Rindler Quantum Gravity

TL;DR

This work demonstrates that asymptotically global AdS spacetimes admit a Rindler-like holographic description as an entangled pair of Hd CFTs, with each Hd CFT’s reduced density matrix describing physics in a single Rindler wedge. The authors show how the global AdS vacuum corresponds to a thermally entangled Hd CFT state, and explore the microstate geometries that underlie wedge physics, arguing that typical microstates resemble wedge AdS away from the horizon but replace the horizon with a singular boundary. They substantiate the role of entanglement in reconstructing bulk geometry through both field-theoretic (entanglement structure and stress-energy cancellations) and gravitational (hyperbolic black hole) analyses, and illustrate how disentangling alters the spacetime by increasing wedge separation and modifying minimal-surface areas. The work further connects these ideas to cosmological holography, suggesting observer-dependent patches offer a path toward non-perturbative quantum gravity descriptions of cosmologies where no observer has access to the full spacetime, albeit with caveats and open questions. Overall, it provides a concrete framework linking observer-bound patches, entanglement, and bulk geometry in AdS/CFT with potential implications for holography in cosmology.

Abstract

In this note, we explain how asymptotically globally AdS spacetimes can be given an alternate dual description as entangled states of a pair of hyperbolic space CFTs, which are associated with complementary Rindler wedges of the AdS geometry. The reduced density matrix encoding the state of the degrees of freedom in one of these CFTs describes the physics in a single wedge, which we can think of as the region of spacetime accessible to an accelerated observer in AdS. For pure AdS, this density matrix is thermal, and we argue that the microstates in this thermal ensemble correspond to spacetimes that are almost indistinguishable from a Rindler wedge of pure AdS away from the horizon, but with the horizon replaced by some kind of singularity where the geometrical description breaks down. This alternate description of AdS, based on patches associated with particular observers, may give insight into the holographic description of cosmologies where no observer has access to the full spacetime.

Figures (9)

• Figure 1: A pair of accelerating observers in pure global AdS. The spacetime region accessible to each is a wedge whose boundary geometry can be chosen as $H^d \times R$. Each wedge has a dual description as a thermal state of a CFT on this $H^d \times R$ boundary geometry. The full spacetime is described by an entangled state of the two $H^d$ CFTs.
• Figure 2: Quantum superposition of microstate geometries yielding pure AdS spacetime. Each choice of complementary Rindler wedges leads to a different decomposition of AdS into a superposition of disconnected spacetimes.
• Figure 3: Static observer in de Sitter space (left) and accelerated observer in AdS. Both have access to only a portion of the full spacetime, bounded (on one side in the AdS case) by a horizon with a thermal character.
• Figure 4: Conformal map from the boundary of a Poincare patch to Minkowski space. Region $D_L$ (solid) maps to one Rindler wedge of Minkowski space, while the dotted region, $D_R$, maps to the other wedge. The Poincare patch boundary $D_P$ is the region bounded by dashed lines.
• Figure 5: Wedges of pure AdS spacetime. Field theory observables in $D_R$ (the shaded part of the boundary cylinder) probe the bulk region $J^+(D_R) \cap J^-(D_R)$ (the shaded region of the bulk). Any point in this region can receive a light signal (blue line) from and send a light signal to $D_R$. Physics outside this region can be altered by changes on the boundary that do not affect the state of the fields in $D_R$. One trajectory along which such changes propagate is shown in red.