We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
To save content items to your account,
please confirm that you agree to abide by our usage policies.
If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.
Find out more about saving content to .
To save content items to your Kindle, first ensure [email protected]
is added to your Approved Personal Document E-mail List under your Personal Document Settings
on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part
of your Kindle email address below.
Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations.
‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi.
‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
In the chosen family of Einstein space-times one can give an ADM formulation of tetrad gravity and of its first-class constraints, so that fermions can be described in this framework. There are 16 configuration variables, 16 momenta, and 14 first-class constraints. Then one can define a new canonical basis adapted to 10 of the 14 constraints (not to the super-Hamiltonian and super-momentum ones) with a Shanmugadhasan canonical transformation. This allows identifying two pairs of canonical variables describing the tidal effects (the gravitational waves after linearization). However, they are not Dirac observables.
After a review of regular Lagrangians, their Hamiltonian formulation, and the first Noether theorem, there is the exposition of theory of singular Lagrangians and of Dirac–Bergmann theory of first- and second-class constraints. Also, the gauge transformations of field theory and general relativity are analyzed.
There is a description of the 3+1 approach allowing definition of global non-inertial frames in Minkowski space-time. One gives a time-like observer and a nice foliation with 3-spaces (namely a clock synchronization convention). Then one introduces Lorentz scalar radar 4-coordinates: the time is an increasing function of the proper time of the observer and the 3-coordinates live in the instantaneous 3-spaces. The connection of the radar coordinates with the standard ones defines the four embedding functions describing the foliation with 3-spaces. Then there is the definition of parametrized Minkowski theories for every kind of matter admitting a Lagrangian description. The new Lagrangian is a function of the matter and of the embedding, but is singular so that the embedding variables are gauge variables. As a consequence, the transition from a non-inertial frame to either an inertial or non-inertial frame is a gauge transformation not changing the physics but only the inertial forces.
After a description of inertial and non-inertial frames in the Galilei space-time of non-relativistic Newtonian physics with a discussion of inertial forces, there is metrological definition of what is time and space in special relativity. Then there is a review of the standard 1+3 approach for the “local” description of non-inertial frames and of its limitations.
The following family of Einstein space-times allows the use of the 3+1 approach: (1) globally hyperbolic (this allows the ADM Hamiltonian formulation); (2) asymptotically Minkowskian at spatial infinity (all the 3-spaces approach parallel space-like hyper-planes); (3) without super-translations (at spatial infinity there is the asymptotic ADM Poincaré algebra needed for particle physics). It turns out that the asymptotic ADM Poincaré 4-momentum is orthogonal to the asymptotic hyper-planes. Therefore, the 3+1 approach allows describing the Hamiltonian formulation of metric gravity and of its first-class constraints in the family of the non-inertial rest-frames.
In this chapter there is the description of fields and fluids in the rest-frame instant form of dynamics with the definition of their Wigner-covariant degrees of freedom inside the Wigner 3-spaces after the decoupling of the external center of mass. This is done for the Klein–Gordon, electromagnetic, Dirac, and Yang–Mills fields. In the case of the electromagnetic field there is the identification of the Wigner-covariant Dirac observables. This procedure can be applied also to Yang–Mills fields, but to get the Dirac observables one needs the knowledge of an explicit solution of the Gauss’s law constraints. Then there is the description of relativistic fluids in this framework. In particular a definition of the relativistic micro-canonical ensemble in the Wigner 3-spaces is given and it is shown which equations have to be solved to get a consistent relativistic statistical mechanics.
The post-Minkowskian limit of ADM tetrad gravity in the 3-orthogonal gauges of the non-inertial rest-frames is defined with particles and the electromagnetic field as matter. Then, the post-Newtonian expansion of the post-Minkowskian linearization is studied. For binaries, the results are compatible with the standard one in harmonic gauges. However, there is the new result that a non-local version of the inertial gauge variable York time may explain many of the experimental data giving rise to the existence of dark matter, which would be reduced to a relativistic inertial effect to be treated by means of relativistic celestial metrology.
