Combining gravitational and electromagnetic waves observations to
  investigate local structure and the Hubble tension
  Recent estimations of the Hubble parameter $H_0$ based on gravitational waves
(GW) observations can be used to shed some light on the discrepancy between the
value of the Hubble parameter $H_0^P$ obtained from large scale observations
such as the Planck mission, and the small scale value $H_0^R$, obtained from
low redshift supernovae (SNe).
  In order to investigate the origin of this discrepancy we perform a combined
analysis of the luminosity distance of SNe and GW sources, using different
methods, finding that the impact of the GW data is very limited, due to the
small number of data points, and their large errors. We analyze separately data
from the Pantheon and the Union 2.1 catalogues, finding that a model with
$H_0^P$ and a small local void can fit the data as well as a homogeneous model
with $H_0^R$, resolving the apparent $H_0$ tension. We find that there is a
significant difference between the size and depth of the inhomogeneity obtained
using the two datasets, which could be due to the different sky coverage of the
two catalogues. For Pantheon we obtain evidence of a local inhomogeneity with a
density contrast $\delta_v=-0.155 \pm 0.026$, extending up to a redshift of
$z_v = 0.056 \pm 0.0002$, while for Union 2.1 we obtain $\delta_v=-0.461 \pm
0.032$ and $z_v= 0.081\pm 0.008$. We also perform some analysis using redshift
shell averaged data, and obtain approximately the same results, hinting to the
fact that the effects of the monopole component of the local inhomogeneity are
the dominant ones
