Simple solutions to the Einstein Equations in spaces with unusual topology

We discuss simple vacuum solutions to the Einstein Equations in five dimensional space-times compactified in two different ways. In such spaces, one black hole phase and more then one black string phase may exist. Several old metrics are adapted to new background topologies to yield new solutions to the Einstein Equations. We then briefly talk about the angular momentum they may carry, the horizon topology and phase transitions that may occur.Comment: Published versions. Includes referee input. 10 pages, 3 figure

The Potential of Continuous, Local Atomic Clock Measurements for Earthquake Prediction and Volcanology

Modern optical atomic clocks along with the optical fiber technology currently being developed can measure the geoid, which is the equipotential surface that extends the mean sea level on continents, to a precision that competes with existing technology. In this proceeding, we point out that atomic clocks have the potential to not only map the sea level surface on continents, but also look at variations of the geoid as a function of time with unprecedented timing resolution. The local time series of the geoid has a plethora of applications. These include potential improvement in the predictions of earthquakes and volcanoes, and closer monitoring of ground uplift in areas where hydraulic fracturing is performed.Comment: 7 pages, one figure, proceeding for ICNFP 201

Numerical Simulations of Oscillating Soliton Stars: Excited States in Spherical Symmetry and Ground State Evolutions in 3D

Excited state soliton stars are studied numerically for the first time. The stability of spherically symmetric S-branch excited state oscillatons under radial perturbations is investigated using a 1D code. We find that these stars are inherently unstable either migrating to the ground state or collapsing to black holes. Higher excited state configurations are observed to cascade through intermediate excited states during their migration to the ground state. This is similar to excited state boson stars. Ground state oscillatons are then studied in full 3D numerical relativity. Finding the appropriate gauge condition for the dynamic oscillatons is much more challenging than in the case of boson stars. Different slicing conditions are explored, and a customized gauge condition that approximates polar slicing in spherical symmetry is implemented. Comparisons with 1D results and convergence tests are performed. The behavior of these stars under small axisymmetric perturbations is studied and gravitational waveforms are extracted. We find that the gravitational waves damp out on a short timescale, enabling us to obtain the complete waveform. This work is a starting point for the evolution of real scalar field systems with arbitrary symmetries.Comment: 12 pages, 11 figures, typos corrected, includes referee input, references corrected, published versio

A New Family of Light Beams and Mirror Shapes for Future LIGO Interferometers

Advanced LIGO's present baseline design uses arm cavities with Gaussian light beams supported by spherical mirrors. Because Gaussian beams have large intensity gradients in regions of high intensity, they average poorly over fluctuating bumps and valleys on the mirror surfaces, caused by random thermal fluctuations (thermoelastic noise). Flat-topped light beams (mesa beams) are being considered as an alternative because they average over the thermoelastic fluctuations much more effectively. However, the proposed mesa beams are supported by nearly flat mirrors, which experience a very serious tilt instability. In this paper we propose an alternative configuration in which mesa-shaped beams are supported by nearly concentric spheres, which experience only a weak tilt instability. The tilt instability is analyzed for these mirrors in a companion paper by Savov and Vyatchanin. We also propose a one-parameter family of light beams and mirrors in which, as the parameter alpha varies continuously from 0 to pi, the beams and supporting mirrors get deformed continuously from the nearly flat-mirrored mesa configuration ("FM") at alpha=0, to the nearly concentric-mirrored mesa configuration ("CM") at alpha=pi. The FM and CM configurations at the endpoints are close to optically unstable, and as alpha moves away from 0 or pi, the optical stability improves.Comment: Submitted to Physical Review D on 21 September 2004; RevTeX, 6 pages, 4 Figure

Atomic clocks as a tool to monitor vertical surface motion

Atomic clock technology is advancing rapidly, now reaching stabilities of $\Delta f/f \sim 10^{-18}$, which corresponds to resolving $1$ cm in equivalent geoid height over an integration timescale of about 7 hours. At this level of performance, ground-based atomic clock networks emerge as a tool for monitoring a variety of geophysical processes by directly measuring changes in the gravitational potential. Vertical changes of the clock's position due to magmatic, volcanic, post-seismic or tidal deformations can result in measurable variations in the clock tick rate. As an example, we discuss the geopotential change arising due to an inflating point source (Mogi model), and apply it to the Etna volcano. Its effect on an observer on the Earth's surface can be divided into two different terms: one purely due to uplift and one due to the redistribution of matter. Thus, with the centimetre-level precision of current clocks it is already possible to monitor volcanoes. The matter redistribution term is estimated to be 2-3 orders of magnitude smaller than the uplift term, and should be resolvable when clocks improve their stability to the sub-millimetre level. Additionally, clocks can be compared over distances of thousands of kilometres on a short-term basis (e.g. hourly). These clock networks will improve our ability to monitor periodic effects with long-wavelength like the solid Earth tide.Comment: 11 pages, 5 figures, accepted as express letter in the Geophysical Journal Internationa

Finite Mirror Effects in Advanced Interferometric Gravitational Wave Detectors

Thermal noise is expected to be the dominant source of noise in the most sensitive frequency band of second generation ground based gravitational wave detectors. Reshaping the beam to a flatter wider profile which probes more of the mirror surface reduces this noise. The "Mesa" beam shape has been proposed for this purpose and was subsequently generalized to a family of hyperboloidal beams with two parameters: twist angle alpha and beam width D. Varying alpha allows a continuous transition from the nearly-flat to the nearly-concentric Mesa beam configurations. We analytically prove that in the limit of infinite D hyperboloidal beams become Gaussians. The Advanced LIGO diffraction loss design constraint is 1 ppm per bounce. In the past the diffraction loss has often been calculated using the clipping approximation that, in general, underestimates the diffraction loss. We develop a code using pseudo-spectral methods to compute the diffraction loss directly from the propagator. We find that the diffraction loss is not a strictly monotonic function of beam width, but has local minima that occur due to finite mirror effects and leads to natural choices of D. For the Mesa beam a local minimum occurs at D = 10.67 cm and leads to a diffraction loss of 1.4 ppm. We find that if one requires a diffraction loss of strictly 1 ppm, the alpha = 0.91 pi hyperboloidal beam is optimal, leading to the coating thermal noise being lower by about 10% than for a Mesa beam while other types of thermal noise decrease as well. We then develop an iterative process that reconstructs the mirror to specifically account for finite mirror effects. This allows us to increase the D parameter and lower the coating noise by about 30% compared to the original Mesa configuration.Comment: 13 pages, 12 figures, 4 tables. Referee input included and typos fixed. Accepted by Phys. Rev.