# Mass in Higher Dimensions

How does mass operate in higher dimensional spaces? I am well aware that Mass is not intrinsically linked to any particular dimensionality, but with how dimensions operate I am not exactly sure how it would not rocket up to infinitely massive with even a singular added dimension, due to how it would be ℵ(0) many slices which hold mass.

But I have seen mass applied to two dimensions, as the derivation of Gravitational Binding Energy applies a mass to infinitely many (n-1) dimensional slices. Yet it ultimately adds up to a normal amount of mass, how exactly does this occur? And how can it be extrapolated to even higher dimensionalities?

• Welcome to Physics! Can I ask why you're not concerned about how 3-D objects have finite mass? After all, there ℵ(0) 2-D slices of a 3-D object, each one of which holds mass. Apr 23, 2021 at 20:15
• I am concerned about that, as I did mention in my comment. "But I have seen mass applied to two dimensions, as the derivation of Gravitational Binding Energy applies a mass to infinitely many (n-1) dimensional slices. Yet it ultimately adds up to a normal (finite) amount of mass, how exactly does this occur?"
– Zoey
Apr 23, 2021 at 20:19
• PSE user rediscovers calculus. More news at seven. Apr 23, 2021 at 21:13
• I know about Calculus, I have taken classes in it. I am just trying to see how to calculate mass in N > 3. I was talking about integrals and such in the original post. No need to get hostile.
– Zoey
Apr 24, 2021 at 0:09