Universality in logarithmic temperature corrections to near-extremal rotating black hole thermodynamics in various dimensions
Sabyasachi Maulik, Leopoldo A. Pando Zayas, Augniva Ray, Jingchao Zhang
Abstract
A bstract 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 $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 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 $$ \frac{3}{2}\log {T}_{\textrm{Hawking}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mn>3</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> <mml:mo>log</mml:mo> <mml:msub> <mml:mi>T</mml:mi> <mml:mtext>Hawking</mml:mtext> </mml:msub> </mml:math> to the low-temperature thermodynamics. We identify the root cause of this universality in two facts: (i) the universal presence of a SL(2, 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.