= Solution
Use <geometrized units> $G=c=1$. For a stationary <asymptotically flat spacetime>, normalize the timelike <Killing vector field> $\xi$ to have squared norm $-1$ at infinity. The <Komar mass> is
$$
M_K=-\frac1{8\pi}\lim_{S\to\infty}\int_S\nabla^a\xi^b\,dS_{ab}.
$$
Here the oriented binormal is chosen so that an ordinary positive-mass static solution gives a positive integral. Equivalently, on a static slice with lapse $N=\sqrt{-\xi^2}$ and outward spatial unit normal $s^i$,
$$
M_K=\frac1{4\pi}\lim_{S\to\infty}\int_Ss^iD_iN\,dA.
$$
This second expression fixes the orientation unambiguously and is convenient for the <Majumdar–Papapetrou solution>.
The spatial metric is $\gamma_{ij}=H^2\delta_{ij}$ and $N=H^{-1}$. On a large coordinate sphere, $s^i=H^{-1}\widehat r^i$ and $dA=H^2r^2d\Omega$. Thus
$$
s^iD_iN\,dA=-\frac{r^2}{H}\partial_rH\,d\Omega,\qquad M_K=-\frac1{4\pi}\lim_{r\to\infty}\int_{S^2}\frac{r^2\partial_rH}{H}\,d\Omega.
$$
The original PDF has the <Euclidean norm> in each source denominator, which is missing in the TeX aid. With that norm, the <harmonic function> has asymptotics
$$
H=1+\frac{\sum_iM_i}{r}+O(r^{-2}),\qquad\partial_rH=-\frac{\sum_iM_i}{r^2}+O(r^{-3}).
$$
Therefore
$$
\boxed{M_K=\sum_{i=1}^NM_i.}
$$
If $M_i$ are retained as length parameters while $G$ is restored, the physical mass is $\sum_iM_i/G$. This is the charge at infinity. A <Komar integral> is not generally surface-independent here, since <Einstein-Maxwell theory> has the electromagnetic <stress-energy tensor> between the surfaces; in particular it should not be confused with a sum of vacuum horizon <Komar charges>.
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