Black branes in asymptotically Lifshitz spacetimes with arbitrary exponents in κ -Horndeski gravity

In this work, we consider Horndeski gravity deformed by a parameter in its kinetic terms embedded in asymptotically Lifshitz spacetimes. We obtain black brane solutions in this geometry and study their thermodynamical properties. We show that the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>κ</a:mi></a:math> deformation on the Horndeski kinetic terms allows for arbitrary values of the critical exponents characteristic of Lifshitz spacetimes. These solutions present local and global thermodynamical stabilities.