Given an isolated system of either free or interacting particles and the associated realization of the ten conserved Poincaré generators its total conserved time-like 4-momentum defines its inertial rest-frame as the 3+1 splitting whose space-like 3-spaces (named Wigner 3-spaces) are orthogonal to it and whose inertial observer is the Fokker–Pryce 4-center of inertia. There is a discussion of the problem of the relativistic center of mass based on the fact that the 4-center functions “only” of the Poincaré generators of the isolated system are the following three non-local quantities: the non-canonical covariant Fokker–Pryce 4-center of inertia, the canonical non-covariant Newton–Wigner 4-center of mass and the non-canonical non-covariant Mőller 4-center of energy. At the Hamiltonian level one is able to express the canonical world-lines of the particles and their momenta in terms of the Jacobi variables of the external Newton–Wigner center of mass (a non-local non-covariant non-measurable quantity) and of Wigner-covariant relative 3-coordinates and 3-momenta inside the Wigner 3-spaces. This solves the problem of the elimination of relative times in relativistic bound states and to formulate a consistent Wigner-covariant relativistic quantum mechanics of point particles. The non-relativistic limit gives the Hamilton–Jacobi description of the system after the separation of Newtonian center of mass. Finally there is the definition of the non-inertial rest-frames whose 3-spaces are orthogonal to the total 4-momentum of the isolated system at spatial infinity.
Interpreting general relativity relies on a proper description of non-inertial frames and Dirac observables. This book describes global non-inertial frames in special and general relativity. The first part covers special relativity and Minkowski space time, before covering general relativity, globally hyperbolic Einstein space-time, and the application of the 3+1 splitting method to general relativity. The author uses a Hamiltonian description and the Dirac–Bergmann theory of constraints to show that the transition between one non-inertial frame and another is a gauge transformation, extra variables describing the frame are gauge variables, and the measureable matter quantities are gauge invariant Dirac observables. Point particles, fluids and fields are also discussed, including how to treat the problems of relative times in the description of relativistic bound states, and the problem of relativistic centre of mass. Providing a detailed description of mathematical methods, the book is perfect for theoretical physicists, researchers and students working in special and general relativity.
Through vertical resonances, bars can produce pseudo-bulges, within secular evolution. Bulges and pseudo-bulges have doubled their mass since z=1. The frequency of bulge-less galaxies at z=0 is difficult to explain, especially since clumpy galaxies at high z should create classical bulges in all galaxies. This issue is solved in modified gravity models. Bars and spirals in a galaxy disk, produce gravity torques that drive the gas to the center and fuel central star formation and nuclear activity. At 0.1-1kpc scale, observations of gravity torques show that only about one third of Seyfert galaxies experience molecular inflow and central fueling, while in most cases the gas is stalled in resonant rings. At 10-20pc scale, some galaxies have clearly revealed AGN fueling due to nuclear trailing spirals, influenced by the black hole potential. Thanks to ALMA, and angular resolution of up to 80mas, it is possible to reach the central black hole (BH) zone of influence, discover molecular tori, circum-nuclear disks misaligned with the galaxy, and the BH mass can be derived more directly from the kinematics.
We investigate the stellar and dynamical mass profiles of 32 brightest cluster galaxies (BCGs, MK = −25.7 to −27.8 mag) in massive clusters (0.05 < z < 0.30), and in particular the rising velocity dispersion profiles of 23 of these BCGs found in Loubser et al. (2018). We make comprehensive measurements of the Gauss-Hermite higher order velocity moments h3 and h4, and find positive central values for h4 for all the BCGs. We model the stellar and dynamical mass profiles of 25 of the BCGs using the Multi-Gaussian Expansion (MGE) and Jeans Anisotropic Method (JAM) for an axisymmetric case, deriving the stellar mass-to-light ratio (ϒ*DYN), and anisotropy (βz). We further explicitly add a dark matter halo mass component (MDM within r200) which we constrain from weak lensing results. In this proceedings, we summarise the study and show an example of the results.
