Higher-derivative Heterotic Kerr-Sen Black Holes

TL;DR

The paper derives four-derivative corrections to the Kerr-Sen black hole within heterotic supergravity by embedding Kerr, dualizing the NS sector to an axion, and applying an $O(2,1)$ boost (with necessary field redefinitions and higher-dimensional uplifts) to generate the corrected Kerr-Sen solution. It then computes thermodynamic quantities and multipole moments for the four-derivative Kerr-Sen solution, showing that the corrections to the multipole structure are distinct from both the two-derivative Kerr solution in heterotic supergravity and the Kerr-Newman solution in Einstein-Maxwell theory. The analysis demonstrates that four-derivative Kerr-Sen multipoles cannot be matched by any choice of four-derivative parameters in Einstein-Maxwell theory, providing a potentially observable string-theory imprint in gravitational-wave data. The work also discusses the role of $O(d+p,d)$ symmetry beyond leading order and outlines future avenues, including higher-order corrections and extremal/near-horizon analyses, to broaden the phenomenological implications.

Abstract

We obtain the four-derivative corrections to the Kerr-Sen solution in heterotic supergravity, which includes the Gibbons-Maeda-Garfinkle-Horowitz-Strominger solution as a limiting case. In particular, we first embed the Kerr solution into heterotic supergravity and compute the higher-derivative corrections. We then obtain the corrections to the Kerr-Sen solution by performing an $O(2,1)$ boost of the Kerr solution, which, in contrast to the two-derivative case, requires field redefinitions to make the $O(2,1)$ invariance of the action manifest. Finally, we compute the multipole moments and find that they are distinct from those of the Kerr solution at the four-derivative level. We also find that the multipole moments are distinct from those of the Kerr-Newman solution in Einstein-Maxwell theory at the four-derivative level, even for the most general choice of four-derivative corrections. This gives a way to experimentally distinguish traces of string theory in gravitational wave data.

Figures (1)

• Figure 1: A schematic depiction of the series of uplifts, field redefinitions, and transformations we perform to obtain the Kerr-Sen solution.