Geometric Horizons in the Szekeres Spacetime
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A new conjecture for geometric horizons has been introduced which may provide a potential alternative to using apparent horizons and related surfaces for analyzing the dynamics of black hole spacetimes. In particular, using two examples of black hole formation in a collapsing universe in the Szekeres spacetime, the formation, evolution, and detection of geometric horizons are shown. In addition, a function for detecting apparent horizons in the Szekeres spacetime is also considered, and it is shown that the apparent horizon in the Szekeres model, is in fact, a geometric horizon. The Cartan-Karlhede algorithm for determining local equivalences of spacetimes is used to compute an invariant frame in the Newman Penrose frame formalism, and Cartan invariants derived from the spacetime in this frame are shown to detect the geometric horizons under various conditions on the curvature tensors of the spacetime. One model for primordial black hole formation and another for galactic black hole formation are considered with non-zero cosmological constants, generalizing work published previously on these models with zero cosmological constant. Future work utilizing geometric horizons may provide benefits in gravitational wave research involving black hole mergers.