Higher-Spin Flat Space Cosmologies with Soft Hair

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.

arXiv comment22 pages, A Mathematica workbook on ihs[$\lambda$] is included as an ancilliary file; v2: corrected minor misprints; v3: fixed minor issues with the display of some references

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• Symmetries at Null Boundaries: Two and Three Dimensional Gravity Cases
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• Carrollian and Galilean conformal higher-spin algebras in any dimensions
• Generalized Chern-Simons higher-spin gravity theories in three dimensions
• Boundary conditions for General Relativity in three-dimensional spacetimes, integrable systems and the KdV/mKdV hierarchies
• Spectral Flow in 3D Flat Spacetimes
• Warped Black Holes in Lower-Spin Gravity
• Interpolating Between Asymptotic and Near Horizon Symmetries
• Log corrections to entropy of three dimensional black holes with soft hair
• Kerr-Newman Black Hole Entropy and Soft Hair
• Scalar Fields in 3D Asymptotically Flat Higher-Spin Gravity
• The Maxwell group in 2+1 dimensions and its infinite-dimensional enhancements
• Soft hairy warped black hole entropy
• Integrable systems and the boundary dynamics of higher spin gravity on AdS${}_3$
• Higher-spin gauge theories in three spacetime dimensions
• Supertranslation Hair of Schwarzschild Black Hole: A Wilson Line Perspective
• Semi-classical BMS-blocks from the Oscillator Construction
• Higher Spin Gravity in $Ad{S}_3$ and Folds on Fermi Surface
• Unfolded Fierz-Pauli Equations in Three-Dimensional Asymptotically Flat Spacetimes
• Chern-Simons Holography: Boundary Conditions, Contractions and Double Extensions for a Journey Beyond Anti-de Sitter
• Supersymmetric Localization on dS: Sum over topologies
• A Lie algebra based approach to asymptotic symmetries in general relativity
• Free-field construction of Carrollian $W_N$-algebras