In this paper general solutions are found for domain walls in Lyra geometry in the plane symmetric spacetime metric given by Taub. Expressions for the energy density and pressure of domain walls are derived in both cases of uniform and time varying displacement field β. It is also shown that the results obtained by Rahaman et al [IJMPD, 10, 735 (2001)] are particular case of our solutions. Fina...

We compute the Kazhdan-Lusztig polynomial of the uniform matroid of rank n − 1 on n elements by proving that the coefficient of t is equal to the number of ways to choose i non-intersecting chords in an (n − i + 1)-gon. We also show that the corresponding intersection cohomology group is isomorphic to the irreducible representation of Sn associated to the partition [n− 2i, 2, . . . , 2].

We construct a new class of plane-symmetric solutions possessing a curvature singularity which is null and weak, like the spacetime singularity at the Cauchy horizon of spinning (or charged) black holes. We then analyse the stability of this singularity using a rigorous non-perturbative method. We find that within the framework of (linearly-polarized) plane-symmetric spacetimes this type of nul...