show what? my confusion is why they are equal. because komar mas is the total energy of a system. and $$E_{\mathrm{total}} = E_{\mathrm{matter}}+E_{\mathrm{field}}$$ And by definition,komar mass are defined as :$$M_{\mathrm{K}} =-\frac{1}{8 \pi} \int_{S} \varepsilon_{a b c d} \nabla^{c} \xi^{d}$$, which is total energy but M is central body's mass,which is matter,not field . they should be different. but as you said, "As I asked before, what is the difference between "the mass of the body" and "the total mass of the whole spacetime"? (Hint: there actually is no difference.) ", i think you discuss a different thing from mine.Calculating the Komar mass gives ##M##. But you have not shown any calculation of "the energy of matter" which gives a different result. In fact you have shown no calculations at all, despite my repeated requests. Can you show a calculation of "the energy of matter" which gives a different result from ##M##?