36 research outputs found
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 gauge group. One of these 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
, 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