Signature Change in $f(R, T_\phi)$ Theory

TL;DR

This paper explores a modified gravity model coupled with a scalar field that allows for classical solutions where the spacetime signature smoothly transitions from Euclidean to Lorentzian, providing insights into signature change phenomena.

Contribution

It introduces a simple $f(R, T_)$ gravity model that admits classical solutions demonstrating a dynamical signature change, extending previous understanding in general relativity.

Findings

Identified degenerate metric solutions in the $f(R, T_)$ model.

Found a class of solutions with smooth Euclidean to Lorentzian transition.

Demonstrated the classical realization of signature change in modified gravity.

Abstract

We investigate a simple $f(R, T_\phi)$ gravity model coupled to a scalar field and demonstrate that the theory admits classical degenerate metric solutions, analogous to those known in general relativity. In particular, we identify a class of solutions that exhibits a smooth transition from a Euclidean to a Lorentzian domain, thus yielding a classical dynamical realization of signature change.