Quasi-local variables, non-linear perturbations and back-reaction in spherically symmetric spacetimes

Understand

We introduce a quasi-local integral functional and scalar quasi-local variables to examine a wide class of spherically symmetric inhomogeneous spacetimes that generalize the Lemaitre-Tolman-Bondi (LTB) dust solutions ("LTB" spacetimes).

• By using these variables, we can transform the fluid flow evolution equations into evolution equations for non-linear, covariant, gauge--invariant perturbations of Friedman-Lemaitre-Robertson-Walker (FLRW) cosmologies.
• In the linear limit, we obtain spherical perturbations in the synchronous gauge under the long wavelength approximation.
• The formalism has a significant potential for cosmological applications, as it allows one to examine a wide variety of sources with different "equations of state", generalizing known FLRW solutions to idealized but non-trivial and non-linear inhomogeneous conditions.