Graviton emission into non-Z2 symmetric brane world spacetimes

The equations for the evolution of a homogeneous brane world that emits gravitons at early times, and into a non-Z2 symmetric bulk, are derived using an AdS–Vaidya spacetime approximation. The behaviour of the black hole mass parameters either side of the brane is analysed, and it is found that in general graviton emission leads to a decrease in the non-Z2 symmetry. However, the behaviour of the dark radiation term in the Friedmann equation is more complex: it is shown that this term can increase or decrease due to the non-Z2 symmetry, and can become negative in some cases, leading to H = 0 and the brane universe collapsing. Constraints on the initial (non-zero) sizes of the mass parameters are therefore derived.