Monthly Archives: July 2018

Finding order in a sea of chaos

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By Alejandro Cárdenas-Avendaño, Andrés F. Gutiérrez, Leonardo A. Pachón, and Nicolás Yunes

Hunting for constants of the motion in dynamical systems is hard. How can one find a combination of dynamical variables that remains unchanged during a complicated evolution? While it is true that answering this question is not trivial, symmetries can sometimes come to the rescue. The motion of test particles around a spinning (Kerr) black hole, for example, has a conserved mass, energy and angular momentum. Nevertheless, simple symmetries can only go so far. Given the complexity of the radial and polar sector of Kerr geodesics, it came as a complete surprise when Carter found, in 1968, a fourth constant of the motion, which was later found to be associated with the existence of a Killing tensor by Walker and Penrose. This fourth constant then allowed the complete separability of the geodesic equations, thus proving the integrability of the system, and as a consequence, that the motion of a test particle around a Kerr black hole is not chaotic in General Relativity (GR).

 

● Alejandro Cárdenas-Avendaño is a graduate student at Montana State University and holds a junior researcher position at Fundación Universitaria Konrad Lorenz.
● Andrés F. Gutierrez is a graduate student at Universidad de Antioquia.
● Leonardo A. Pachón is an associate professor at Universidad de Antioquia.
● Nicolás Yunes is an associate professor at Montana State University, and co-founder of the eXtreme Gravity Institute.

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Holography inside out: from 3D gravity to 2D statistical models

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By Bianca Dittrich, Christophe Goeller, Etera R. Livine, and Aldo Riello

Despite many years of research, quantum gravity remains a challenge. One of the reasons is that the many tools developed for perturbative quantum field theory are, in general, not applicable to quantum gravity. On the other hand, non-perturbative approaches have a difficult time in finding and extracting computable observables. The foremost problem here is a lack of diffeomorphism-invariant observables.

Aldo Riello ) is a senior postdoctoral fellow at Perimeter Institute.
Christophe Goeller is a PhD student at ENS Lyon and Perimeter Institute.
Etera Livine is a senior researcher at ENS Lyon.
Bianca Dittrich is a senior faculty at Perimeter Institute. Together they are the ABCE team, still looking for the right D to go deeper into holographic Duals.

The situation can be improved very much by considering space-time regions with boundaries. This is also physically motivated, since one would like to be able to describe the physics of a given bounded region in a quasi-local way, that is without requiring a detailed description of the rest of the space-time outside. The key point is that the boundary can be used as an anchor, allowing to define observables in relation to this boundary. Then we can consider different boundary conditions, which translates at the quantum level into a rich zoo of boundary wave-functions. These boundary states can correspond to semi-classical boundary geometries or superpositions of those. The states can also describe asymptotic flat boundaries, thus allowing us to compare with perturbative approaches. In this context, holography in quantum gravity aims to determine how much of the bulk geometry can be reconstructed from the data encoded in the boundary state.

Bianca_1_2018

The boundary wave function Ψ are described by  dual theories defined on the boundary of the solid torus. These 2D boundary theories, obtained by integrating over all the bulk degrees of freedom of the geometry, encode the full 3D quantum gravity partition function.

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Fast Self-forced Inspirals

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by Niels Warburton and Maarten van de Meent

LISA will fly. Since being given the green light by the European Space Agency a year ago, the scientific consortium around the Laser Interferometer Space Antenna (LISA) has been reorganising as it gears up to meet the challenge of building and operating a gravitational wave detector in space. This process has led to a renewed focus on the waveform templates that will be needed to extract the signals and estimate source parameters.

One of the key sources for LISA are extreme mass-ratio inspirals (EMRIs). In these binaries a stellar mass compact object (such as a black hole or neutron star) spirals into a massive black hole. Emitting hundreds of thousands of gravitational wave cycles in the millihertz band, LISA will detect individual EMRIs for months or even years. The low instantaneous signal-to-noise-ratio of the gravitational waves necessitates accurate waveform templates that can be used with matched filtering techniques to extract the signal from the detectors data stream. Coherently matching a signal over months or even years requires going beyond leading-order, flux-based black hole perturbation models and calculating the so-called ‘self-force’ that drives the inspiral [1]. Roughly, one can think of this self-force as arising from the smaller orbiting body interacting with its own perturbation to the metric of the massive black hole. To this end the recent “LISA Data Analysis Work Packages” document defined a number of source-modelling challenges that must be overcome before LISA flies [2]. One of these requires the community to:

“Design and implement a framework for incorporating self-force-based numerical calculations, as they become available, into a flexible semi-analytical Kludge model that enables fast production of waveform templates”

Our work [3], “Fast Self-forced Inspirals”, is a response to this challenge. Continue reading →