Universality in Logarithmic Temperature Corrections to Near-Extremal Rotating Black Hole Thermodynamics in Various Dimensions

Abstract

The low-temperature thermodynamics of near-extremal rotating black holes has recently been revisited to incorporate one-loop contributions that are dominant in this regime. We discuss these quantum corrections to the gravitational path integral for asymptotically Anti de-Sitter black holes in four and five dimensions. In four dimensions we explicitly consider Kerr-AdS${}_4$, Kerr-Newman-AdS${}_4$ and the rotating black hole in $\mathcal{N}=4$ gauged supergravity with two scalars and two electric charges turned on. In five dimensions we explicitly address the asymptotically flat Myers-Perry black hole and the Kerr-AdS${}_5$ black hole. In every case we find that tensor modes contribute $\frac{3}{2}\log T_{\mathrm{Hawking}}$ to the low-temperature thermodynamics. We identify the root cause of this universality in two facts: (i) the universal presence of a $SL(2,\mathbb{R})$ subgroup of isometries in the near-horizon geometry and (ii) a set of cancellations in the Lichnerowicz operator. We show that these two conditions hold for near-extremal black holes in asymptotically flat and asymptotically AdS spacetimes of various dimensions.

42 pages