New stable phase of non - uniform charged black strings

Non-uniform black strings coupled to a gauge field are constructed by a perturbative method in a wide range of spacetime dimensions. At the linear order of perturbations, we see that the Gregory-Laflamme instability vanishes at the point where the background solution becomes ther-modynamically stable. The emergence/vanishing of the static mode resembles phase transitions, and in fact we find that its critical exponent is nearly 1/2, which means a second-order transition. By employing higher-order perturbations, the physical properties of the non-uniform black strings are investigated in detail. For fixed spacetime dimensions, we find the critical charges at which the stability of non-uniform states changes. For some range of charge, non-uniform black strings are entropically favored over uniform ones. The gauge charge works as a control parameter that controls not only the stability of uniform black strings but also the non-uniform states. In addition, we find that for a fixed background charge the uniform state is not necessarily the state carrying the largest tension. The phase diagram and a comparison with the critical dimension are also discussed.