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This study examines the angular eigenvalue problem of extremely charged C-metric spacetimes, a class of solutions in general relativity describing accelerating black holes. The researchers use a mathematical correspondence with four-dimensional gauge theory (specifically an N=2 supersymmetric quiver theory) to derive analytical solutions for the angular spectrum in the extreme charge limit, where the differential equation transforms from a Fuchsian equation into a Confluent Extended Heun Equation. Their algebraic quantization condition, based on instanton counting methods, produces angular eigenvalues that match numerical calculations.
Why it matters
This work advances our theoretical understanding of black hole physics and demonstrates how gauge theory-gravity dualities can solve complex problems in general relativity. The analytical methods developed could be applied to other extreme gravitational systems and may inform future studies of gravitational wave signatures from accelerating black holes.
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arXiv:2607.08747v1 Announce Type: cross
Abstract: We investigate the angular eigenvalue problem of the extreme charged C-metric. In the extreme limit ($Q to M$), the governing differential equation degenerates from a Fuchsian equation with five regular singular points into a Confluent Extended Heun Equation. To evaluate the angular spectrum analytically, we formulate a decoupling limit within the dual four-dimensional $mathcal{N}=2$, $mathrm{SU(2)}times mathrm{SU(2)}$ linear quiver gauge theory. Within this framework, we derive the parameter dictionary and renormalized Matone relations, which absorb the macroscopic residue shifts induced by the singularity fusion. Based on the regular boundary conditions of the angular equation, we utilize the instanton counting method to establish an algebraic quantization condition, yielding angular eigenvalues consistent with numerical results.
Source: Decoupling Limit of Quiver Theories and the Angular Spectra of Extreme C-metrics