Does the third law of black hole thermodynamics really have a serious failure?

The almost perfect correspondence between certain laws of classical black hole mechanics and the ordinary laws of thermodynamics is spoiled by the failure of the conventional back hole analogue of the third law. Our aim here is to contribute to the associated discussion by flashing light on some simple facts of black hole physics. However, no attempt is made to lay to rest the corresponding long lasting debate. Instead, merely some evidence is provided to make it clear that although the borderline between extremal and non-extremal black holes is very thin they are essentially different. Hopefully, a careful investigation of the related issues will end up with an appropriate form of the third law and hence with an unblemished setting of black hole thermodynamics.Comment: 6 pages, Latex. accepted for publication in Class. Quant. Gra

On the Rigidity Theorem for Spacetimes with a Stationary Event Horizon or a Compact Cauchy Horizon

We consider smooth electrovac spacetimes which represent either (A) an asymptotically flat, stationary black hole or (B) a cosmological spacetime with a compact Cauchy horizon ruled by closed null geodesics. The black hole event horizon or, respectively, the compact Cauchy horizon of these spacetimes is assumed to be a smooth null hypersurface which is non-degenerate in the sense that its null geodesic generators are geodesically incomplete in one direction. In both cases, it is shown that there exists a Killing vector field in a one-sided neighborhood of the horizon which is normal to the horizon. We thereby generalize theorems of Hawking (for case (A)) and Isenberg and Moncrief (for case (B)) to the non-analytic case.Comment: 16 pages, no figure

Probability of the emergence of helical precipitation patterns in the wake of reaction-diffusion fronts

Helical and helicoidal precipitation patterns emerging in the wake of reaction-diffusion fronts are studied. In our experiments, these chiral structures arise with well-defined probabilities P_H controlled by conditions such as e.g., the initial concentration of the reagents. We develop a model which describes the observed experimental trends. The results suggest that P_H is determined by a delicate interplay among the time and length scales related to the front and to the unstable precipitation modes and, furthermore, the noise amplitude also plays a quantifiable role.Comment: 7 pages, 5 composite figure

Methods for identifying high-redshift galaxy cluster candidates

Recent theories linked long gamma ray bursts (GRBs) to galaxies with rapid star formation or starburst; thus, we expect that long GRBs (LGRBs) are more frequent in midcluster galaxies where mergers and tidal interactions between gas-rich galaxies are more likely to occur. Yet there is no galaxy cluster known to be associated with LGRBs. We demonstrate that, based on deep, single-band Subaru Hyper Suprime-Cam observations, we may provide constraints on photometric redshifts of groups of galaxies. We compare three methods: cosmological approach, pseudoinverse matrix, and random forests to estimate galaxy and quasar redshifts. Comparing our results to spectroscopic redshifts of Sloan Digital Sky Survey's-detected extragalactic sources, random forests may provide the highest accuracy with as low as 17 percentage error. This is a powerful method to find clusters to place GRB host galaxies in their local environment

Population dynamics and genetic changes of Picea abies in the South Carpathians revealed by pollen and ancient DNA analyses

Background: Studies on allele length polymorphism designate several glacial refugia for Norway spruce (Picea abies) in the South Carpathian Mountains, but infer only limited expansion from these refugia after the last glaciation. To better understand the genetic dynamics of a South Carpathian spruce lineage, we compared ancient DNA from 10,700 and 11,000-year-old spruce pollen and macrofossils retrieved from Holocene lake sediment in the Retezat Mountains with DNA extracted from extant material from the same site. We used eight primer pairs that amplified short and variable regions of the spruce cpDNA. In addition, from the same lake sediment we obtained a 15,000-years-long pollen accumulation rate (PAR) record for spruce that helped us to infer changes in population size at this site.Results: We obtained successful amplifications for Norway spruce from 17 out of 462 pollen grains tested, while the macrofossil material provided 22 DNA sequences. Two fossil sequences were found to be unique to the ancient material. Population genetic statistics showed higher genetic diversity in the ancient individuals compared to the extant ones. Similarly, statistically significant Ks and Kst values showed a considerable level of differentiation between extant and ancient populations at the same loci.Lateglacial and Holocene PAR values suggested that population size of the ancient population was small, in the range of 1/10 or 1/5 of the extant population. PAR analysis also detected two periods of rapid population growths (from ca. 11,100 and 3900 calibrated years before present (cal yr BP)) and three bottlenecks (around 9180, 7200 and 2200 cal yr BP), likely triggered by climatic change and human impact.Conclusion: Our results suggest that the paternal lineages observed today in the Retezat Mountains persisted at this site at least since the early Holocene. Combination of the results from the genetic and the PAR analyses furthermore suggests that the higher level of genetic variation found in the ancient populations and the loss of ancient allele types detected in the extant individuals were likely due to the repeated bottlenecks during the Holocene; however our limited sample size did not allow us to exclude sampling effect.This study demonstrates how past population size changes inferred from PAR records can be efficiently used in combination with ancient DNA studies. The joint application of palaeoecological and population genetics analyses proved to be a powerful tool to understand the influence of past population demographic changes on the haplotype diversity and genetic composition of forest tree species