Geoids in General Relativity: Geoid Quasilocal Frames

We develop, in the context of general relativity, the notion of a geoid -- a surface of constant "gravitational potential". In particular, we show how this idea naturally emerges as a specific choice of a previously proposed, more general and operationally useful construction called a quasilocal frame -- that is, a choice of a two-parameter family of timelike worldlines comprising the worldtube boundary of the history of a finite spatial volume. We study the geometric properties of these geoid quasilocal frames, and construct solutions for them in some simple spacetimes. We then compare these results -- focusing on the computationally tractable scenario of a non-rotating body with a quadrupole perturbation -- against their counterparts in Newtonian gravity (the setting for current applications of the geoid), and we compute general-relativistic corrections to some measurable geometric quantities.Comment: 24 pages, 8 figures; v2: reference added; v3: introduction clarified, reference adde

Entropy theorems in classical mechanics, general relativity, and the gravitational two-body problem

In classical Hamiltonian theories, entropy may be understood either as a statistical property of canonical systems, or as a mechanical property, that is, as a monotonic function of the phase space along trajectories. In classical mechanics, there are theorems which have been proposed for proving the non-existence of entropy in the latter sense. We explicate, clarify and extend the proofs of these theorems to some standard matter (scalar and electromagnetic) field theories in curved spacetime, and then we show why these proofs fail in general relativity; due to properties of the gravitational Hamiltonian and phase space measures, the second law of thermodynamics holds. As a concrete application, we focus on the consequences of these results for the gravitational two-body problem, and in particular, we prove the non-compactness of the phase space of perturbed Schwarzschild-Droste spacetimes. We thus identify the lack of recurring orbits in phase space as a distinct sign of dissipation and hence entropy production.Comment: 39 pages, 3 figures; v2: version to appear in Phys. Rev. D, references adde

Gravitational Waves from Preheating in M-flation

Matrix inflation, or M-flation, is a string theory motivated inflationary model with three scalar field matrices and gauge fields in the adjoint representation of the $\mathbf{U}(N)$ gauge group. One of these $3N^2$ scalars appears as the effective inflaton while the rest of the fields (scalar and gauge fields) can play the role of isocurvature fields during inflation and preheat fields afterwards. There is a region in parameter space and initial field values, "the hilltop region," where predictions of the model are quite compatible with the recent Planck data. We show that in this hilltop region, if the inflaton ends up in the supersymmetric vacuum, the model can have an embedded preheating mechanism. Couplings of the preheat modes are related to the inflaton self-couplings and therefore are known from the CMB data. Through lattice simulations performed using a symplectic integrator, we numerically compute the power spectra of gravitational waves produced during the preheating stage following M-flation. The preliminary numerical simulation of the spectrum from multi-preheat fields peaks in the GHz band with an amplitude $\Omega_{\mathrm{gw}}h^{2} \propto 10^{-16}$, suggesting that the model has concrete predictions for the ultra-high frequency gravity-wave probes. This signature could be used to distinguish the model from rival inflationary modelsComment: v1:27 pages and 7 figures; v2: typos corrected; v3: references added; v4: matched the JCAP versio

Energy of cosmological spacetimes and perturbations: a quasilocal approach

Quasilocal definitions of stress-energy-momentum -- that is, in the form of boundary densities (rather than local volume densities) -- have proven generally very useful in formulating and applying conservation laws in general relativity. In this paper, we present a detailed application of such definitions to cosmology, specifically using the Brown-York quasilocal stress-energy-momentum tensor for matter and gravity combined. We compute this tensor, focusing on the energy and its associated conservation law, for FLRW spacetimes with no pertubrations and with scalar cosmological perturbations. For unperturbed FLRW spacetimes, we emphasize the importance of the vacuum energy (for both flat and curved space), which is almost universally underappreciated (and usually "subtracted"), and discuss the quasilocal interpretation of the cosmological constant. For the perturbed FLRW spacetime, we show how our results recover or relate to the more typical effective local treatment of energy in cosmology, with a view towards better studying the issues of the cosmological constant and of cosmological back-reactions.Comment: v1: 28 pages, 3 figures; v2: 30 pages. References and comments added; v3: 35 pages. New subsection (IV A) adde

Quasilocal conservation laws in cosmology: a first look

Quasilocal definitions of stress-energy-momentum---that is, in the form of boundary densities (in lieu of local volume densities)---have proven generally very useful in formulating and applying conservation laws in general relativity. In this essay, we take a first basic look into applying these to cosmology, specifically using the Brown-York quasilocal stress-energy-momentum tensor for matter and gravity combined. We compute this tensor and present some simple results for a flat FLRW spacetime with a perfect fluid matter source.Comment: 8 pages, 3 figures. Essay awarded Honorable Mention in the Gravity Research Foundation 2020 Awards for Essays on Gravitatio

Compression methods for mechanical vibration signals: Application to the plane engines

International audienceA novel approach for the compression of mechanical vibration signals is presented in this paper. The method relies on a simple and flexible decomposition into a large number of subbands, implemented by an orthogonal transform. Compression is achieved by a uniform adaptive quantization of each subband. The method is tested on a large number of real vibration signals issued by plane engines. High compression ratios can be achieved, while keeping a good quality of the reconstructed signal. It is also shown that compression has little impact on the detection of some commonly encountered defects of the plane engine