You said "in general relativity mass and energy are the same thing essentially."I don't understand what you are asking me, are you questioning the validity of e=mc^2 or just that the Earth doesn't have a uniform mass?
I am not trying to say anything but am trying to understand.
Are you saying:
Earth mass = 5.9742 × 1024 kilograms
Earth energy = 5.9742 × 1024 kilograms
Earth energy = ???