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We present general relativistic correction terms appearing in Newton'sgravity to the second-order perturbations of cosmological fluids. In ourprevious work we have shown that to the second-order perturbations, the densityand velocity perturbation equations of general relativistic zero-pressure,irrotational, single-component fluid in a flat background coincide exactly withthe ones known in Newton's theory. Here, we present the general relativisticsecond-order correction terms arising due to (i) pressure, (ii)multi-component, (iii) background curvature, and (iv) rotation. In case ofmulti-component zero-pressure, irrotational fluids under the flat background,we effectively do not have relativistic correction terms, thus the relativisticresult again coincides with the Newtonian ones. In the other three cases wegenerally have pure general relativistic correction terms. In case of pressure,the relativistic corrections appear even in the level of background and linearperturbation equations. In the presence of background curvature, or rotation,pure relativistic correction terms directly appear in the Newtonian equationsof motion of density and velocity perturbations to the second order. In thesmall-scale limit (far inside the horizon), relativistic equations includingthe rotation coincide with the ones in Newton's gravity.

Second-order perturbations of cosmological fluids: Relativistic effects of pressure, multi-component, curvature, and rotation