End point of Hawking radiation

The formation and semiclassical evaporation of two-dimensional black holes is studied in an exactly solvable model. Above a certain threshold energy flux, collapsing matter forms a singularity inside an apparent horizon. As the black hole evaporates the apparent horizon recedes and meets the singularity in a finite proper time. The singularity emerges naked, and future evolution of the geometry requires boundary conditions to be imposed there. There is a natural choice of boundary conditions which matches the evaporated black hole solution onto the linear dilaton vacuum. Below the threshold energy flux no horizon forms and boundary conditions can be imposed where infalling matter is reflected from a timelike boundary. All information is recovered at spatial infinity in this case.

Timeframe of speciation inferred from secondary contact zones in the European tree frog radiation (Hyla arborea group).

BACKGROUND: Hybridization between incipient species is expected to become progressively limited as their genetic divergence increases and reproductive isolation proceeds. Amphibian radiations and their secondary contact zones are useful models to infer the timeframes of speciation, but empirical data from natural systems remains extremely scarce. Here we follow this approach in the European radiation of tree frogs (Hyla arborea group). We investigated a natural hybrid zone between two lineages (Hyla arborea and Hyla orientalis) of Mio-Pliocene divergence (~5 My) for comparison with other hybrid systems from this group. RESULTS: We found concordant geographic distributions of nuclear and mitochondrial gene pools, and replicated narrow transitions (~30 km) across two independent transects, indicating an advanced state of reproductive isolation and potential local barriers to dispersal. This result parallels the situation between H. arborea and H. intermedia, which share the same amount of divergence with H. orientalis. In contrast, younger lineages show much stronger admixture at secondary contacts. CONCLUSIONS: Our findings corroborate the negative relationship between hybridizability and divergence time in European tree frogs, where 5 My are necessary to achieve almost complete reproductive isolation. Speciation seems to progress homogeneously in this radiation, and might thus be driven by gradual genome-wide changes rather than single speciation genes. However, the timescale differs greatly from that of other well-studied amphibians. General assumptions on the time necessary for speciation based on evidence from unrelated taxa may thus be unreliable. In contrast, comparative hybrid zone analyses within single radiations such as our case study are useful to appreciate the advance of speciation in space and time.