Energy as a Fifth Geometric Dimension: a 5D Extension of Spacetime for Cosmology, Black Holes, Entropy and Entanglement

This work explores the hypothesis that energy is not only a scalar quantity but can be treated as an additional geometric dimension (E), extending spacetime to a five-dimensional manifold. The proposed 5D metric is a block-diagonal extension of the effective four-dimensional metric, incorporating a scale factor associated with the energetic dimension. Within this framework, we discuss: Cosmological extensions of the FRW model with the possibility of avoiding the Big Bang singularity through a 5D bounce. 5D black hole models in which the internal singularity is regularized and replaced by a region that can be interpreted as the beginning of a new universe (Black Hole Universe scenario). A geometric reinterpretation of black hole entropy and information, linked to the extrinsic curvature along E. A geometric interpretation of quantum entanglement, where entangled pairs are co-localized in the E-dimension, making seemingly non-local correlations in 4D compatible with a notion of locality in 5D. The work does not claim to be a complete theory but proposes a coherent and conceptually unifying mathematical framework, suggesting possible connections between general relativity, quantum mechanics, black hole thermodynamics, and information theory.