Spherically symmetric solutions of higher-spin gravity in the IKKT matrix model

TL;DR

This paper systematically explores spherically symmetric vacuum solutions in the IKKT matrix model, revealing asymptotically flat geometries that resemble Schwarzschild at large distances but include additional fields and deviations at non-linear levels.

Contribution

It provides explicit solutions within semi-classical covariant quantum geometries and addresses the reconstruction of matrix configurations from given frames, advancing understanding of pre-gravity in matrix models.

Findings

Solutions reproduce linearized Schwarzschild geometry at large r

Deviations from Schwarzschild include dilaton and axion effects

Reconstruction of matrix configurations from frames is always possible at the geometric level

Abstract

We present a systematic study of spherically symmetric vacuum solutions of the IKKT matrix model, within the framework of semi-classical covariant quantum geometries. All asymptotically flat solutions of the equations of motion of the frame are found explicitly. They reproduce the linearized Schwarzschild geometry for large $r$ but deviate from it at the non-linear level, and include contributions from dilaton and axion. They are pertinent to the pre-gravity theory arising on classical brane solutions within the classical matrix model, before taking into account the Einstein-Hilbert term induced by quantum effects. We also address the problem of reconstructing matrix configurations corresponding to some given frame, and show that this problem can always be solved at the geometrical level of the underlying higher spin theory, ignoring possible higher spin modes.