2024/12/20 by Dionysios Anninos, Anninos, Dionysios, Raúl Arias +5 · 1 citation
Engineering · Physics and Astronomy · #Astronomical Observations and Instrumentation #Astrophysical Phenomena and Observations #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #History and Developments in Astronomy
paper · pdf · doi:10.48550/arxiv.2412.16305
openalex publication_date 2024/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider four-dimensional general relativity with a negative cosmological constant in the presence of a finite size boundary, Γ, for both Euclidean and Lorentzian signature. As our boundary condition, we consider the `conformal' boundary condition that fixes the conformal class of the induced metric at Γ and the trace of the extrinsic curvature, K(xm). In Lorentzian signature, we must supplement these with appropriate initial data comprising the standard Cauchy data along a spatial slice and, in addition, initial data for a boundary mode that appears due to the presence of the finite size boundary. We perform a linearised analysis of the gravitational field equations for both an S2× ℝ as well as a Minkowskian, ℝ1,2, boundary. In the S2× ℝ case, in addition to the usual AdS4 normal modes, we uncover a novel linearised perturbation, \boldsymbolω(xm), which can exhibit complex frequencies at sufficiently large angular momentum. Upon moving Γ toward the infinite asymptotic AdS4 boundary, the complex frequencies appear at increasingly large angular momentum and vanish altogether in the strict limit. In the ℝ2,1 case, although we uncover an analogous novel perturbation, we show it does not exhibit complex frequencies. In Euclidean signature, we show that K(xm) plays the role of a source for \boldsymbolω(xm). When close to the AdS4 asymptotic boundary, we speculate on the holographic interpretation of \boldsymbolω(xm).