Horizon area bound and MOTS stability in locally rotationally symmetric solutions

In this paper, we study the stability of marginally outer trapped surfaces (MOTS), foliating horizons of the form $r=X(τ)$, embedded in locally rotationally symmetric class II perfect fluid spacetimes. An upper bound on the area of stable MOTS is obtained. It is shown that any stable MOTS of the types considered in these spacetimes must be strictly stably outermost, that is, there are no MOTS ``outside" of and homologous to $\mathcal{S}$. Aspects of the topology of the MOTS, as well as the case when an extension is made to imperfect fluids, are discussed. Some non-existence results are also obtained. Finally, the ``growth" of certain matter and curvature quantities on certain unstable MOTS are provided under specified conditions.

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