  We study the problem of extracting information about composition and equation
of state of dense matter in neutron star interior using axial w-modes. We
determine complex frequencies of axial w-modes for a set of equations of state
involving hyperons as well as Bose-Einstein condensates of antikaons adopting
the continued fraction method. Hyperons and antikaon condensates result in
softer equations of state leading to higher frequencies of first axial w-modes
than that of nuclear matter case, whereas the opposite happens in case of
damping times. The presence of condensates may lead to the appearance of a new
stable branch of superdense stars beyond the neutron star branch called the
third family. The existence of same mass compact stars in both branches are
known as neutron star twins. Further investigation of twins reveal that first
axial w-mode frequencies of superdense stars in the third family are higher
than those of the corresponding twins in the neutron star branch.
