Topics in the Dynamics or General Relativity

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Maximal Hypersurfaces and Positivity of Mass

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Perturbations of Spatially Closed Bianchi III Spacetimes

Motivated by the recent interest in dynamical properties of topologically nontrivial spacetimes, we study linear perturbations of spatially closed Bianchi III vacuum spacetimes, whose spatial topology is the direct product of a higher genus surface and the circle. We first develop necessary mode functions, vectors, and tensors, and then perform separations of (perturbation) variables. The perturbation equations decouple in a way that is similar to but a generalization of those of the Regge--Wheeler spherically symmetric case. We further achieve a decoupling of each set of perturbation equations into gauge-dependent and independent parts, by which we obtain wave equations for the gauge-invariant variables. We then discuss choices of gauge and stability properties. Details of the compactification of Bianchi III manifolds and spacetimes are presented in an appendix. In the other appendices we study scalar field and electromagnetic equations on the same background to compare asymptotic properties.Comment: 61 pages, 1 figure, final version with minor corrections, to appear in Class. Quant. Gravi

Speed Limits in General Relativity

Some standard results on the initial value problem of general relativity in matter are reviewed. These results are applied first to show that in a well defined sense, finite perturbations in the gravitational field travel no faster than light, and second to show that it is impossible to construct a warp drive as considered by Alcubierre (1994) in the absence of exotic matter.Comment: 7 pages; AMS-LaTeX; accepted for publication by Classical and Quantum Gravit

Thermal Conductivity of Single Wall Carbon Nanotubes: Diameter and Annealing Dependence

The thermal conductivity, k(T), of bulk single-wall carbon nanotubes (SWNT's) displays a linear temperature dependence at low T that has been attributed to 1D quantization of phonons. To explore this issue further, we have measured the k(T) of samples with varying average tube diameters. We observe linear k(T) up to higher temperatures in samples with smaller diameters, in agreement with a quantization picture. In addition, we have examined the effect of annealing on k(T). We observe an enhancement in k(T) for annealed samples which we attribute to healing of defects and removal of impurities. These measurements demonstrate how the thermal properties of an SWNT material can be controlled by manipulating its intrinsic nanoscale properties.Comment: Proc. of the XV. Int. Winterschool on Electronic Properties of Novel Materials, Kirchberg/Tirol, Austria, 200

Spacelike surfaces with free boundary in the Lorentz-Minkowski space

We investigate a variational problem in the Lorentz-Minkowski space \l^3 whose critical points are spacelike surfaces with constant mean curvature and making constant contact angle with a given support surface along its common boundary. We show that if the support surface is a pseudosphere, then the surface is a planar disc or a hyperbolic cap. We also study the problem of spacelike hypersurfaces with free boundary in the higher dimensional Lorentz-Minkowski space \l^{n+1}.Comment: 16 pages. Accepted in Classical and Quantum Gravit

SO(4) Invariant States in Quantum Cosmology

The phenomenon of linearisation instability is identified in models of quantum cosmology that are perturbations of mini-superspace models. In particular, constraints that are second order in the perturbations must be imposed on wave functions calculated in such models. It is shown explicitly that in the case of a model which is a perturbation of the mini-superspace which has $S^3$ spatial sections these constraints imply that any wave functions calculated in this model must be SO(4) invariant. (This replaces the previous corrupted version.)Comment: 15 page

Emissivity measurements of reflective surfaces at near-millimeter wavelengths

We have developed an instrument for directly measuring the emissivity of reflective surfaces at near-millimeter wavelengths. The thermal emission of a test sample is compared with that of a reference surface, allowing the emissivity of the sample to be determined without heating. The emissivity of the reference surface is determined by one’s heating the reference surface and measuring the increase in emission. The instrument has an absolute accuracy of Δe = 5 x 10^-4 and can reproducibly measure a difference in emissivity as small as Δe = 10^-4 between flat reflective samples. We have used the instrument to measure the emissivity of metal films evaporated on glass and carbon fiber-reinforced plastic composite surfaces. We measure an emissivity of (2.15 ± 0.4) x 10^-3 for gold evaporated on glass and (2.65 ± 0.5) x 10^-3 for aluminum evaporated on carbon fiber-reinforced plastic composite

Observations of solar small-scale magnetic flux-sheet emergence

Aims. Moreno-Insertis et al. (2018) recently discovered two types of flux emergence in their numerical simulations: magnetic loops and magnetic sheet emergence. Whereas magnetic loop emergence has been documented well in the last years, by utilising high-resolution full Stokes data from ground-based telescopes as well as satellites, magnetic sheet emergence is still an understudied process. We report here on the first clear observational evidence of a magnetic sheet emergence and characterise its development. Methods. Full Stokes spectra from the Hinode spectropolarimeter were inverted with the SIR code to obtain solar atmospheric parameters such as temperature, line-of-sight velocities and full magnetic field vector information. Results. We analyse a magnetic flux emergence event observed in the quiet-sun internetwork. After a large scale appearance of linear polarisation, a magnetic sheet with horizontal magnetic flux density of up to 194 Mx/cm$^{2}$ hovers in the low photosphere spanning a region of 2 to 3 arcsec. The magnetic field azimuth obtained through Stokes inversions clearly shows an organised structure of transversal magnetic flux density emerging. The granule below the magnetic flux-sheet tears the structure apart leaving the emerged flux to form several magnetic loops at the edges of the granule. Conclusions. A large amount of flux with strong horizontal magnetic fields surfaces through the interplay of buried magnetic flux and convective motions. The magnetic flux emerges within 10 minutes and we find a longitudinal magnetic flux at the foot points of the order of $\sim$$10^{18}$ Mx. This is one to two orders of magnitude larger than what has been reported for small-scale magnetic loops. The convective flows feed the newly emerged flux into the pre-existing magnetic population on a granular scale.Comment: 6 pages, 5 figures, accepted as a letter in A&

An Introduction to Conformal Ricci Flow

We introduce a variation of the classical Ricci flow equation that modifies the unit volume constraint of that equation to a scalar curvature constraint. The resulting equations are named the Conformal Ricci Flow Equations because of the role that conformal geometry plays in constraining the scalar curvature. These equations are analogous to the incompressible Navier-Stokes equations of fluid mechanics inasmuch as a conformal pressure arises as a Lagrange multiplier to conformally deform the metric flow so as to maintain the scalar curvature constraint. The equilibrium points are Einstein metrics with a negative Einstein constant and the conformal pressue is shown to be zero at an equilibrium point and strictly positive otherwise. The geometry of the conformal Ricci flow is discussed as well as the remarkable analytic fact that the constraint force does not lose derivatives and thus analytically the conformal Ricci equation is a bounded perturbation of the classical unnormalized Ricci equation. That the constraint force does not lose derivatives is exactly analogous to the fact that the real physical pressure force that occurs in the Navier-Stokes equations is a bounded function of the velocity. Using a nonlinear Trotter product formula, existence and uniqueness of solutions to the conformal Ricci flow equations is proven. Lastly, we discuss potential applications to Perelman's proposed implementation of Hamilton's program to prove Thurston's 3-manifold geometrization conjectures.Comment: 52 pages, 1 figur