Black Hole Interiors as a Laboratory for Time-Dependent Classical Double Copy

TL;DR

This paper demonstrates that black hole interior regions, especially trapped Kerr--Schild geometries, serve as exact, time-dependent settings for the classical double copy correspondence between gravity and gauge theory.

Contribution

It establishes that trapped black hole interiors can be used as a local, exact laboratory for studying time-dependent classical double copy, including explicit examples like Bardeen and Schwarzschild solutions.

Findings

Bardeen solution yields a finite, regular single-copy field inside the trapped region.

Schwarzschild's single-copy electric field diverges during interior evolution.

Bardeen horizon phase structure is encoded in the single-copy scalar.

Abstract

The classical double copy provides a powerful bridge between gravity and gauge theory, but its most explicit realizations remain concentrated in stationary or highly symmetric settings. We show that trapped regions of black-hole geometries furnish an exact setting for time-dependent classical double copy. In the static, spherically symmetric case, each trapped interval admits a local single-copy description on the associated Kantowski--Sachs patch that is intrinsically time dependent, although it can be derived from static Kerr--Schild data and does not require knowledge of any exterior black-hole completion. We prove that this class is characterized intrinsically by a distinguished relation between the Kantowski--Sachs scale factors, equivalently by the longitudinal relation \(p_{\parallel}=-\rho\), and that the Kerr--Schild scalar and single-copy field are uniquely reconstructible from interior cosmological data. Schwarzschild provides the singular benchmark, for which the single-copy electric field diverges along the interior evolution, while the regular Bardeen solution yields a finite single-copy field throughout the trapped region and a smooth extension into a regular static core. The Bardeen core violates the strong energy condition in a compact region, whereas the corresponding single-copy Maxwell field remains regular and satisfies the standard classical energy conditions. We further show that the Bardeen horizon phase structure is encoded in the single-copy scalar. These results identify trapped Kerr--Schild interiors as an exact local laboratory for time-dependent classical double copy.