Inside the extremal dyonic Kerr-Sen black hole, scalar field modes have purely imaginary frequencies, so they do not propagate; the growing modes can destroy the region containing closed timelike curves, supporting the Chronology Protection Conjecture.
The spacetime where CTC is allowed will be deformed and in short period of time be destroyed by the backreaction of the growing modes
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Scalar Instabilities Inside The Extremal Dyonic Kerr-Sen Black Hole: Novel Exact Solutions and Chronology Protection Conjecture
Inside the extremal dyonic Kerr-Sen black hole, scalar field modes have purely imaginary frequencies, so they do not propagate; the growing modes can destroy the region containing closed timelike curves, supporting the Chronology Protection Conjecture.