Multipolar Expansions for the Relativistic N-Body Problem in the Rest-Frame Instant Form

Dixon's multipoles for a system of N relativistic positive-energy scalar particles are evaluated in the rest-frame instant form of dynamics. The Wigner hyperplanes (intrinsic rest frame of the isolated system) turn out to be the natural framework for describing multipole kinematics. In particular, concepts like the {\it barycentric tensor of inertia} can be defined in special relativity only by means of the quadrupole moments of the isolated system.Comment: 46 pages, revtex fil

The Hamiltonian formulation of General Relativity: myths and reality

A conventional wisdom often perpetuated in the literature states that: (i) a 3+1 decomposition of space-time into space and time is synonymous with the canonical treatment and this decomposition is essential for any Hamiltonian formulation of General Relativity (GR); (ii) the canonical treatment unavoidably breaks the symmetry between space and time in GR and the resulting algebra of constraints is not the algebra of four-dimensional diffeomorphism; (iii) according to some authors this algebra allows one to derive only spatial diffeomorphism or, according to others, a specific field-dependent and non-covariant four-dimensional diffeomorphism; (iv) the analyses of Dirac [Proc. Roy. Soc. A 246 (1958) 333] and of ADM [Arnowitt, Deser and Misner, in "Gravitation: An Introduction to Current Research" (1962) 227] of the canonical structure of GR are equivalent. We provide some general reasons why these statements should be questioned. Points (i-iii) have been shown to be incorrect in [Kiriushcheva et al., Phys. Lett. A 372 (2008) 5101] and now we thoroughly re-examine all steps of the Dirac Hamiltonian formulation of GR. We show that points (i-iii) above cannot be attributed to the Dirac Hamiltonian formulation of GR. We also demonstrate that ADM and Dirac formulations are related by a transformation of phase-space variables from the metric $g_{\mu\nu}$ to lapse and shift functions and the three-metric $g_{km}$, which is not canonical. This proves that point (iv) is incorrect. Points (i-iii) are mere consequences of using a non-canonical change of variables and are not an intrinsic property of either the Hamilton-Dirac approach to constrained systems or Einstein's theory itself.Comment: References are added and updated, Introduction is extended, Subsection 3.5 is added, 83 pages; corresponds to the published versio

Phenomenology of the Lense-Thirring effect in the Solar System

Recent years have seen increasing efforts to directly measure some aspects of the general relativistic gravitomagnetic interaction in several astronomical scenarios in the solar system. After briefly overviewing the concept of gravitomagnetism from a theoretical point of view, we review the performed or proposed attempts to detect the Lense-Thirring effect affecting the orbital motions of natural and artificial bodies in the gravitational fields of the Sun, Earth, Mars and Jupiter. In particular, we will focus on the evaluation of the impact of several sources of systematic uncertainties of dynamical origin to realistically elucidate the present and future perspectives in directly measuring such an elusive relativistic effect.Comment: LaTex, 51 pages, 14 figures, 22 tables. Invited review, to appear in Astrophysics and Space Science (ApSS). Some uncited references in the text now correctly quoted. One reference added. A footnote adde

As Leguminosae arbóreas das florestas estacionais do Parque Estadual do Itacolomi, Minas Gerais, Brasil

Este estudo consiste do tratamento taxonômico das Leguminosae arbóreas das florestas estacionais do Parque Estadual do Itacolomi (PEI). As coletas de material botânico ocorreram mensalmente, entre setembro de 2004 e novembro de 2005, ao longo de oito trilhas distribuídas em áreas de florestas estacionais submontana, montana e altimontana. O levantamento resultou em 39 táxons reunidos em 22 gêneros e distribuídos entre as três subfamílias: Caesalpinioideae (9 espécies), Mimosoideae (17) e Papilionoideae (13). Os gêneros mais representativos foram Inga (8 espécies), Machaerium (4), Senna e Dalbergia (3, cada), Abarema, Anadenanthera e Tachigali (2, cada). Bauhinia, Cassia, Copaifera, Melanoxylon, Calliandra, Mimosa, Piptadenia, Pseudopiptadenia, Stryphnodendron, Andira, Bowdichia, Ormosia, Platypodium, Pterocarpus e Swartzia apresentaram uma espécie cada. Ormosia friburgensis e Tachigali friburgensis são registradas pela primeira vez para o estado de Minas Gerais. São fornecidos chave de identificação, descrições, ilustrações, dados fenológicos, comentários taxonômicos e preferência por habitats de cada táxon no PEI.This study presents the taxonomic treatment of woody Leguminosae in seasonal forests of Itacolomi State Park (PEI). Botanical material was collected monthly, from September 2004 to November 2005, along eight trails in submontane, montane and upper montane seasonal forests. Woody Leguminosae were represented by 39 taxa in 22 genera distributed among the three subfamilies: Cesalpinioideae (9 species), Mimosoideae (17), and Papilionoideae (13). The most representative genera were Inga (8 species), followed by Machaerium (4), Senna and Dalbergia (3 each), Abarema, Anadenanthera, and Tachigali (2 each). Bauhinia, Cassia, Copaifera, Melanoxylon, Calliandra, Mimosa, Piptadenia, Pseudopiptadenia, Stryphnodendron, Andira, Bowdichia, Ormosia, Platypodium, Pterocarpus, and Swartzia were represented by one species each. Ormosia friburgensis and Tachigali friburgensis are reported for the first time in Minas Gerais state. Analytical key, descriptions, illustrations, data on phenology, and comments on taxonomy and preferred habitat in PEI are provided for all taxa

Phylogenomics and the rise of the angiosperms

Angiosperms are the cornerstone of most terrestrial ecosystems and human livelihoods1,2. A robust understanding of angiosperm evolution is required to explain their rise to ecological dominance. So far, the angiosperm tree of life has been determined primarily by means of analyses of the plastid genome3,4. Many studies have drawn on this foundational work, such as classification and first insights into angiosperm diversification since their Mesozoic origins5,6,7. However, the limited and biased sampling of both taxa and genomes undermines confidence in the tree and its implications. Here, we build the tree of life for almost 8,000 (about 60%) angiosperm genera using a standardized set of 353 nuclear genes8. This 15-fold increase in genus-level sampling relative to comparable nuclear studies9 provides a critical test of earlier results and brings notable change to key groups, especially in rosids, while substantiating many previously predicted relationships. Scaling this tree to time using 200 fossils, we discovered that early angiosperm evolution was characterized by high gene tree conflict and explosive diversification, giving rise to more than 80% of extant angiosperm orders. Steady diversification ensued through the remaining Mesozoic Era until rates resurged in the Cenozoic Era, concurrent with decreasing global temperatures and tightly linked with gene tree conflict. Taken together, our extensive sampling combined with advanced phylogenomic methods shows the deep history and full complexity in the evolution of a megadiverse clade