounting of superradiance

We mentioned in Section 2.1 that extremal spinning black holes that do not admit a globally-defined timelike Killing vector spontaneously emit quanta in the range of frequencies (11View Equation). This quantum effect is related by detailed balance to the classical effect of superradiant wave emission, which occur in the same range of frequencies.

It has been argued that the bound (11View Equation) essentially follows from Fermi–Dirac statistics of the fermionic spin-carrying degrees of freedom in the dual two-dimensional CFT [121] (see also [132Jump To The Next Citation Point]). These arguments were made for specific black holes in string theory but one expects that they can be applied to generic extremal spinning black holes, at least qualitatively. Let us review these arguments here.

One starts with the assumption that extremal spinning black holes are modeled by a 2d CFT, where the left and right sectors are coupled only very weakly. Therefore, the total energy and entropy are approximately the sum of the left and right energies and entropies. The state corresponding to an extremal spinning black hole is modeled as a filled Fermi sea on the right sector with zero entropy and a thermal state on the left sector, which accounts for the black-hole entropy. The right-moving fermions form a condensate of aligned spins s = +1 ∕2, which accounts for the macroscopic angular momentum. It is expected from details of emission rates in several parametric regimes that fermions are only present on the right sector, while bosons are present in both sectors [105, 106Jump To The Next Citation Point].

Superradiant spontaneous emission is then modeled as the emission of quanta resulting from interaction of a left and a right-moving mode. Using details of the model such as the fact that the Fermi energy should be proportional to the angular velocity ΩJ, one can derive the bound (11View Equation). We refer the reader to [132] for further details. It would be interesting to better compare these arguments to the present setup, and to see how these arguments could be generalized to the description of the bound (12View Equation) for static extremal rotating black holes. Let us finally argue that the existence of a qualitative process of superradiant emission in these models further supports the conjecture that the dual theory to extremal black holes is a chiral limit of a 2d CFT instead of a chiral CFT with no right-moving sector.

  Go to previous page Go up Go to next page