Relativistic corrections for measuring Hubble's constant to 1% using
  stellar standard candles
  Relativistic corrections are estimated for classical Cepheids and the Tip of
the Red Giant Branch (TRGB stars), to enable future unbiased 1% measurements of
Hubble's constant, $H_0$. We considered four effects: $K-$corrections,
time-dilation, the apparent change of host dust extinction due to non-comoving
reference frames, and the change of observed color due to redshift.
Extinction-dependent $K-$corrections were computed using stellar atmosphere
models applicable to giant stars for $0.005 < z < 0.03$ in HST, JWST, and 2MASS
filters. The optical-NIR Wesenheit function advantageously combines filters
with oppositely signed $K-$corrections and avoids complications due to host
extinction. For TRGB stars, the JWST/NIRCAM F277W filter combines insensitivity
to reddening with $K-$corrections $<1$% at Coma cluster distances. Missing
corrections for host extinction due to circumgalactic or circumstellar material
are discussed as potential systematics for TRGB distances although their
impacts are insufficient to explain differences between $H_0$ based on Cepheid
or TRGB supernova calibrations. All stellar standard candles require
relativistic corrections to achieve an unbiased 1% $H_0$ measurement in the
future. The combined relativistic correction involving $K$, redshift-Leavitt
bias, and the redshift-dependence of the Wesenheit function yield an increase
of the Cepheid-based $H_0$ by $0.45 \pm 0.05$ km/s/Mpc to $73.65 \pm 1.30$
km/s/Mpc and raises the tension with the {\it Planck} value from $4.2\sigma$ to
$4.4\sigma$. For TRGB stars, we estimate a $\sim 0.5\%$ increase of $H_0$
reported by Freedman et al. (to $70.2\pm1.7$km/s/Mpc) and a small decrease by
$-0.15\%$ for $H_0$ reported by Anand et al. (to $71.4 \pm 1.8$km/s/Mpc). The
opposite sign of these corrections is due to different reddening systematics
and reduces the difference between the studies by $\sim
0.46$km/s/Mpc.[abridged]
