  In agreement with the gravitational-wave events which are constantly
increasing, new aspects of the internal structure of compact stars have come to
light. A scenario in which a first order transition takes place inside these
stars is of particular interest as it can lead, under conditions, to a third
gravitationally stable branch (besides white dwarfs and neutron stars). This is
known as the twin star scenario. The new branch yields stars with the same mass
as normal compact stars but quite different radii. In the current work, we
focus on hybrid stars undergone a hadron to quark phase transition near their
core and how this new stable configuration arises. Emphasis is to be given
especially in the aspects of the phase transition and its parameterization in
two different ways, namely with Maxwell construction and with Gibbs
construction. Qualitative findings of mass-radius relations of these stars will
also be presented.
