Gravitomagnetic-Hydrodynamics and Turbulence in Early Universe

Abstract: This work tries to establish the theoretical framework for gravitomagnetic-hydrodynamics (GMHD), revealing a fundamental correspondence between geometrodynamics and magnetohydrodynamic phenomena in general relativity. By introducing the gravitoelectromagnetic formalism to relativistic fluids, a set of leading-order GMHD equations is derived that govern the co-evolution of spacetime geometry and matter dynamics in the early Universe. This analysis reveals that, under high-temperature and high-density conditions such as those during the electroweak phase transition, the gravitomagnetic Reynolds number becomes large, leading to a strongly coupled fluid-spacetime system. This coupling supports the emergence of gravitational Alfven waves and a turbulent energy cascade. Our findings suggest that GMHD turbulence may leave imprints on the stochastic gravitational wave background, offering a new window into the nonlinear dynamics of the primordial Universe.