# 4D Higher Spin Black Holes with Nonlinear Scalar Fluctuations

## TL;DR

This paper constructs a new class of four-dimensional higher spin black hole solutions with scalar fluctuations, using large gauge transformations and twistor space techniques, revealing insights into black hole microstates and higher spin gravity.

## Contribution

It introduces an infinite-dimensional solution space to Vasiliev's equations, incorporating scalar and black hole modes via twistor space and gauge transformations, advancing higher spin black hole understanding.

## Key findings

- Black hole backreaction appears at second order in perturbation theory.
- Solutions relate scalar and black hole modes through twistor Fourier transform.
- Speculation on moduli space branches free of black hole modes.

## 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.