Initial value formulation for gravitational junction conditions in dS3

Establish whether a classical initial value formulation exists for the gravitational junction conditions that glue two identical three-dimensional de Sitter spacetimes across a codimension-1 hypersurface with localized string tension T0; specifically, ascertain whether appropriate initial data on a Cauchy slice determine the subsequent evolution of the junction variables (tau_d, sigma_d, theta_s, theta_d) subject to the induced worldsheet metric continuity and the extrinsic curvature jump equations.

Background

The paper analyzes gravitational two-way junctions in three-dimensional de Sitter spacetime, showing a correspondence between solutions of the junction conditions and solutions of the Nambu–Goto equation for a string embedded in dS3. The junction introduces four worldsheet variables—time and angular shifts across the fragments (tau_d, sigma_d) and symmetric/asymmetric polar angles (theta_s, theta_d)—that obey continuity of the induced metric and a specific jump condition for the extrinsic curvature set by the string tension.

While the authors construct well-behaved perturbative solutions (notably transient fluctuations about the equator that encode and dissolve into gravitational memory at past and future infinity), they explicitly note that it is unclear whether these junction conditions admit an initial value formulation at the classical level. Resolving this would clarify whether evolution can be uniquely determined from suitable initial data, a foundational requirement for dynamical treatments of such junctions in dS3. The question is posed after establishing existence of self-consistent solutions, underscoring its importance for a complete dynamical framework.