Matching the linear spectra of twinlike defects

Twinlike defects refer to topological defect solutions of some apparently different field models that share the same defect configuration and the same energy density. Usually, one can distinguish twinlike defects in terms of their linear spectra, but in some special cases twinlike defects even share the same linear spectrum. In this paper, we derive the algebraic conditions for two twinlike defects to share an identical linear spectrum from the viewpoint of the normal modes of the linear fluctuations. We also extend our discussion to braneworld models, where gravity plays an important role.