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Register a new userEffective Field Theory of Hairy Black Holes and Their flat/dS limit
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Effective theory of fluctuations based on underlying symmetry plays very important role in understanding the low energy phenomena. Using this powerful technique we study the fluctuation dynamics keeping in mind the following central question: does the effective theory of black hole provide any information about the possible existence of hair? Assuming the symmetry of the hair being that of the underlying black hole space-time, we start by writing down the most general action for the background and the fluctuation in the effective field theory framework. Considering the asymptotically flat and de Sitter black hole background with a spherically symmetric hair we derived the most general equation of motion for the fluctuation. For a particular choice of theory parameters, quasinormal modes corresponding to those fluctuations appeared to have distinct features compared to that of the usual black hole quasinormal modes. The background equations from the effective theory Lagrangian, on the other hand, seemed to suggest that the underlying theory of the hair under consideration should be higher derivative in nature. Therefore as a concrete example we construct a class of higher derivative scalar field theory which gives rise to spherically symmetric hair through background cosmological constant. We also calculate the quasinormal modes whose behaviour turned out to be similar to the one discussed from the effective theory.
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A numerical analysis shows that a class of scalar-tensor theories of gravity with a scalar field minimally and nonminimally coupled to the curvature allows static and spherically symmetric black hole solutions with scalar-field hair in asymptotically flat spacetimes. In the limit when the horizon radius of the black hole tends to zero, regular scalar solitons are found. The asymptotically flat solutions are obtained provided that the scalar potential $V(phi)$ of the theory is not positive semidefinite and such that its local minimum is also a zero of the potential, the scalar field settling asymptotically at that minimum. The configurations for the minimal coupling case, although unstable under spherically symmetric linear perturbations, are regular and thus can serve as counterexamples to the no-scalar-hair conjecture. For the nonminimal coupling case, the stability will be analyzed in a forthcoming paper.
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