Exact WKB methods achieve higher accuracy for zero-damped modes in black holes.

When near-extremal black holes vibrate, their late-time ringdown dynamics are expected to be dominated by zero-damped modes. These are long-lasting vibrations whose decay rates are suppressed compared to ordinary black hole ringdown modes. Calculating these modes accurately is difficult. In this paper, researchers study massless, neutral scalar fields around a charged, near-extremal Reissner--Nordström black hole. They use a mathematical technique called exact WKB methods. By working out the full Stokes geometry from the radial eigenvalue problem, they establish an exact quantization condition. This rule determines the allowed vibration spectrum. Using analytic calculations of Voros symbols within this condition, they reach higher-order accuracy for the spectrum than earlier studies. Their systematically improvable approach also serves as a proof of concept for studying other systems.

Why it matters

Physicists studying black holes need accurate models for how they settle down after collisions. This work provides a better method for computing slow-decaying vibrations in nearly extreme black holes, which could improve predictions for gravitational wave observations.

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