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Geometry of Carrollian Stretched Horizons
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In this paper, we present a comprehensive toolbox for studying Carrollian stretched horizons, encompassing their geometry, dynamics, symplectic geometry, symmetries, and corresponding Noether charges. We introduce a precise definition of ruled stretched Carrollian structures (sCarrollian structures) on any surface, generalizing the conventional Carrollian structures of null surfaces, along with the notions of sCarrollian connection and sCarrollian stress tensor. Our approach unifies the sCarrollian (intrinsic) and stretched horizon (embedding) perspectives, providing a universal framework for any causal surface, whether timelike or null. We express the Einstein equations in sCarrollian variables and discuss the phase space symplectic structure of the sCarrollian geometry. Through Noether's theorem, we derive the Einstein equation and canonical charge and compute the evolution of the canonical charge along the transverse (radial) direction. The latter can be interpreted as a spin-2 symmetry charge. Our framework establishes a novel link between gravity on stretched horizons and Carrollian fluid dynamics and unifies various causal surfaces studied in the literature, including non-expanding and isolated horizons. We expect this work to provide insights into the hydrodynamical description of black holes and the quantization of null surfaces.
Forward citations
Cited by 5 Pith papers
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The Energy-Momentum-News Complex near Future Null Infinity
A Carroll-covariant energy-momentum-news complex at future null infinity yields Ward identities that generalise the Bondi loss equations, with an anomalous Carroll boost.
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Boundary Energy-Momentum Tensors for Asymptotically Flat Spacetimes
Varying a renormalized Einstein-Hilbert action with respect to Carrollian metric and shear data yields an EMT-news complex whose diffeomorphism Ward identity reproduces the Bondi mass and angular momentum loss equatio...
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Quantum Area Fluctuations from Gravitational Phase Space
The variance of area fluctuations of a causal diamond in Minkowski spacetime is claimed to satisfy ⟨(ΔA)²⟩ ≥ (2πG/d)⟨A⟩, using quantized gravitational phase space on a stretched horizon.
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Black hole thermodynamics at null infinity. Part 2: Open systems, Markovian dynamics and work extraction from non-rotating black holes
Null-infinity black hole thermodynamics is recast as Markovian open-system thermodynamics, with chemical-potential terms identified as extractable work and used to formulate generalized grand-potential laws for Schwar...
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Aspects of Carrollian field theory from holography
The holographic stress tensor at null infinity in three-dimensional flat gravity reproduces the known BMS3 central charges c_L=0 and c_M=3/G_N, and yields the expected Ward identities and Schwarzian boundary action.
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