A generalized momentum/complexity correspondence. (English) Zbl 1462.83004
Summary: Holographic complexity, in the guise of the Complexity = Volume prescription, comes equipped with a natural correspondence between its rate of growth and the average infall momentum of matter in the bulk. This Momentum/Complexity correspondence can be related to an integrated version of the momentum constraint of general relativity. In this paper we propose a generalization, using the full Codazzi equations as a starting point, which successfully accounts for purely gravitational contributions to infall momentum. The proposed formula is explicitly checked in an exact pp-wave solution of the vacuum Einstein equations.
MSC:
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
| 83C35 | Gravitational waves |
| 83E05 | Geometrodynamics and the holographic principle |
| 81T35 | Correspondence, duality, holography (AdS/CFT, gauge/gravity, etc.) |
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