Structure formation in the presence of relativistic heat conduction: corrections to the Jeans wave number with a stable, first order in the gradients, formalism

The problem of structure formation in relativistic dissipative fluids was analyzed in a previous work within Eckart's framework, in which the heat flux is coupled to the hydrodynamic acceleration, additional to the usual temperature gradient term. It was shown that in such case, the pathological behavior of fluctuations leads to the disappearance of the gravitational instability responsible for structure formation (Mondragon-Suarez and Sandoval-Villalbazo in Gen Relativ Gravit 44:139-145, 2012). In the present work the problem is revisited using a constitutive equation derived from relativistic kinetic theory. This new relation, in which the heat flux is not coupled to the hydrodynamic acceleration, leads to a consistent first order in the gradients formalism. In this case the gravitational instability remains, and only relativistic corrections to the Jeans wave number are obtained. In the calculation here shown the non-relativistic limit is recovered, opposite to what happens in Eckart's case (Hiscock and Lindblom in Phys Rev D 31:725-733, 1985).