  We study the magnon contribution to the gravitomagnetoelectric (gravito-ME)
effect, in which the magnetization is induced by a temperature gradient, in
noncentrosymmetric antiferromagnetic insulators. This phenomenon is totally
different from the ME effect, because the temperature gradient is coupled to
magnons but an electric field is not. We derive a general formula of the
gravito-ME susceptibility in terms of magnon wave functions and find that a
difference in $g$ factors of magnetic ions is crucial. We also apply our
formula to a specific model. Although the obtained gravito-ME susceptibility is
small, we discuss several ways to enhance this phenomenon.
