  Motivated by previous studies in literature about the potential importance of
relativistic corrections to galaxy cluster hydrostatic masses, we calculate the
masses of 12 relaxed clusters (with Chandra X-ray data) using the
Tolman-Oppenheimer-Volkov (TOV) equation of hydrostatic equilibrium and the
ideal gas equation of state. Analytical formulae for gas density and
temperature profiles for these clusters, previously derived by Vikhlinin et al
(astro-ph/0507092) were used to obtain these masses. We compare the TOV-based
masses with those obtained using the corresponding Newtonian equation of
hydrostatic equilibrium. We find that the fractional relative difference
between the two masses are negligible, corresponding to $\sim
\mathcal{O}(10^{-5})$.
