  The implications of perturbative QCD (PQCD) calculations on neutron stars are
carefully examined. While PQCD calculations above baryon chemical potential
$\mu_B\sim2.4$ GeV demonstrate the potential of ruling out a wide range of
neutron star equations of state (EOSs), these types of constraints only affect
the most massive neutron stars in the vicinity of the
Tolman-Oppenheimer-Volkoff (TOV) limit, resulting in bounds on neutron star
EOSs that are orthogonal to those from current or future astrophysical
observations, even if observations near the TOV limit are made. Assuming the
most constraining scenario, PQCD considerations favor low values of the speed
of sound squared $C_s$ at high $\mu_B$ relevant for heavy neutron stars, but
leave predictions for the radii and tidal deformabilities almost unchanged for
all the masses. Such considerations become irrelevant if the maximum speed of
sound squared inside neutron stars does not exceed about
$C_{s,\mathrm{max}}\sim0.5$, or if the matching to PQCD is performed above
$\mu_B\simeq2.9$ GeV. Furthermore, the large uncertainties associated with the
current PQCD predictions make it impossible to place any meaningful bounds on
neutron star EOSs as of now. Interestingly, if PQCD predictions for pressure at
around $\mu_B\simeq2.4$ GeV is refined and found to be low ($\lesssim 1.5$
GeV/fm$^3$), evidence for a soft neutron star inner core EOS would point to the
presence of a strongly interacting phase dominated by non-perturbative physics
beyond neutron star densities.
