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Because most large galaxies contain a central black hole, and galaxies oftenmerge, black-hole binaries are expected to be common in galactic nuclei.Although they cannot be imaged, periodicities in the light curves of quasarshave been interpreted as evidence for binaries, most recently in PG~1302-102,with a short rest-frame optical period of 4 years. If the orbital periodmatches this value, then for the range of estimated black hole masses thecomponents would be separated by 0.007-0.017 pc, implying relativistic orbitalspeeds. There has been much debate over whether black hole orbits could besmaller than 1 pc. Here we show that the amplitude and the sinusoid-like shapeof the variability of PG~1302-102 can be fit by relativistic Doppler boostingof emission from a compact, steadily accreting, unequal-mass binary. We predictthat brightness variations in the ultraviolet light curve track those in theoptical, but with a 2-3 times larger amplitude. This prediction is relativelyinsensitive to the details of the emission process, and is consistent witharchival UV data. Follow-up UV and optical observations in the next few yearscan test this prediction and confirm the existence of a binary black hole inthe relativistic regime.

Relativistic boost as the cause of periodicity in a massive black-hole binary candidate