arXiv subjects

Janna Levin

Publications and source records attributed to Janna Levin.

At least 55 records · Page 3Linked to original sources

arXiv2003

A Test of a Test for Chaos

A simple new binary test for chaos has been proposed by Gottwald and Melbourne. We apply this test successfully to the Henon-Heiles and Lorenz systems, demonstrating its applicability to conservative systems, as well as dissipative systems. The binary test is effective for highly chaotic Hamiltonian systems and orbits on a strange attractor and is particularly useful as a marker of the transition from regularity to chaos. However, we find it is not able to detect more subtle instances of transient chaos.

nlin.CD↗

arXiv2002

Comment on "Ruling out chaos in compact binary systems"

In a recent Letter, Schnittman and Rasio argue that they have ruled out chaos in compact binary systems since they find no positive Lyapunov exponents. In stark constrast, we find that the chaos discovered in the original paper under discussion, J.Levin, PRL, 84 3515 (2000), is confirmed by the presence of positive Lyapunov exponents.

gr-qc↗

arXiv2002

Gravitational Waves from Spinning Compact Binaries

Binary systems of rapidly spinning compact objects, such as black holes or neutron stars, are prime targets for gravitational wave astronomers. The dynamics of these systems can be very complicated due to spin-orbit and spin-spin couplings. Contradictory results have been presented as to the nature of the dynamics. Here we confirm that the dynamics - as described by the second post-Newtonian approximation to general relativity - is chaotic, despite claims to the contrary. When dissipation due to higher order radiation reaction terms are included, the chaos is dampened. However, the inspiral-to-plunge transition that occurs toward the end of the orbital evolution does retain an imprint of the chaotic behaviour.

gr-qc↗

arXiv2002

The fate of chaotic binaries

A typical stellar mass black hole with a lighter companion is shown to succumb to a chaotic precession of the orbital plane. As a result, the optimal candidates for the direct detection of gravitational waves by Earth based interferometers can show irregular modulation of the waveform during the last orbits before plunge. The precession and the subsequent modulation of the gravitational radiation depends on the mass ratio, eccentricity, and spins. The smaller the mass of the companion, the more prominent the effect of the precession. The most important parameters are the spin magnitudes and misalignments. If the spins are small and nearly aligned with the orbital angular momentum, then there will be no chaotic precession while increasing both the spin magnitudes and misalignments increases the erratic precession. A large eccentricity can be induced by large, misaligned spins but does not seem to be required for chaos. An irregular precession of the orbital plane will generate irregularities in the gravitational wave frequency but may have a lesser effect on the total number of cycles observed.

gr-qc↗

arXiv2001

Topology and the Cosmic Microwave Background

Nature abhors an infinity. The limits of general relativity are often signaled by infinities: infinite curvature as in the center of a black hole, the infinite energy of the singular big bang. We might be inclined to add an infinite universe to the list of intolerable infinities. Theories that move beyond general relativity naturally treat space as finite. In this review we discuss the mathematics of finite spaces and our aspirations to observe the finite extent of the universe in the cosmic background radiation.

gr-qc↗

arXiv2001

The twin paradox in compact spaces

Twins travelling at constant relative velocity will each see the other's time dilate leading to the apparent paradox that each twin believes the other ages more slowly. In a finite space, the twins can both be on inertial, periodic orbits so that they have the opportunity to compare their ages when their paths cross. As we show, they will agree on their respective ages and avoid the paradox. The resolution relies on the selection of a preferred frame singled out by the topology of the space.

gr-qc↗

arXiv2000

Gravity Waves, Chaos, and Spinning Compact Binaries

Spinning compact binaries are shown to be chaotic in the Post-Newtonian expansion of the two body system. Chaos by definition is the extreme sensitivity to initial conditions and a consequent inability to predict the outcome of the evolution. As a result, the spinning pair will have unpredictable gravitational waveforms during coalescence. This poses a challenge to future gravity wave observatories which rely on a match between the data and a theoretical template.

gr-qc↗

arXiv1999

Gravity waves from relativistic binaries

The stability of binary orbits can significantly shape the gravity wave signal which future Earth-based interferometers hope to detect. The inner most stable circular orbit has been of interest as it marks the transition from the late inspiral to final plunge. We consider purely relativistic orbits beyond the circular assumption. Homoclinic orbits are of particular importance to the question of stability as they lie on the boundary between dynamical stability and instability. We identify these, estimate their rate of energy loss to gravity waves, and compute their gravitational waveforms.

gr-qc↗

arXiv1999

Fractals and Scars on a Compact Octagon

A finite universe naturally supports chaotic classical motion. An ordered fractal emerges from the chaotic dynamics which we characterize in full for a compact 2-dimensional octagon. In the classical to quantum transition, the underlying fractal can persist in the form of scars, ridges of enhanced amplitude in the semiclassical wave function. Although the scarring is weak on the octagon, we suggest possible subtle implications of fractals and scars in a finite universe.

