Gauge-invariant observables in gravity and electromagnetism: Black hole backgrounds and null dressings

Abstract

We address questions regarding construction and implications of gauge-invariant "dressed" observables in nontrivial background geometries such as that of a black hole. Formally, such observables can be constructed, e.g., by locating points with geodesics launched from infinity. However, practical complications arise in nontrivial geometries, and in particular for observables behind black hole horizons. Greater simplicity can be achieved by considering null constructions where the dressing lies along a null geodesic, or null surface such as a cone. We first investigate basic properties of these null dressings in the simpler context of electromagnetism. Since null constructions provide simple dressings for gauge-invariant observables inside black holes, they also allow us to investigate the question of compatibility of observables inside and outside black holes, and in particular the idea of black hole complementarity. While such observables in general have nonvanishing state-dependent commutators, the failure to commute does not appear particularly enhanced by the presence of the horizon.

Schrödinger evolution of two-dimensional black holes

“…Of course, inclusion of even the leading gravitational backreaction modifies this structure [52,69] (see also [70]), since the gravitational dressing associated to an internal excitation extends outside the horizon [71]. However, the arguments of [72] suggest that there is still a subsystem structure, since the gravitational degrees of freedom may be taken to be in a state where the external structure of the dressing depends only the total Poincaré charges of the internal matter, and not on other features of the internal state.…”

Unruh detectors and quantum chaos in JT gravity

“…This implicit dependence on F (t) of bulk operators couples bulk matter to the Schwarzian reparameterization mode. We note that the definition (2.11) of bulk operators in quantum gravity corresponds in the language of [53,54,[64][65][66][67][68][69] to specifying a particular gravitational dressing of a bare bulk matter operator such that the dressed operator is diff-invariant. In every fixed metric (2.10), the two-point function of two operators of the type (2.11) is then by definition of (2.10) just the reparameterization of (2.5)…”

Schrödinger evolution of two-dimensional black holes

“…Of course, inclusion of even the leading gravitational backreaction modifies this structure [52,69] (see also [70]), since the gravitational dressing associated to an internal excitation extends outside the horizon [71]. However, the arguments of [72] suggest that there is still a subsystem structure, since the gravitational degrees of freedom may be taken to be in a state where the external structure of the dressing depends only the total Poincaré charges of the internal matter, and not on other features of the internal state.…”