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arXiv · 2601.14239

Peculiar velocity fields from analytic solutions of General Relativity

Roberto A. Sussman·Sebastián Nájera·Fernando A. Pizaña·Juan Carlos Hidalgo
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Abstract

Peculiar velocities are analyzed through cosmological perturbations in the Newtonian longitudinal gauge characterized by irrotational shear-free congruences in an Eulerian frame. We show that non-trivial peculiar velocity fields can be generated through Lorentzian boosts in the non-relativistic limit, where the Eulerian frame is obtained from analytic solutions of Einstein's equations sourced by an irrotational shear-free fluid with nonzero energy flux. This approach provides a physically viable interpretation of these analytic solutions, which (in general) admit no isometries, thus allowing, in principle, for modeling time and space varying 3-dimensional fields of peculiar velocities that can be contrasted with observational data on our local cosmography. As a ``proof of concept'' we examine the peculiar velocities of varying dark matter and dark energy perfect fluids with respect to the CMB frame using a simple, spherically symmetric particular solution. The resulting peculiar velocities are qualitatively compatible with observational data on the CMB dipole.

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Roberto A. Sussman, Sebastián Nájera, Fernando A. Pizaña, Juan Carlos Hidalgo. 2026-01-20. Peculiar velocity fields from analytic solutions of General Relativity. https://arxiv.org/abs/2601.14239

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