Abstract. This article presents a theoretical model that establishes a framework to describe natural time machines in certain particular circumstances. Time machines are viewed as resulting from deformations of the spacetime itself, being such deformations originated only in the spatial part of the continuum. Spacetime is treated as the very target of quantization, instead of gravitational field, undergoing shrinkage in determinate conditions of gravitational compression. Singularity functions are applied in the formal representation of the invariant element of spacetime shrinkage in commoving coordinates. Time travel without displacement in space is considered possible in odd regions under gravitational compression. Space compression is discussed from the model of interaction between two black holes. Geodesic equation is rewritten in accordance with the proposal of representation by singularity functions. Standard Friedmann equation is recovered in its version for loop quantum gravity.

Full-text: PDF