Eternal Higher Spin Black Holes: a Thermofield Interpretation

Abstract

We study Lorentzian eternal black holes in the Chern-Simons sector of AdS$_3$ higher spin gravity. We probe such black holes using bulk Wilson lines and motivate new regularity conditions that must be obeyed by the bulk connections in order for the geometry to be consistent with an interpretation as a thermofield state in the dual CFT$_2$. We demonstrate that any higher spin black hole may be placed in a gauge that satisfies these conditions: this is the Chern-Simons analogue of the construction of Kruskal coordinates that permit passage through the black hole horizon. We also argue that the Wilson line provides a higher-spin notion of causality in higher spin gravity that can be used to associate a Penrose diagram with the black hole. We present some applications of the formalism, including a study of the time-dependent entanglement entropy arising from the higher spin black hole interior and evidence for an emergent AdS$_2$ region in the extremal limit.