A family of static multicentered solutions to modified Einstein-Maxwell equations coupled with a dilaton is constructed in $(1+N)$ dimensional space-time ($N\ge 2$). For $N\ge 3$, the solutions are generalizations of the Majumdar-Papapetrou solution. We also find the solution in $(1+2)$ dimensions, where the scalar and vector forces cancel each other in the static case. The interaction between two extreme charged dilaton black holes in the low-energy limit is investigated in $(1+N)$ dimensions ($N\ge 3$). We find that there remains the residual velocity-dependent force in general cases, except for the case with $N=a^2$.
The classical and the quantum scattering of two maximally-charged dilaton black holes which have low velocities are studied. We find a critical value for the dilaton coupling, $a^2=1/3$. For $a^2>1/3$, two black holes are always scattered away and never coalesce together, regardless of the value of the impact parameter.
We consider couplings of electrically and magnetically charged sources to the maximally symmetric non-linear extension of Maxwell's theory called ModMax. The aim is to reveal physical effects which distinguish ModMax from Maxwell's electrodynamics. We find that, in contrast to generic models of non-linear electrodynamics, Lienard-Wiechert fields induced by a moving electric or magnetic particle, or a dyon are exact solutions of the ModMax equations of motion. We then study whether and how ModMax non-linearity affects properties of electromagnetic interactions of charged objects, in particular …
