Rotating Carroll Black Holes: A No Go Theorem

Abstract

Recently, there has been a lot of interest in Carroll black holes and in particular whether or not one could find a Carrollian analogue of a rotating black hole spacetime. Here we show that every stationary and axisymmetric solution (and thence also a black hole) of Carrollian general relativity in any number of $d>3$ dimensions is necessarily also static (up to a "topological rotation"). The case of $d=3$ dimensions is special. There, the topological rotation is important and one can have a rotating Carroll BTZ black hole, obtained from a static one by the Carroll boost accompanied by the re-identification of the angular coordinate, similar to what happens in the Lorentzian case. We also find a Carrollian analogue of an accelerating black hole, showing that Schwarzschild is not the only possible stationary and axisymmetric Carroll black hole in four dimensions. A generalization of the no go theorem to include Maxwell, dilatonic, and axionic matter fields is also discussed.

11 pages, no figures v2: improved 3d discussion, added references

References in corpus (31)

• The Black Hole in Three Dimensional Space Time
• Black hole chemistry: thermodynamics with Lambda
• Rotating Charged Black Hole Solution in Heterotic String Theory
• Charged Rotating Black Hole in Three Spacetime Dimensions
• Carrollian Perspective on Celestial Holography
• Carrollian Physics at the Black Hole Horizon
• Bridging Carrollian and Celestial Holography
• Interpreting the C-metric
• Fractons, dipole symmetries and curved spacetime
• Spinning charged BTZ black holes and self-dual particle-like solutions
• Carroll Expansion of General Relativity
• Magnetic Carrollian gravity from the Carroll algebra
• Carroll/fracton particles and their correspondence
• Carrollian hydrodynamics from symmetries
• Carrollian Origins of Bjorken Flow
• Carroll black holes
• The tensionless path from closed to open strings
• A Rindler Road to Carrollian Worldsheets
• BMS-like symmetries in cosmology
• Carrollian fluids and spontaneous breaking of boost symmetry
• Strong-coupled Relativity without Relativity
• Oddity in nonrelativistic, strong gravity
• Heavy-ion collisions, Gubser flow, and Carroll hydrodynamics
• Carrollian Motion in Magnetized Black Hole Horizons
• Carroll Hawking effect
• Memory Effect and Carroll Symmetry: 50 years later
• Mixmasters in Wonderland: Chaotic dynamics from Carroll limits of gravity
• Fracton and Non-Lorentzian Particle Duality: Gauge Field Couplings and Geometric Implications
• Carroll black holes in (A)dS and their higher-derivative modifications
• Unique Carrollian manifolds emerging from Einstein spacetimes
• AdS${}_3$ Carroll gravity: asymptotic symmetries and C-thermal configurations