We review what has been learnt and what remains unknown about the physics of hot enhancons following studies in supergravity. We recall a rather general family of static, spherically symmetric, non-extremal enhancon solutions describing D4 branes wrapped on K3 and discuss physical aspects of the solutions. We embed these solutions in the six dimensional supergravity describing type IIA strings on K3 and generalize them to have arbitrary charge vector. This allows us to demonstrate the equivalence with a known family of hot fractional D0 brane solutions, to widen the class of solutions of this second type and to carry much of the discussion across from the D4 brane analysis. In particular we argue for the existence of a horizon branch for these branes.
Dimitriadis and Ross did a preliminary search @cite_6 for a classical instability that would provide evidence that the two branches are connected. Such an instability, which is fundamentally different in nature from the Gregory-Laflamme instability, could be interpreted as signalling a phase transition in the dual gauge theory. Such instability was not found. Also presented was an entropic argument that, at high mass, the horizon branch should dominate over the shell branch in a canonical ensemble. In later work @cite_7 , a numerical study of perturbations of the non-BPS shell branch was completed, but still no instability was found. An analytic proof of non-existence of such instabilities could not be found either, owing to the non-linearity of the coupled equations. Furthermore, @cite_7 investigated whether the shell branch might violate a standard gravitational energy condition. Indeed, they found that the shell branch violates the weak energy condition (WEC). This matter will be important for us in a later section, and so we review it here.
@cite_7 @cite_6
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We study the supergravity solutions describing nonextremal enhan c c ons. There are two branches of solutions: a shell branch'' connected to the extremal solution, and a horizon branch'' which connects to the Schwarzschild black hole at large mass. We show that the shell branch solutions violate the weak energy condition, and are hence unphysical. We investigate linearized perturbations of the horizon branch and the extremal solution numerically, completing an investigation initiated in a previous paper. We show that these solutions are stable against the perturbations we consider. This provides further evidence that these latter supergravity solutions are capturing some of the true physics of the enhan c c on. We consider the stability of the two branches of nonextremal enhan c c on solutions. We argue that one would expect a transition between the two branches at some value of the nonextremality, which should manifest itself in some instability. We study small perturbations of these solutions, constructing a sufficiently general ansatz for linearized perturbations of the nonextremal solutions, and show that the linearized equations are consistent. We show that the simplest kind of perturbation does not lead to any instability. We reduce the problem of studying the more general spherically symmetric perturbation to solving a set of three coupled second-order differential equations.