Deep learning metric detectors in general relativity

We consider conceptual issues of deep learning (DL) for metric detectors using test particle geodesics in curved spacetimes. Advantages of DL metric detectors are emphasized from a viewpoint of general coordinate transformations. Two given metrics (two spacetimes) are defined to be connected by a DL isometry if their geodesic image data cannot be discriminated by any DL metric detector at any time. The fundamental question of when the DL isometry appears is extensively explored. If the two spacetimes connected by the DL isometry are in superposition of quantum gravity theory, the postmeasurement state may be still in the same superposition even after DL metric detectors observe the superposed state. We also demonstrate metric-detection DL methods in 2 thorn 1-dimensional anti-de Sitter (AdS) spacetimes to estimate the cosmological constants and Brown-Henneaux charges. In the AdS/CFT correspondence dictionary, it may be expected that such metric detectors in the AdS bulk region correspond to quantum measurement devices in the conformal field theory at the AdS boundary.