Emergence of Einstein-frame geometry: Geodesically complete black holes and cosmologies from phantom Chaplygin gas

The phantom Dirac–Born–Infeld (DBI) model exhibits superluminal propagation. This model can dynamically develop sudden singularities, where the pressure diverges, and evolution seemingly grinds to a halt. We demonstrate that the former property cures the latter, making all equations of motion nonsingular throughout. This is accomplished by promoting the “induced” metric defined by the DBI scalar field to the fundamental "causal-frame" metric, relegating the Einstein-frame metric to the status of emergent. By choosing the causal-frame metric’s lapse function to be everywhere positive, the Einstein-frame lapse function emerges as a dynamical field that smoothly changes sign. This has the effect of spontaneously reversing the flow of time for general relativity, as well as for any degrees of freedom minimally coupled to the Einstein-frame metric. The DBI scalar field propagates on the causal frame metric, and thus always evolves forward in time, realizing a transient mismatch in thermodynamic arrows of time. While the cosmological solutions to this model exhibit robust non-singular bounces, the spherically symmetric solutions include non-singular black holes, known as gravastars. All previous gravastar-like solutions require anisotropic fluid "crusts", whereas our DBI model (equivalent to the isotropic perfect fluid known as phantom Chaplygin gas) is isotropic. It thus evades both the Buchdahl--Bondi bound and the Cattoen--Faber--Viser theorem.