The formation of binaries during the dynamical evolution of globular clusters can occur either through tidal capture or through -body interactions. Tidal capture occurs when an encounter between two stars is close enough that significant tides are raised on each. The tides excite non-radial oscillations in the stars. If the energy absorbed in these oscillations is great enough to leave the two stars with negative total energy, then the system will form a binary. This process was originally thought to be the dominant channel through which binaries were formed in globular clusters [19, 43]. It is now thought to be quite rare, as detailed calculations have shown that the final result is more likely to be coalescence of the two stars [11, 83, 134]. Although -body interactions are less likely to occur than tidally significant two-body interactions, they are now thought to be the dominant channel for the formation of binaries during the evolution of a globular cluster. This process, however, is not likely to produce more than a few binaries during the lifetime of a cluster [19, 117].
If the initial binding energy of the binary is large, the result of these interactions is to shrink the orbit of the new binary as the gravitational energy of the binary is used to bring the field star up to the speeds of the binary components. However, if the binding energy is low, the field star contributes energy to the components of the binary, thereby widening the orbit. This is an example of “Heggie’s Law” , which can be summarized as hard binaries get harder and soft binaries get softer. For roughly equal mass stars, a binary is considered “hard” if its binding energy is greater than the average kinetic energy of a field star in the cluster and “soft” if its binding energy is less. For unequal mass encounters, Hills  has shown that the ratio of the orbital speeds of the binary components to the speed of the impactor is a better indicator of whether the binding energy will increase or decrease.
The average kinetic energy of a field star in the cluster is sometimes related to an effective temperature of the cluster [70, 105, 127] so that . Numerical studies of the outcome of hard binary interactions indicate that the binding energy of the binary will increase by about 20% with each encounter [85, 127]. Since the encounter rate is proportional to the semi-major axis (or ) and the energy increase per encounter is proportional to , the rate of hardening per relaxation time is independent of the energy and is . A common feature of numerical studies of hard binary interactions is the preferential exchange of high-mass stars and stellar remnants with the least massive member of the binary . Thus, the dynamical interactions in a globular cluster drive the initial orbital period distribution toward shorter periods by hardening the short period binaries while disrupting the softer binaries. Through exchange interactions, the mass distribution of the binary components is also driven toward higher mass stars, which further enhances the number of mass-transferring systems that can evolve to become relativistic binaries.
Because stellar remnants can also be exchanged into hard binaries, globular cluster evolution opens up a new channel for the formation of relativistic binaries by introducing evolved components into binary systems that have not yet undergone a mass transfer phase. A particularly promising channel involves the exchange of a neutron star into a binary with a main-sequence star. The binary then undergoes case B or case C mass transfer with a common envelope phase, resulting in a NS-WD binary . Podsiadlowski et al. describe a similar process without requiring the common envelope phase . Similar interactions can occur to produce WD-WD binaries if a massive CO or ONe white dwarf is exchanged into a hard binary.
Black hole binaries can also form as a result of exchange interactions, but the process is different because black hole progenitors will evolve so quickly in relation to the relaxation time of most globular clusters [96, 150]. One scenario that generates black hole binaries in globular clusters is described by Portegies Zwart and McMillan . Stellar mass black holes of mass will be born early in the life of a globular cluster and, through mass segregation, they will quickly sink to the core. Once in the core, these black holes will be so much more massive than the field stars that they will effectively form their own cluster and interact solely with themselves. Single black holes will form binaries with other black holes through three-body encounters; any black holes which are in binaries with other stars will team up with another black hole through exchange encounters. This population of black holes and black hole binaries will then evolve separately from the rest of the cluster as no other stars will be massive enough to affect its dynamics.
We have seen how the dynamics of globular clusters can enhance the population of progenitors to relativistic binaries, making the standard channels of mass-transfer more likely to occur. In addition, globular cluster dynamics can open up new channels for the formation of relativistic binaries by inserting evolved, stellar remnants such as neutron stars or white dwarfs into binary systems and by shrinking the orbits of binary systems to enhance the likelihood of mass exchange. Finally, binary-single star encounters can simply create relativistic binaries by inserting two evolved objects into a binary and then shrinking the orbit to ultracompact periods. We next discuss the probable rates for the formation of such systems and the dynamical simulations that are used to synthesize globular cluster populations of relativistic binaries.