Matt Reeves explains how his version of Batman is a "Batman Kurt Cobain"
The Batman director talks about Kurt Cobain influencing the character in an interview with Esquire

From the first look at Matt Reeves’ The Batman, you could tell this version of the vigilante hero wouldn’t be like the others. This Batman—played by Robert Pattinson—is lanky, moody, and looks like he’s the frontman of a band rather than someone who regularly fights off Gotham’s villains.
The use of a slowed-down, remixed version of Nirvana’s “Something In The Way” in the first official trailer set the mood, too. This Batman apparently loves to sulk. Reeves previously mentioned in an interview with Empire that he envisioned this Bruce Wayne as being a “fictionalized version of Kurt Cobain being in this kind of decaying manor.” And now he has further explained how this Batman will feel akin to the late Nirvana frontman in a new interview with Esquire.