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Next-generation galaxy surveys will increasingly rely on the galaxybispectrum to improve cosmological constraints, especially on primordialnon-Gaussianity. A key theoretical requirement that remains to be developed isthe analysis of general relativistic effects on the bispectrum, which arisefrom observing galaxies on the past lightcone, {as well as from relativisticcorrections to the dynamics}. {As an initial step towards a fully relativisticanalysis of the galaxy bispectrum, we compute for the first time the localrelativistic lightcone effects on the bispectrum,} which come from Doppler andgravitational potential contributions. For the galaxy bispectrum, the problemis much more complex than for the power spectrum, since we need the lightconecorrections at second order. Mode-coupling contributions at second order meanthat relativistic corrections can be non-negligible at smaller scales than inthe case of the power spectrum. In a primordial Gaussian universe, we show thatthe local lightcone corrections for squeezed shapes at $z\sim1$ mean that thebispectrum can differ from the Newtonian prediction by $\gtrsim 10\%$ when theshort modes are $k\lesssim (50\,{\rm Mpc})^{-1}$. These relativistic projectioneffects, if ignored in the analysis of observations, could be mistaken forprimordial non-Gaussianity. For upcoming surveys which probe equality scalesand beyond, {all relativistic lightcone effects and relativistic dynamicalcorrections should be included} for an accurate measurement of primordialnon-Gaussianity.

A general relativistic signature in the galaxy bispectrum: the local effects of observing on the lightcone