Hydrodynamics of a System of Gravitational Charges and Jeans Instability

In connection with a recent experiment on the falling of antihydrogen in Earth’s gravitational field, the problem of modifying the Jeans instability for a two-component medium with gravitational attraction and repulsion is considered. Due to the possibility of the existence, in addition to the gravitational attraction of the same gravitational charges, of the gravitational repulsion of particles and antiparticles, the hydrodynamics of such a system assumes a nonstandard form. The dispersion equation, the increment of the modified Jeans instability for an arbitrary fraction of the repulsive mass of antihydrogen, and the sound mode are found.