# Higher-Spin Flat Space Cosmologies with Soft Hair

## TL;DR

This paper explores higher-spin gravity in three-dimensional flat space, establishing boundary conditions, analyzing asymptotic symmetries, and deriving an entropy formula that aligns with previous complex results, highlighting the role of soft hair.

## Contribution

It introduces new near horizon boundary conditions for flat space higher-spin gravity and derives a simple entropy formula matching earlier complex calculations.

## Key findings

- Asymptotic symmetry algebra consists of $$ current algebras.
- Entropy is linear in spin-2 charges and independent of spin-3 charges.
- Derived entropy matches earlier complex higher-spin results.

## Abstract

We present and discuss near horizon boundary conditions for flat space higher-spin gravity in three dimensions. As in related work our boundary conditions ensure regularity of the solutions independently of the charges. The asymptotic symmetry algebra is given by a set of $\hat{\mathfrak{u}}(1)$ current algebras. The associated charges generate higher-spin soft hair. We derive the entropy for solutions that are continuously connected to flat space cosmologies and find the same result as in the spin-2 case: the entropy is linear in the spin-2 zero-mode charges and independent from the spin-3 charges. Using twisted Sugawara-like constructions of higher-spin currents we show that our simple result for entropy of higher-spin flat space cosmologies coincides precisely with the complicated earlier results expressed in terms of higher-spin zero mode charges.