Generalized Chern-Simons Modified Gravity in First-Order Formalism

We propose a generalization of Chern-Simons (CS) modified gravity in first-order formalism. CS modified gravity action has a term that comes from the chiral anomaly which is Pontryagin invariant. First-order CS modified gravity is a torsional theory and in a space-time with torsion the chiral anomaly includes a torsional topological term called Nieh-Yan invariant. We generalize the CS modified gravity by adding the Nieh-Yan term to the action and find the effective theory. We compare the generalized theory with the first-order CS modified gravity and comment on the similarities and differences.Comment: 8 pages, an author added, new paragraphs, comments and references added, published in Gen. Relativ. Gravi

Measuring the gravitational field in General Relativity: From deviation equations and the gravitational compass to relativistic clock gradiometry

How does one measure the gravitational field? We give explicit answers to this fundamental question and show how all components of the curvature tensor, which represents the gravitational field in Einstein's theory of General Relativity, can be obtained by means of two different methods. The first method relies on the measuring the accelerations of a suitably prepared set of test bodies relative to the observer. The second methods utilizes a set of suitably prepared clocks. The methods discussed here form the basis of relativistic (clock) gradiometry and are of direct operational relevance for applications in geodesy.Comment: To appear in "Relativistic Geodesy: Foundations and Application", D. Puetzfeld et. al. (eds.), Fundamental Theories of Physics, Springer 2018, 52 pages, in print. arXiv admin note: text overlap with arXiv:1804.11106, arXiv:1511.08465, arXiv:1805.1067

Conservation of energy-momentum of matter as the basis for the gauge theory of gravitation

According to Yang \& Mills (1954), a {\it conserved} current and a related rigid (`global') symmetry lie at the foundations of gauge theory. When the rigid symmetry is extended to a {\it local} one, a so-called gauge symmetry, a new interaction emerges as gauge potential $A$; its field strength is $F\sim {\rm curl} A$. In gravity, the conservation of the energy-momentum current of matter and the rigid translation symmetry in the Minkowski space of special relativity lie at the foundations of a gravitational gauge theory. If the translation invariance is made local, a gravitational potential $\vartheta$ arises together with its field strength $T\sim {\rm curl}\,\vartheta$. Thereby the Minkowski space deforms into a Weitzenb\"ock space with nonvanishing torsion $T$ but vanishing curvature. The corresponding theory is reviewed and its equivalence to general relativity pointed out. Since translations form a subgroup of the Poincar\'e group, the group of motion of special relativity, one ought to straightforwardly extend the gauging of the translations to the gauging of full Poincar\'e group thereby also including the conservation law of the {\it angular momentum} current. The emerging Poincar\'e gauge (theory of) gravity, starting from the viable Einstein-Cartan theory of 1961, will be shortly reviewed and its prospects for further developments assessed.Comment: 46 pages, 4 figures, minor corrections, references added, contribution to "One Hundred Years of Gauge Theory" edited by S. De Bianchi and C. Kiefe

Ward identity for elastic wave transport in disordered media

For elastic wave transport in non-uniform static media, we derive a Ward-Takahashi identity that is a consequence of energy conservation. Making use of this basic identity, and with the help of an integral equation, essentially equivalent to the Bethe-Salpeter equation, we derive another version of the Ward identity that is important in describing the multiply scattered, diffusive transport of elastic waves in disordered media. (C) 1997 Published by Elsevier Science B.V

Trapped Bose-Einstein condensate in the weakly interacting limit

We study the Bose-Einstein condensate in a harmonic trap in the weakly interacting limit well below the temperature for Bose-Einstein condensation transition. We show that the ground state is a canonical coherent state. The energy spectrum, the chemical potential, and the order parameter for the condensate are obtained analytically. (C) 1997 Elsevier Science B.V

Performance of thin-film lithium energy cells under uniaxial pressure

The objective of this study was two-fold. The first objective was to determine if the all-solid-state thin-film lithium energy cells could withstand the minimal 550 kPa uniaxial pressure required for composite manufacturing, which both specimens successfully did. The second objective was to determine the upper boundary uniaxial pressure limit of operation for the all-solid-state thin-film lithium energy cells. The two all-solid- state thin-film lithium energy cells tested in the present study under uniaxial pressure performed well even when subjected to uniaxial pressures up to about 2.0 MPa. However, pressures higher than this value led to their degradation. The observed degradation was due to the mechanical failure of the sealant. Above this pressure, the sealant was squeezed out of the space between the two mica substrates and the lithium-metal anode layer, which in turn allowed the ambient air to penetrate into the energy cell core, thus leading to the rapid degradation of the charge and discharge performance and the ultimate demise of the energy cell. We found out that, within the observed range, uniformly distributed packaging characteristics, we found that allsolid- state thin-film energy cells charge/discharge cycles under upwardly increasing uniform uniaxial pressure are extraordinarily robust and resilient to the effects of uniaxial, uniformly distributed uniaxial pressure had little or no effect on the charge/discharge performance of the all-solid-state thin-film lithium energy cells. Other power charge/draws outside of 1 mAh were not of interest in this study for the reasons already pointed out, albeit that they may be considered for future studies. Apart from other considerations for failure due to the current and constant power charge/sink of 1mAh. If the overall structure of the energy cell is mechanically robust, i.e., of high structural integrity, the maximum pressure that can be imposed is expected to be much higher than the maximum values noted earlier. The present study indicates that all-solidstate thin-film energy cells can be used as an integral part of a load-bearing multifunctional, smart material structure if their packaging is of sufficiently high structural integrity. Hence, the goal of using fiber reinforced laminated composites as the packaging material for all-solid-state thin-film batteries in multifunctional smart materials structures is well within reach