  In a universe of the Randall-Sundrum type, black holes are unstable and emit
gravitational modes in the extra dimension. This leads to dramatically
shortened lifetimes of astrophysical black holes and to an observable change of
the orbital period of black-hole binaries. I obtain an upper limit on the rate
of change of the orbital period of the binary XTE J1118+480 and constrain the
asymptotic curvature radius of the extra dimension to a value that is of the
same order as the constraints from other 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 of a black-hole binary and impose the tightest constraint to date on
the size of one extra dimension of the order of 35 microns.
