Near-Extremal Black Holes in Modified Gravity via Spectral Methods

Abstract

Rapidly-rotating black-hole spacetimes outside general relativity are key to many tests of Einstein's theory. We here develop an efficient spectral method to represent such spacetimes analytically, in closed-form, and to high accuracy, in a large class of effective-field-theory extensions of general relativity. We exemplify this method by constructing, for the first time, closed-form and analytic representations of spinning black holes in scalar-Gauss-Bonnet, dynamical Chern-Simons, and axidilaton gravity to an accuracy better than $10^{-8}$ for all dimensionless spins below 0.99.

Figures (2)

• Figure 1: Scalar field and metric components on the equator (solid) and polar axis (dashed). The top, middle and bottom panels display the behavior of the $g_{tt}$ and $g_{rr}$ components of the metric and the scalar field $\varphi$ respectively, all for a Kerr (black), a scalar Gauss-Bonnet (orange), a dynamical Chern-Simons (blue), and an axi-dilaton gravity (green) black hole with coupling constant $\zeta = 0.01$ and dimensionless spin $a = 0.99$. Observe that the non-Kerr black holes have a smaller ergosphere and an event horizon at $r = r_+$, while their scalar fields have different parity depending on the theory considered.
• Figure 2: Error measure in the satisfaction of the field equations [Eq. (\ref{['eq:EEResidual']})] when using the spectral (with $N=45$, markers), the analytic (solid), and the series-in-$a$ (to ${\cal{O}}(a^{15})$, dashed) black hole solutions in dynamical Chern-Simons (blue), scalar Gauss-Bonnet (orange), and axi-dilaton (green) gravity, as a function of black hole spin. Note that the dashed lines for all three theories overlap completely. Observe that the spectral and the analytic solutions are the only ones capable of accurately representing non-Kerr black hole solutions in these theories.