[2211.06415] Carrollian hydrodynamics and symplectic structure on stretched horizons

[Submitted on 11 Nov 2022]

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Abstract: The membrane paradigm displays underlying connections between a timelike
stretched horizon and a null boundary (such as a black hole horizon) and
bridges the gravitational dynamics of the horizon with fluid dynamics. In this
work, we revisit the membrane viewpoint of a finite distance null boundary and
present a unified geometrical treatment to the stretched horizon and the null
boundary based on the rigging technique of hypersurfaces. This allows us to
provide a unified geometrical description of null and timelike hypersurfaces,
which resolves the singularity of the null limit appearing in the conventional
stretched horizon description. We also extend the Carrollian fluid picture and
the geometrical Carrollian description of the null horizon, which have been
recently argued to be the correct fluid picture of the null boundary, to the
stretched horizon. To this end, we draw a dictionary between gravitational
degrees of freedom on the stretched horizon and the Carrollian fluid quantities
and show that Einstein’s equations projected onto the horizon are the
Carrollian hydrodynamic conservation laws. Lastly, we report that the
gravitational pre-symplectic potential of the stretched horizon can be
expressed in terms of conjugate variables of Carrollian fluids and also derive
the Carrollian conservation laws and the corresponding Noether charges from
symmetries.