gr-qc↗

arXiv1999

Chaos may make black holes bright

Black holes cannot be seen directly since they absorb light and emit none, the very quality which earned them their name. We suggest that black holes may be seen indirectly through a chaotic defocusing of light. A black hole can capture light from a luminous companion in chaotic orbits before scattering the light in random directions. To a distant observer, the black hole would appear to light up. If the companion were a bright radio pulsar, this estimate suggests the black hole echo could be detectible.

astro-ph↗

arXiv1999

Chaos and order in a finite universe

All inhabitants of this universe, from galaxies to people, are finite. Yet the universe itself is often assumed to be infinite. If instead the universe is topologically finite, then light and matter can take chaotic paths around the compact geometry. Chaos may lead to ordered features in the distribution of matter throughout space.

astro-ph↗

arXiv1999

Topological Pattern Formation

We provide an informal discussion of pattern formation in a finite universe. The global size and shape of the universe is revealed in the pattern of hot and cold spots in the cosmic microwave background. Topological pattern formation can be used to reconstruct the geometry of space, just as gravitational lensing is used to reconstruct the geometry of a lens.

astro-ph↗

arXiv1998

Temperature Correlations in a Finite Universe

We study the effect of a finite topology on the temperature correlations of the cosmic microwave background in a flat universe. Analytic expressions for the angular power spectrum are given for all possible finite flat models. We examine the angular correlation function itself, pointing out visible and discrete features that arise from topology. While observations of the power spectrum on large angular scales can be used to place bounds on the minimum topology length, cosmic variance generally restricts us from differentiating one flat topology from another. Schemes that acknowledge anisotropic structures, such as searches for ghosts, circles or geometric patterns, will be needed to further probe topology.

astro-ph↗

arXiv1998

How the Universe got its Spots

The universe displays a three-dimensional pattern of hot and cold spots in the radiation remnant from the big bang. The global geometry of the universe can be revealed in the spatial distribution of these spots. In a topologically compact universe, distinctive patterns are especially prominent in spatial correlations of the radiation temperature. Whereas these patterns are usually washed out in statistical averages, we propose a scheme which uses the universe's spots to observe global geometry in a manner analogous to the use of multiple images of a gravitationally lensed quasar to study the geometry of the lens. To demonstrate how the geometry of space forms patterns in observations of the microwave sky, we develop a simple real-space approximation to estimate temperature correlations for any set of cosmological parameters and any global geometry. We present correlated spheres which clearly show geometric pattern formation for compact flat universes as well as for the compact negatively curved space introduced by Weeks and another discovered by Best. These examples illustrate how future satellite-based observations of the microwave background can determine the full geometry of the universe.

astro-ph↗

arXiv1998

Curing singularities: From the big bang to black holes

Singular spacetimes are a natural prediction of Einstein's theory. Most memorable are the singular centers of black holes and the big bang. However, dilatonic extensions of Einstein's theory can support nonsingular spacetimes. The cosmological singularities can be avoided by dilaton driven inflation. Furthermore, a nonsingular black hole can be constructed in two dimensions.

gr-qc↗

arXiv1998

The topology of the universe: the biggest manifold of them all

Clues as to the geometry of the universe are encoded in the cosmic background radiation. Hot and cold spots in the primordial radiation may be randomly distributed in an infinite universe while in a universe with compact topology distinctive patterns can be generated. With improved vision, we could actually see if the universe is wrapped into a hexagonal prism or a hyperbolic horn. We discuss the search for such geometric patterns in predictive maps of the microwave sky.

gr-qc↗

arXiv1998

Is The Universe Infinite Or Is It Just Really Big?

The global geometry of the universe is in principle as observable an attribute as local curvature. Previous studies have established that if the universe is wrapped into a flat hypertorus, the simplest compact space, then the fundamental domain must be at least 0.4 times the diameter of the observable universe. Despite a standard lore that the other five compact, orientable flat spaces are more weakly constrained, we find the same bound holds for all. Our analysis provides the first limits on compact cosmologies built from the identifications of hexagonal prisms.

astro-ph↗

arXiv1997

Chaos in the Einstein-Yang-Mills Equations

Yang-Mills color fields evolve chaotically in an anisotropically expanding universe. The chaotic behaviour differs from that found in anisotropic Mixmaster universes. The universe isotropizes at late times, approaching the mean expansion rate of a radiation-dominated universe. However, small chaotic oscillations of the shear and color stresses continue indefinitely. An invariant, coordinate-independent characterisation of the chaos is provided by means of fractal basin boundaries.

gr-qc↗