Damghan University Press Journal of Holography Applications in Physics 2783-4778 5 4 2025 10 23 The BTZ Black Hole, Thermofield Double State, and SPT Phases: A Duality 82 94 1915 10.22128/jhap.2025.3023.1131 EN Fabiano Francisco Dos Santos Centro de Ciências Exatas, Naturais e Tecnológicas, UEMASUL, 65901-480, Imperatriz, MA, Brazil 0000-0001-5473-8797 Journal Article 2025 08 19 This letter present an investigation of the relationship between the interior and exterior solutions of the BTZ black hole, emphasizing the effects of interchanging spatial and temporal roles. By deriving the interior BTZ metric and its associated thermofield double state, we uncover a duality that complements the exterior solution, providing a comprehensive perspective on the full BTZ black hole geometry. The bulk partition function is shown to correspond to a non-orientable spacetime, specifically a Klein bottle, which establishes links to symmetry-protected topological (SPT) phases characterized by orientation-reversing symmetries. These results align with recent developments in understanding entanglement and topological phases in non-orientable geometries, as well as the role of thermofield double states in the AdS/CFT framework. This work bridges black hole physics, quantum entanglement, and topological invariants, offering fresh insights into the geometric and physical properties of non-orientable spacetimes. https://jhap.du.ac.ir/article_1915_86c343e0f7cc13f331d0b630fc1f21de.pdf