  We study a static system of self-gravitating radiations confined in a sphere
by using numerical and analytical calculations. Due to the scaling symmetry of
radiations, most of main properties of a solution can be represented as a
segment of a solution curve on a plane of two-dimensional scale invariant
variables. We define an `approximate horizon' (AH) from the analogy with an
apparent horizon. Any solution curve contains a unique point which corresponds
to the AH. A given solution is uniquely labelled by three parameters
representing the solution curve, the size of the AH, and the sphere size, which
are an alternative of the data at the outer boundary. Various geometrical
properties including the existence of an AH and the behaviors around the center
can be identified from the parameters. We additionally present an analytic
solution of the radiations on the verge of forming a blackhole. Analytic
formulae for the central mass of the naked singularity are given.

General Relativity and Quantum Cosmology