A finite action principle for Chern-Simons AdS gravity is presented. The construction is carried out in detail first in five dimensions, where the bulk action is given by a particular combination of the Einstein-Hilbert action with negative cosmological constant and a Gauss-Bonnet term; and is then generalized for arbitrary odd dimensions. The boundary term needed to render the action finite is singled out demanding the action to attain an extremum for an appropriate set of boundary conditions. The boundary term is a local function of the fields at the boundary and is sufficient to render the action finite for asymptotically AdS solutions, without requiring background fields. It is shown that the Euclidean continuation of the action correctly describes black hole thermodynamics in the canonical ensemble. Additionally, background independent conserved charges associated with the asymptotic symmetries can be written as surface integrals by direct application of Noether's theorem.1 A submanifold that satisfies this condition is also known as totally umbilical [20]

A gauge invariant action principle, based on the idea of transgression forms, is proposed. The action extends the Chern-Simons form by the addition of a boundary term that makes the action gauge invariant (and not just quasi-invariant). Interpreting the spacetime manifold as cobordant to another one, the duplication of gauge fields in spacetime is avoided. The advantages of this approach are particularly noticeable for the gravitation theory described by a Chern-Simons lagrangian for the AdS group, in which case the action is regularized and finite for black hole geometries in diverse situations. Black hole thermodynamics is correctly reproduced using either a background field approach or a background-independent setting, even in cases with asymptotically nontrivial topologies. It is shown that the energy found from the thermodynamic analysis agrees with the surface integral obtained by direct application of Noether's theorem.

The two published lithium peroxide structures, both ascribed to the hexagonal P6 space group, were subjected to reinterpretation, and another more symmetric structure, now belonging to the P6(3)/mmc space group, was found. Detailed density-functional quantum mechanical calculations and crystal structure optimizations were carried out on both structures and the energetic arguments obtained therewith helped to rule out one of them.

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The 5d electron-based Sr2−xLaxIrO4 system (0≤x≤0.2) has been synthesized by a solid-state route. The x = 0 composition is a nonmetallic weak ferromagnet with a Curie temperature at about 240 K. The crystal structure behaviour and magnetic properties exhibited by this Sr2−xLaxIrO4 system can be explained on the basis of the extended character of the 5d electrons of the Ir cation and its valence states. Rietveld analysis of x-ray powder diffraction on Sr2IrO4 agrees well with previous structural neutron experiments. Furthermore, density functional theory (DFT) calculations predict that I41/acd represents a more stable crystal structure than K2NiF4 (I4/mmm). Electrical resistivity and magnetic properties of Sr2−xLaxIrO4 are strongly dependent on the Ir3+ content. The Sr2−xLaxIrO4 magnetic behaviour in the range of 2–240 K can be ascribed to a weak ferromagnet, produced by an array of canted antiferromagnetically ordered Ir4+ magnetic moments.