The Gravitational Lensing Effect on the CMB Polarisation Anisotropy in
  the {\Lambda}-LTB Model
  A local void modifies the sky distribution pattern of the cosmic microwave
background (CMB) polarisation by gravitational lensing and produces B-modes
from E-modes for an off-center observer. In order to see whether this effect
can be used to observationally test the validity of the local void model, we
calculate this lensing effect by solving the propagation of CMB polarisation
along null geodesics close to the central light cone in the general
Lema\^itre-Tolman-Bondi (LTB) model perturbatively. In particular, we give
general formulas for the correlations of E and B observed by an off-center
observer and show that E_l^m and B_l^m are correlated for the same value of l,
i.e., <E_l^m B_l'^m'> is proportional to {\delta}_{l, l'}, while <E_l^m
E_l'^m'> is proportional to {\delta}_{|l'-l|, 1}. This feature can be used to
distinguish the gravitational lensing effect by a local void from those by
normal shear field of galaxies.
