Nonreciprocal black holes with primary hair in beyond Horndeski gravity: Exact solutions and stability

We develop a novel systematic method for constructing exact, static, and asymptotically flat black-hole solutions in shift-symmetric and $Z_2$-symmetric beyond Horndeski theories. In contrast to previous studies, our approach does not rely on the restrictive reciprocal condition $g_{tt}g_{rr}=-1$, a