Godel Universe in $f(Q,T)$ gravity: Exploring causality violation and closed time-like curves

TL;DR

This paper extends Gödel-type solutions to $f(Q,T)$ gravity, showing that closed timelike curves (CTCs) can persist in this framework due to non-metricity and matter–geometry coupling. By working in the coincident gauge and analyzing Gödel-type metrics with both perfect-fluid and scalar-field sources, it derives modified field equations and finds explicit solutions where CTCs occur, along with conditions under which energy conditions are satisfied. The results indicate that $f(Q,T)$ gravity can realize a broader spectrum of causal structures than GR and related theories, with the non-metricity coupling providing additional control over the critical radius and the viability of solutions. This work lays groundwork for further stability analyses, constraints, and observational tests of non-metricity-based modified gravity in rotating non-Riemannian spacetimes.

Abstract

In this work, the classical Godel solution from general relativity is extended into the framework of modified gravity theories based on non-metricity $Q$ and the trace of the energy-momentum tensor $T$ in the context of $f(Q,T)$ gravity. The main feature of the Godel solution is the existence of closed time-like curves, which allow for causality violation and time travel. Since general relativity and its extensions do not demand spacetime to be globally causal, there is good motivation to explore such solutions. We have found classes of solutions with different matter content, like perfect fluid, cosmological constant, massless scalar field, etc. It is observed that, for suitable initial conditions, there is always a possibility of obtaining feasible solutions that violate causality in our setup. The presence of non-metricity in such solutions produces crucial deviations that are noteworthy.

Figures (6)

• Figure 1: The figure shows the plot of $f_{1}(Q,T)$ against $Q$ and $T$ for Model-1. The parameters are taken as $\alpha=0.1, \beta=7, n=3, m_{1}=0.2$ .
• Figure 2: The figure shows the plot of $f_{2}(Q,T)$ against $Q$ and $T$ for Model-1. Other parameters are given by $\alpha=0.1, \beta=7, n=3, m_{1}=0.2$ .
• Figure 3: The figure shows the plot of $f_{3}(Q,T)$ against $Q$ and $T$ for Model-1. Other parameters are given by $\alpha=0.1, \beta=7, n=3, m_{1}=0.2$ .
• Figure 4: The figure shows the plot of $f_{5}(Q,T)$ against $Q$ and $T$ for Model-2. Other parameters are given by $n=3, m_{1}=0.2, \lambda=1$.
• Figure 5: The figure shows the plot of $f_{5}(Q,T)$ against $Q$ and $T$ for Model-2. Other parameters are given by $n=3, m_{1}=0.2, \lambda=1$.