Probing the gravitational geon

The Brill-Hartle gravitational geon construct as a spherical shell of small amplitude, high frequency gravitational waves is reviewed and critically analyzed. The Regge-Wheeler formalism is used to represent gravitational wave perturbations of the spherical background as a superposition of tensor spherical harmonics and an attempt is made to build a non-singular solution to meet the requirements of a gravitational geon. High-frequency waves are seen to be a necessary condition for the geon and the field equations are decomposed accordingly. It is shown that this leads to the impossibility of forming a spherical gravitational geon. The attempted constructs of gravitational and electromagnetic geons are contrasted. The spherical shell in the proposed Brill-Hartle geon does not meet the regularity conditions required for a non-singular source and hence cannot be regarded as an adequate geon construct. Since it is the high frequency attribute which is the essential cause of the geon non-viability, it is argued that a geon with less symmetry is an unlikely prospect. The broader implications of the result are discussed with particular reference to the problem of gravitational energy.Comment: Replaced with revised version (substantial changes and additions, conclusions unchanged), 36 pages, LaTex, 3 figures available from the author

Stability of Gravitational and Electromagnetic Geons

Recent work on gravitational geons is extended to examine the stability properties of gravitational and electromagnetic geon constructs. All types of geons must possess the property of regularity, self-consistency and quasi-stability on a time-scale much longer than the period of the comprising waves. Standard perturbation theory, modified to accommodate time-averaged fields, is used to test the requirement of quasi-stability. It is found that the modified perturbation theory results in an internal inconsistency. The time-scale of evolution is found to be of the same order in magnitude as the period of the comprising waves. This contradicts the requirement of slow evolution. Thus not all of the requirements for the existence of electromagnetic or gravitational geons are met though perturbation theory. From this result it cannot be concluded that an electromagnetic or a gravitational geon is a viable entity. The broader implications of the result are discussed with particular reference to the problem of gravitational energy.Comment: 40 pages, 5 EPS figures, uses overcite.st

Perturbative Tamm-Dancoff Renormalization

A new two-step renormalization procedure is proposed. In the first step, the effects of high-energy states are considered in the conventional (Feynman) perturbation theory. In the second step, the coupling to many-body states is eliminated by a similarity transformation. The resultant effective Hamiltonian contains only interactions which do not change particle number. It is subject to numerical diagonalization. We apply the general procedure to a simple example for the purpose of illustration.Comment: 20 pages, RevTeX, 10 figure

Nonperturbative renormalization group in a light-front three-dimensional real scalar model

The three-dimensional real scalar model, in which the $Z_2$ symmetry spontaneously breaks, is renormalized in a nonperturbative manner based on the Tamm-Dancoff truncation of the Fock space. A critical line is calculated by diagonalizing the Hamiltonian regularized with basis functions. The marginal ($\phi^6$) coupling dependence of the critical line is weak. In the broken phase the canonical Hamiltonian is tachyonic, so the field is shifted as $\phi(x)\to\varphi(x)+v$. The shifted value $v$ is determined as a function of running mass and coupling so that the mass of the ground state vanishes.Comment: 23 pages, LaTeX, 6 Postscript figures, uses revTeX and epsbox.sty. A slight revision of statements made, some references added, typos correcte

Faddeev eigenfunctions for two-dimensional Schrodinger operators via the Moutard transformation

We demonstrate how the Moutard transformation of two-dimensional Schrodinger operators acts on the Faddeev eigenfunctions on the zero energy level and present some explicitly computed examples of such eigenfunctions for smooth fast decaying potentials of operators with non-trivial kernel and for deformed potentials which correspond to blowing up solutions of the Novikov-Veselov equation.Comment: 11 pages, final remarks are adde

In-situ temperature calibration procedure for temperature and strain fibre Bragg grating sensors for monitoring pre-stressing strands

In this work, we demonstrate active and passive methods for in-situ temperature calibration of fibre Bragg grating strain and temperature sensors. The method is suitable for characterizing sensors which are already attached to the steel reinforcements of civil structures. The proposed method, which involves the use of active induction heating or passive room temperature fluctuations, can be implemented using portable equipment, is time efficient, and can be used to calibrate attached sensors on-site, rather than in lab conditions. Preliminary results of the induction heating calibration show good agreement with pre-calibrated temperature sensors. In-situ calibration of fibre strain sensors, attached to a prestressing strand is also successfully carried out

Metal-Packaged fibre Bragg grating strain sensors for surface mounting onto spalled concrete wind turbine foundations

In this work, we demonstrate preliminary results for a hermetically sealed, metal-packaged fibre Bragg grating strain sensor for monitoring existing concrete wind turbine foundations. As the sensor is bolted to the sub-surface of the concrete, it is suitable for mounting onto uneven, wet and degraded surfaces, which may be found in buried foundations. The sensor was able to provide reliable measurements of concrete beam strain during cyclic three- And four- point bend tests. The strain sensitivity of the prototype sensor is currently 10 % of that of commercial, epoxied fibre strain sensors

Conductivity, weak ferromagnetism and charge instability in α−MnS\alpha-MnS single crystal

The temperature dependence of resistivity, magnetization and electron-spin resonance of the $\alpha- MnS$ single crystal were measured in temperature range of $5 K < T < 550 K$. Magnetization hysteresis in applied magnetic field up to 0.7 T at $T=5 K, 77 K, 300 K$, irreversible temperature behavior of magnetization and resistivity were found . The obtained data were explained in terms of degenerate tight binding model using random phase approximation. The contribution of holes in $t_{2g}$ and $e_g$ bands of manganese ions to the conductivity, optical absorbtion spectra and charge instability in $\alpha -MnS$ were studied. Charge susceptibility maxima resulted from the competition of the on-site Coulomb interaction between the holes in different orbitals and small hybridization of sub-bands were calculated at $T=160 K, 250 K, 475 K$.Comment: 6 pages, 12 figure

Gravitational Geons in 1+1 Dimensions

It is well known that general relativity does not admit gravitational geons that are stationary, asymptotically flat, singularity free and topologically trivial. However, it is likely that general relativity will receive corrections at large curvatures and the modified field equations may admit solutions corresponding to this type of geon. If geons are produced in the early universe and survive until today they could account for some of the dark matter that has been "observed" in galaxies and galactic clusters. In this paper I consider gravitational geons in 1+1 dimensional theories of gravity. I show that the Jackiw-Teitelboim theory with corrections proportional to $R^2$ and $\Box R$ admits gravitational geons. I also show that gravitational geons exist in a class of theories that includes Lagrangians proportional to $R^{2/3}$.Comment: 8 pages, a comment added, two references corrected, to appear in Classical and Quantum Gravit