Quadratic Curvature Correction to 5D Myers-Perry Metric

TL;DR

This work develops a perturbative framework for quadratic curvature corrections to the five-dimensional Myers-Perry black hole, solving at linear order in the coupling $\alpha$ and to high order in the two dimensionless spins $χ_a$ and $χ_b$ (up to $\mathcal{O}(χ^{10})$). An axisymmetric, cohomogeneity-2 ansatz yields a set of perturbative functions $H_i(r,x)$ whose coefficients satisfy algebraic conditions, enabling explicit thermodynamic corrections. The authors compute the corrected mass, angular momenta, temperature, angular velocities, and Wald entropy, and verify the first law to $\mathcal{O}(α)$; they also confirm agreement with the Reall-Santos method, after appropriate parameter redefinitions. The results illuminate higher-derivative effects on black hole thermodynamics in higher dimensions and offer a path to studying related observables such as quasinormal modes and multipole moments, albeit with limitations near extremality and increased cohomogeneity in higher dimensions.

Abstract

We consider quadratic curvature perturbation to the Myers-Perry black hole in five dimensions at the linear level in the coupling constant. The solution can then be solved order by order in terms of two dimensionless angular momentum parameters up to an arbitrary order. We present the results up to tenth order. The perturbed solution allows us to obtain the higher-derivative correction to the black hole thermodynamics, which we find is in complete agreement with the Reall-Santos method.