  We construct the marginal loosely trapped surface (marginal LTS) for the Kerr
spacetime with a small Kerr parameter perturbatively, where the LTS condition
is saturated. An LTS is a surface that specifies the strong gravity region,
which is a generalization of the photon sphere in the Schwarzschild spacetime.
It turns out that there are an infinite number of marginal LTSs. At the leading
order of the small Kerr parameter, all of the marginal LTSs have the same area.
However, one can see that the maximal marginal LTS among them is uniquely
determined at the higher order.
