Hi! this is a thematic concept for oathbreakers that i have always thought would be pretty cool while still embracing the core of what they are (and leaning even MORE into that theme and identity)
oathbreakers have lost that divine light that empowers them to do some of their amazing things and have instead embraced a darker power to fuel their abilities. for this reason, i feel it would be a really cool idea to swap all their abilities and spells and attacks that deal radiant damage over to necrotic damage (it's just a straight across the board swap from radiant damage from ANY source to necrotic. oathbreaker paladins have traded away their light for darkness, i feel that it would be demonstrated perfectly this way.
along with the above change i would make one other change; i would remove the paladins lay on hands ability. i feel that those that take this route, while not always guided by selfish ambition, would be at the mercy of the nature of their new darker powers. it would make sense if this dark energy would have a harder time healing others and i feel that loosing this ability makes a lot of sense thematically. the tradeoff i would make is that the oathbreaker would now have the ability to fuel themselves with the dark powers, i would make it so that they would gain temporary HP equal to half of the necrotic damage they deal. this temp HP could be built up to a maximum equal to their oathbreaker lvl X their charisma modifier (so a lvl 12 oathbreaker with a +5 charisma modifier could build up a max of 60 temp HP with this ability, but it would take a LONG time to build it up that high)
