4D higher spin black holes with nonlinear scalar fluctuations

Abstract

Abstract:We construct an infinite-dimensional space of solutions to Vasiliev's equations in four dimensions that are asymptotic to AdS spacetime and superpose massless scalar particle modes over static higher spin black holes. Each solution is obtained by a large gauge transformation of an all-order perturbatively defined particular solution given in a simple gauge, in which the spacetime connection vanishes, the twistor space connection is holomorphic, and all local degrees of freedom are encoded into the residual twistor space dependence of the spacetime zero-forms. The latter are expanded over two dual spaces of Fock space operators, corresponding to scalar particle and static black hole modes, equipped with positive definite sesquilinear and bilinear forms, respectively. Switching on an AdS vacuum gauge function, the twistor space connection becomes analytic at generic spacetime points, which makes it possible to reach Vasiliev's gauge, in which Fronsdal fields arise asymptotically, by another large transformation given here at first order. The particle and black hole modes are related by a twistor space Fourier transform, resulting in a black hole backreaction already at the second order of classical perturbation theory. We speculate on the existence of a fine-tuned branch of moduli space that is free from black hole modes and directly related to the quasi-local deformed Fronsdal theory. Finally, we comment on a possible interpretation of the higher spin black hole solutions as black-hole microstates.

FRW and domain walls in higher spin gravity

“…In this paper, we shall use a solution generating technique [17][18][19] to build g 6 -invariant solutions to Vasiliev's bosonic theory with non-vanishing (positive or negative) cosmological constant from gauge functions, representing large gauge transformations that alter the asymptotics of the gauge fields, and g 6 -invariant scalar field profiles in the maximally symmetric background. Solutions of Vasiliev's equations with g 3 , g 4 and g 6 symmetries, which are subgroups of the AdS 4 symmetry group, were constructed only at the linearized level in [14] (see [19] for a review) by using a different technique.…”

“…As we shall see in section 5, an important advantage of the method we have used to obtain the exact solutions in the holomorphic gauge is the validity of linear superposition principle in constructing solutions, thus facilitating the description of fluctuations around an exact solution. Even though we leave to future work the analysis of a cosmological perturbation theory around our solutions, an inspection of the star product algebra among the master field will lead us to propose that the nonlinear completion of particle excitations over FRW and domain wall solutions requires black hole-like states (see [18] for the study of scalar particle fluctuations over higher-spin black hole modes). 1 The various vacua possess unbroken higher spin symmetries; the unbroken symmetry algebra of the g6-invariant vacua is the intersection of the enveloping algebra of g6 with the unbroken symmetry algebra of the maximally symmetric vacua (see [14] for the case of an so(1, 3)-invariant solution), which is given by the quotient of the enveloping algebra of the (A)dS4 Killing symmetry algebra over the two-sided ideal given by the singleton annihilator.…”

“…Introducing the curvature and twisted-adjoint covariant derivative defined by 18) respectively, one has the Bianchi identities…”

“…In [38,45], it has been proposed that the extensive variables are the zero-form charges [14,37], and in [46] it has been proposed that a complete set of classical observables in the case that X4 has trivial topology is given by the space of twisted open Wilson lines in Z4. According to these proposals, the rigid symmetries of the vacuum should leave the extensive variables invariant while acting nontrivially on the microscopic variables; for related remarks, see [18,46]. 10 The full field configurations are thus assumed to contain contain asymptotically (anti-)de Sitter regions where the full tensor gauge fields φ a(s) approach Fronsdal fields give on shell in terms of polarization tensors that are non-linear functionals of the zero-form initial data C.…”

“…Deformed oscillators: although the master fields S (G) are not sections, one can require that Φ (G) and the twisted open Wilson loops V (M )) form an associative algebra with traces, which can be use to construct a complete set of higher spin invariant observables that one may think of as substitutes for the standard ADM-like charges that can be used to define higher spin ensembles in unbroken phases; for further details, see [18].…”