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A local void modifies the sky distribution pattern of the cosmic microwavebackground (CMB) polarisation by gravitational lensing and produces B-modesfrom E-modes for an off-center observer. In order to see whether this effectcan be used to observationally test the validity of the local void model, wecalculate this lensing effect by solving the propagation of CMB polarisationalong null geodesics close to the central light cone in the generalLema\^itre-Tolman-Bondi (LTB) model perturbatively. In particular, we givegeneral formulas for the correlations of E and B observed by an off-centerobserver 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^mE_l'^m'> is proportional to {\delta}_{|l'-l|, 1}. This feature can be used todistinguish the gravitational lensing effect by a local void from those bynormal shear field of galaxies.

The Gravitational Lensing Effect on the CMB Polarisation Anisotropy in the {\Lambda}-LTB Model