Constraints on the size of extra dimensions from the orbital evolution of the black-hole X-ray binary XTE J1118+480

Context. To constrain Randall-Sundrum type braneworld gravity models and the expected rapid evaporation of astrophysical black holes due to the emission of gravitational modes in the extra dimension. Aims. It is argued that the black-hole X-ray binary XTE J1118+480 is suitable for a constraint on the asymptotic curvature radius of the extra dimension in such braneworld models. An upper limit on the rate of change of the orbital period of XTE J1118+480 is obtained. Methods. The expected black-hole evaporation in the extra dimension leads to a potentially observable rate of change of the orbital period in XTE J1118+480. The time-change of the orbital period is calculated from previous orbital period measurements from the literature. The lack of observed orbital period evolution is used to constrain the asymptotic curvature radius of the extra dimension. Results. The asymptotic AdS radius of curvature is constrained to a value comparable to other limits from astrophysical sources. A unique property of XTE J1118+480 is that the expected rate of change of the orbital period due to magnetic braking alone is so large that only one additional measurement of the orbital period would lead to the first detection of orbital evolution in a black-hole binary and impose the tightest constraint to date on the size of one extra dimension of the order of 35 mu m.