Non-relativistic Holography and Singular Black Hole
Feng-Li Lin, Shang-Yu Wu
TL;DR
This work develops a covariant framework for non-relativistic holography by uplifting Newton–Cartan gravity to a Bargmann manifold and performing a null-like KK reduction, yielding co-dimension-2 holography with Galilean symmetry. It constructs a black hole solution with a null-like bulk Killing vector; the horizon is curvature singular, yet the dual non-relativistic CFT attains finite temperature and thermodynamics. Boundary stress-tensor analysis gives the energy density and pressure scaling consistent with non-relativistic conformal invariance, with ρ = (d/2 − 1) p and entropy s ∼ T^{d_s/2} (d_s = d − 2) after enforcing the first law (q = 4, C_t = 1/2). Finally, the viscosity calculation shows η = 0 under horizon regularity, though relaxing this condition may yield a nonzero η and possible violations of the KSS bound, highlighting the role of horizon singularity in transport.
Abstract
We provide a framework for non-relativistic holography so that a covariant action principle ensuring the Galilean symmetry for dual conformal field theory is given. This framework is based on the Bargmann lift of the Newton-Cartan gravity to the one-dimensional higher Einstein gravity, or reversely, the null-like Kaluza-Klein reduction. We reproduce the previous zero temperature results, and our framework provides a natural explanation about why the holography is co-dimension 2. We then construct the black hole solution dual to the thermal CFT, and find the horizon is curvature singular. However, we are able to derive the sensible thermodynamics for the dual non-relativistic CFT with correct thermodynamical relations. Besides, our construction admits a null Killing vector in the bulk such that the Galilean symmetry is preserved under the holographic RG flow. Finally, we evaluate the viscosity and find it zero if we neglect the back reaction of the singular horizon, otherwise, it could be nonzero.