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We prove a no Cauchy horizon theorem for general nonlinear electrodynamicsblack holes with charged scalar hairs. By constructing a radially conservedcharged, we show that there is no inner Cauchy horizon for both spherical andplanar symmetric cases, independent of the form of scalar potential andnonlinear electrodynamics. After imposing the null energy condition, we arealso able to rule out the existence of the Cauchy horizon for the hyperbolicblack holes. We take the Born-Infeld black hole as a concrete example to studythe interior dynamics beyond the event horizon. When the contribution from thescalar potential can be neglected, the asymptotic near-singularity takes auniversal Kasner form. We also confirm that the intricate interior dynamics isclosely associated with the instability of the inner Cauchy horizon triggeredby scalar hairs.

No Cauchy Horizon Theorem for Nonlinear Electrodynamics Black Holes with Charged Scalar Hairs