  In a nonlinear theory, such as gravity, physically relevant solutions are
usually hard to find. Therefore, starting from a background exact solution with
symmetries, one uses the perturbation theory, which albeit approximately,
provides a lot of information regarding a physical solution. But even this
approximate information comes with a price: the basic premise of a perturbative
solution is that it should be improvable. Namely, by going to higher order
perturbation theory, one should be able to improve and better approximate the
physical problem or the solution. While this is often the case in many theories
and many background solutions, there are important cases where the linear
perturbation theory simply fails for various reasons. This issue is well known
in the context of general relativity through the works that started in the
early 1970s, but it has only been recently studied in modified gravity
theories. This thesis is devoted to the study of linearization instability in
generic gravity theories where there are spurious solutions to the linearized
equations which do not come from the linearization of possible exact solutions.
For this purpose we discuss the Taub charges, the ADT charges and the quadratic
constraints on the linearized solutions. We give the three dimensional chiral
gravity and the $D$ dimensional critical gravity as explicit examples and give
a detailed ADM analysis of the topologically massive gravity with a
cosmological constant.
