Ryuk's world, then, is Hueco Mundo and he and his friends are arrancar. Their referring to themselves as "shinigami" is a half-truth born of jealousy, and perhaps a justification for their murderous actions. * Notably, this means the arrencar have an ability that most shinigami do not - the ability to give living humans additional lifespan (albeit at the rather nasty cost of that being half their lifespan, and they have to die in the process) - which in turn could make them living Holy Grails, like the one that made Indiana Jones have such an extended lifespan!