Black hole extremality and causality constraints on thermodynamics in nonlinear electrodynamics

We investigate the extremality and thermodynamics of black holes in nonlinear electrodynamics (NLED), motivated by the swampland conjectures and causality constraints. Considering general Lagrangians as functions of the electromagnetic field strength tensor, we analyze specific models such as the Euler-Heisenberg and Dirac-Born-Infeld theories in asymptotically flat, de Sitter, and anti-de Sitter spacetimes. We show that the mass-to-charge ratio of extremal black holes exhibits a monotonic behavior consistent with expectations from the weak gravity conjecture, even beyond leading-order corrections to the Einstein-Maxwell theory. In addition, imposing the absence of superluminal propagation, or dominant energy condition, we derive additional thermodynamic constraints from the generalized Smarr formula. These results extend previous studies of higher-derivative corrections and implies deep connections between black hole physics and causality. This talk is based on the collaborations with Maxime Médevielle, Toshifumi Noumi, and Kaho Yoshimura(Tokyo U., Komaba). References: 2305.17062 [hep-th] and 2505.23483 [hep-th].