A recent study has investigated the existence of closed timelike curves (CTCs) in three rotating black hole models arising from modified theories of gravity. CTCs are hypothetical regions of spacetime where an object's trajectory can return to its starting point in time, implying the possibility of time travel to the past and chronological paradoxes. The researchers have shown that additional parameters inherent in these modified theories can control the extent of these causality-violating regions, and even eliminate them entirely under certain configurations.

The models analyzed include the tidally charged braneworld black hole, the Kerr-Newman black hole in Rastall gravity, and the charged Johannsen-Psaltis spacetime. For each, the sign of the gφφ component of the metric tensor on the equatorial plane was examined, as this is a key indicator of the presence of CTCs. It was found that, in all cases, the new parameters introduced by modified gravity theories offer a mechanism to influence spacetime geometry in such a way that CTCs can be suppressed or confined.

In the braneworld black hole case, the CTC region only exists for a positive tidal charge, disappearing if it is zero or negative. For Rastall gravity, the Rastall coupling and surrounding matter jointly determine the extent of the CTC region, and a finite range of coupling values was identified for which CTCs are absent. Finally, in the Johannsen-Psaltis spacetime, the deformation parameter can either increase or decrease the gφφ metric, and a window of values for this parameter was derived that removes CTCs from the considered radial domain. These findings suggest that modified theories of gravity could offer solutions to the temporal paradoxes predicted by General Relativity under certain extreme conditions.