The power of Lorentzian wormholes

TL;DR

The paper develops a real-time gravitational framework for topology change in asymptotically AdS spacetimes by introducing crotches—co-dimension-2 singularities that implement swap identifications and sit at extremal surfaces. By employing constrained instantons, the authors show that each crotch contributes an action $S_{ ext{inst}}=rac{A( ext{γ}_{ ext{extr}})}{4G_{ ext{N}}}$, leading to topological suppression and allowing a Lorentzian analogue of Euclidean wormholes to reproduce ramp-plateau features in the spectral form factor and late-time two-point functions across JT/dilaton gravity and higher dimensions. They provide concrete calculations in 2d dilaton gravity and general dilaton models, demonstrating gauge-equivalence between counting Lorentzian crotch geometries and summing over mostly Euclidean spacetimes, and they connect these constructions to West-Coast replica wormholes. The results imply a universal, real-time rule for gravity with topology change, offering a tractable route to reproduce boundary observables and informing questions about black hole interiors, islands, and information recovery. The work opens multiple avenues for applying Lorentzian wormhole saddles to dynamical questions in quantum gravity and holography.

Abstract

As shown by Louko and Sorkin in 1995, topology change in Lorentzian signature involves spacetimes with singular points, which they called crotches. We modify their construction to obtain Lorentzian semiclassical wormholes in asymptotically AdS. These solutions are obtained by inserting crotches on known saddles, like the double-cone or multiple copies of the Lorentzian black hole. The crotches implement swap-identifications, and are classically located at an extremal surface. The resulting Lorentzian wormholes have an instanton action equal to their area, which is responsible for topological suppression in any number of dimensions. We conjecture that including these Lorentzian wormhole spacetimes is gauge-equivalent to path integrating over all mostly Euclidean smooth spacetimes. We present evidence for this by reproducing semiclassical features of the genus expansion of the spectral form factor, and of a late-time two point function, by summing over the moduli space of Lorentzian wormholes. As a final piece of evidence, we discuss the Lorentzian version of West-Coast replica wormholes.