The closest thing to an Eldritch Abomination known in real life are probably black holes. They literally warp reality to a point where you cannot leave their gravity field any more once you have passed their event horizon. And physics struggles with describing them accurately since classical physics demands them to be infinetesimally small - there cannot be any force strong enough to halt their collapse because in order to do this the force would have to travel faster than light, which is impossible. On the other hand, this idea violates fundamental principles of quantum mechanics, since a zero-space object no longer contains the information of all the matter that fell into it. We are also unsure if you could even survive passing the event horizon or if some deadly obstacle awaits you there, even if tidal forces are small enough to survive them (the latter applies to very massive black holes, since their event horizon grows linearly with their mass, faster than the gravity force at that point). And the worst is that we cannot just look inside the event horizon from outside, since anything that has passed the event horizon will never come back whatsoever. (Though "never" is not absolute - it is theorized that black holes evaporate very slowly, eventually freeing the matter which they have compressed infinitely.) Even if you get close to one of these things, strange things will happen to time, compared to anyone who is far away from it.
Sounds pretty eldritch already, doesn't it?
And then, mathematics can describe things in theory which are totally mind-blowing. Be it multidimensional cubes, different infinities, or numbers so large that you cannot grasp their true form. And if one thing is not yet eldritch enough for you, you can always go one step higher via serial escalation. Four dimensions? Try five. TREE(3) is huge? What about TREE(4)? Or TREE(TREE(3))?