On the Post-linear Quadrupole-Quadrupole Metric

The Hartle-Thorne metric defines a reliable spacetime for most astrophysical purposes, for instance for the simulation of slowly rotating stars. Solving the Einstein field equations, we added terms of second order in the quadrupole moment to its post-linear version in order to compare it with solutions found by Blanchet in the frame of the multi-polar post-Minkowskian framework. We first derived the extended Hartle-Thorne metric in harmonic coordinates and then showed agreement with the corresponding post-linear metric from Blanchet. We also found a coordinate transformation from the post-linear Erez-Rosen metric to our extended Hartle-Thorne spacetime. It is well known that the Hartle-Thorne solution can be smoothly matched with an interior perfect fluid solution with physically appropriate properties. A comparison among these solutions provides a validation of them. It is clear that in order to represent realistic solutions of self-gravitating (axially symmetric) matter distributions of perfect fluid, the quadrupole moment has to be included as a physical parameter

A phylogenomic perspective on the radiation of ray-finned fishes based upon targeted sequencing of ultraconserved elements

Ray-finned fishes constitute the dominant radiation of vertebrates with over 30,000 species. Although molecular phylogenetics has begun to disentangle major evolutionary relationships within this vast section of the Tree of Life, there is no widely available approach for efficiently collecting phylogenomic data within fishes, leaving much of the enormous potential of massively parallel sequencing technologies for resolving major radiations in ray-finned fishes unrealized. Here, we provide a genomic perspective on longstanding questions regarding the diversification of major groups of ray-finned fishes through targeted enrichment of ultraconserved nuclear DNA elements (UCEs) and their flanking sequence. Our workflow efficiently and economically generates data sets that are orders of magnitude larger than those produced by traditional approaches and is well-suited to working with museum specimens. Analysis of the UCE data set recovers a well-supported phylogeny at both shallow and deep time-scales that supports a monophyletic relationship between Amia and Lepisosteus (Holostei) and reveals elopomorphs and then osteoglossomorphs to be the earliest diverging teleost lineages. Divergence time estimation based upon 14 fossil calibrations reveals that crown teleosts appeared ~270 Ma at the end of the Permian and that elopomorphs, osteoglossomorphs, ostarioclupeomorphs, and euteleosts diverged from one another by 205 Ma during the Triassic. Our approach additionally reveals that sequence capture of UCE regions and their flanking sequence offers enormous potential for resolving phylogenetic relationships within ray-finned fishes

Free Variables and the Two Matrix Model

We study the full set of planar Green's functions for a two-matrix model using the language of functions of non-commuting variables. Both the standard Schwinger-Dyson equations and equations determining connected Green's functions can be efficiently discussed and solved. This solution determines the master field for the model in the `$C$-representation.'Comment: 8 pages, harvma