Even-parity perturbations of a two-ended wormhole on the full radial line
- Publicado
- Servidor
- Zenodo
- DOI
- 10.5281/zenodo.21762566
This record contains the article, numerical data, source code, and plotting files associated with a full-line analysis of even-parity perturbations of a static, two-ended wormhole in a preferred-foliation effective theory.
The calculation was motivated by an ambiguity encountered in an earlier finite-interval treatment, where the lowest numerical levels changed when the radial basis and the artificial outer boundary were varied. To distinguish a possible throat-localized bound state from levels produced by radial confinement, the finite boundary is removed and the perturbations are represented directly on the full radial line.
After solving the radial-clock constraints, the lapse perturbation and the polar angular shift are eliminated from the quadratic action. The remaining dynamical amplitudes are expanded in scaled orthonormal Hermite functions. The reduced system retains the gyroscopic couplings and is studied through its kinetic matrix, stiffness matrix, generalized generator, and lowest Ritz values.
The numerical scan covers the even-parity sectors ℓ = 1, 2, 3, 4, using several Hermite dimensions and radial scales. In all sampled cases, the reduced kinetic and stiffness matrices remain positive, and no square-integrable mode with ω² < 0 is found. The lowest positive Ritz values decrease as the Hermite width is increased. In the best-resolved ℓ = 2 sequence, the quantity a²ω²min approaches an approximately constant value. This behavior is consistent with a continuous spectrum beginning at ω = 0 rather than with a positive spectral gap.
The calculation therefore finds no normalizable tachyonic bound state within the trial spaces considered. It does not exclude a bounded, non-square-integrable solution at zero energy, nor does it determine outgoing resonances obtained by analytic continuation. These questions require a separate treatment of the asymptotic matrix equation and two-ended radiation conditions.
The archive includes the manuscript, LaTeX source, bibliography, numerical tables, plotting data, Python scripts, and the full-line Hermite implementation used to reproduce the reported calculations.