Gravity in the 3+1-Split Formalism II: Self-Duality and the Emergence of the Gravitational Chern-Simons in the Boundary

We study self-duality in the context of the 3+1-split formalism of gravity with non-zero cosmological constant. Lorentzian self-dual configurations are conformally flat spacetimes and have boundary data determined by classical solutions of the three-dimensional gravitational Chern-Simons. For Euclidean self-dual configurations, the relationship between their boundary initial positions and initial velocity is also determined by the three-dimensional gravitational Chern-Simons. Our results imply that bulk self-dual configurations are holographically described by the gravitational Chern-Simons theory which can either viewed as a boundary generating functional or as a boundary effective action.Comment: 25 pages; v2: minor improvements, references adde

A classification of local Weyl invariants in D=8

Following a purely algebraic procedure, we provide an exhaustive classification of local Weyl-invariant scalar densities in dimension D=8.Comment: LaTeX, 19 pages, typos corrected, one reference adde

Gravity in the 3+1-Split Formalism I: Holography as an Initial Value Problem

We present a detailed analysis of the 3+1-split formalism of gravity in the presence of a cosmological constant. The formalism helps revealing the intimate connection between holography and the initial value formulation of gravity. We show that the various methods of holographic subtraction of divergences correspond just to different transformations of the canonical variables, such that the initial value problem is properly set up at the boundary. The renormalized boundary energy momentum tensor is a component of the Weyl tensor.Comment: 28 pages; v2: minor improvements, references adde

Wideband-RL-cancel circuit for the E-J property measurement using the third-harmonic voltage method

A precise and generalisable non-destructive measurement technique is required for evaluation of critical current density JC and electric field E vs. current density J properties in large-area and long-length high-temperature superconducting films. We measured E-J properties of a 2-inch phi Y-123 standard film for the calibration of our inductive measurement system using the third-harmonic voltage method. With adoption of a wideband-RL-cancel circuit, frequency normalised third-harmonic resistance contained noise less than 0.2 μΩs and power-law E-J dependencies were in the relatively wide electric field range of 1.4×10-6-1.6×10-4 V/m. Critical current density JC at 10-4 V/m on 7 different positions changed from an average of 2.839×1010A/m2 by a maximum of ±0.52%. As the JC distribution was also included, the maximum error margin of JC became remarkably small in the V3 inductive method. E-J properties of a 20×20mm square Dy-123 film agreed well with the properties measured by another research group. JC at 10-4 V/m and n value were 2.23×1010 A/m2 and 26.74 on the average of four different positions, with estimated systematic errors of -8.6% and +1.4%, respectively, by comparison of the averages of 16 positions measured by the same research group