Relativistic Binary Pulsars with Black-Hole Companions

Binaries containing a stellar-mass black hole and a recycled radio pulsar have so far eluded detection. We present a focused investigation of the formation and evolution of these systems in the Galactic disk, highlighting the factors that limit their numbers and the reasons why they may be extremely rare. We surmise that the birthrate of black-hole/recycled-pulsar binaries in the Galactic disk is probably no higher than ~10^{-7}/yr, and may be much less. Simple arguments regarding common-envelope evolution suggest that these binaries should have orbital periods less than 10 hr and an average lifetime of <~10^8 yr before coalescence due to the emission of gravitational radiation. We expect that fewer than ~10 of these compact, relativistic binaries currently reside in the Galactic disk, less than 0.1--1% of the number of double neutron stars. The discovery of two or more black-hole/recycled-pulsar binaries using current radio telescopes would tightly constrain certain ideas regarding the evolution of massive stars, dynamical mass transfer, and black-hole formation.