On the existence of horizons in spacetimes with vanishing curvature invariants
Jos\'e M M Senovilla
TL;DR
This paper proves that spacetimes with all curvature scalar invariants vanishing cannot contain black hole horizons, and provides examples of dynamical horizons that do not enclose trapped regions.
Contribution
It offers a simple proof of the non-existence of horizons in such spacetimes and presents explicit examples of dynamical horizons without trapped regions.
Findings
No closed trapped surfaces in spacetimes with vanishing curvature invariants
Existence of dynamical horizons not enclosing trapped regions
Clarification of horizon properties in special spacetimes
Abstract
A direct very simple proof that there can be no closed trapped surfaces (ergo no black hole regions) in spacetimes with all curvature scalar invariants vanishing is given. Explicit examples of the recently introduced ``dynamical horizons'' which nevertheless do not enclose any trapped region are presented too.
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