Spatially resolved studies of galaxies in the high-redshift Universe have traditionally been reliant on data at rest-frame optical and UV wavelengths, which can be biased towards the least dust-obscured galaxies. For several years now, we have been able to resolve and probe the morphology of longer-wavelength emission from distant galaxies with ALMA, and a number of recent ALMA studies were presented at the IAU Symposium No. 352. These included our study of the resolved multi-wavelength emission of galaxies at z ∼ 2. As part of the SHiZELS collaboration, we are mapping the Hα emission line (from SINFONI/VLT), UV continuum (from HST), and the far-infrared (from ALMA) emission from a small sample of Hα-selected galaxies. In this proceedings paper, we showcase the high quality of our data, and the spectacular structures displayed by one of our most dusty sources. We also provide an overview of some highly complementary simulation-based work, using galaxies drawn from the FIRE-2 zoom-in cosmological hydrodynamical simulations. Using sophisticated radiative transfer techniques, we have derived predictions for the spatially-resolved emission of a sample of star-forming galaxies, from rest-frame far-ultraviolet to the far-infrared. For both observed and simulated galaxies, emission maps show striking differences with wavelength, with the same galaxy appearing clumpy and extended in the far-ultraviolet yet compact at far-infrared wavelengths.
The Galaxy Zoo project has provided quantitative visual morphologies for over a million galaxies, and has been part of a reinvigoration of interest in the morphologies of galaxies and what they reveal about galaxy evolution. Morphological information collected by GZ has shown itself to be a powerful tool for studying galaxy evolution, and GZ continues to collect classifications - currently serving imaging from DECaLS in its main site, and running a variety of related projects hosted by the Zooniverse; the citizen science platform which came out of the early success of GZ. I highlight some of the results from the last twelve years, with a particular emphasis on linking morphology and dynamics, look forward to future projects in the GZ family, and provide a quick start guide for how you can easily make use of citizen science techniques to analysis your own large and complex data sets.
I will review recent developments in the modeling of high-redshift galaxy spectra, focusing in particular on the rest-frame ultraviolet and optical emission from young stellar populations and the interstellar medium.
The first massive galaxies (z ∼ 6) have (1) very high energy density due to their small diameters and extreme luminosities in young stars and (2) interstellar dust relatively deficient in carbon compared with silicates. Both of these attributes should raise their interstellar dust temperatures compared with lower redshift galaxies. Not only is this temperature trend observed, but the high-z spectral energy distributions (SEDs) are very broad due to very warm dust. As a result total infrared luminosities – and star formation rates – at the highest redshifts estimated by fitting blackbodies to submm- and mm-wave observations can be low by a factor of ∼2.
Theoretical work suggests that AGNs play an important role in quenching star formation in massive galaxies. In addition to molecular outflows observed in the local universe, emission from very high-J CO rotational transitions have been a key piece of evidence for AGN directly affecting the molecular gas reservoirs that fuel star formation. However, very few observations exist of CO rotational lines past the peak of the CO spectral line energy distribution (SLED) for galaxies in the early universe. Here we present new ALMA observations of high-J CO rotational lines (from CO(5–4) to CO(16–15)) in six z > 2 IR-bright systems, including several sources not known to contain a strong AGN for comparison. We detect significant amounts of high-excitation CO emission that suggests the presence of energy sources beyond UV-heating.
We observed the 2 July 2019 total solar eclipse with a variety of imaging and spectroscopic instruments recording from three sites in mainland Chile: on the centerline at La Higuera, from the Cerro Tololo Inter-American Observatory, and from La Serena, as well as from a chartered flight at peak totality in mid-Pacific. Our spectroscopy monitored Fe X, Fe XIV, and Ar X lines, and we imaged Ar X with a Lyot filter adjusted from its original H-alpha bandpass. Our composite imaging has been compared with predictions based on modeling using magnetic-field measurements from the pre-eclipse month. Our time-differenced sites will be used to measure motions in coronal streamers.
The Atacama Large Millimeter/submillimeter Array offers regular observations of our Sun since 2016. After an extended period of further developing and optimizing the post-processing procedures, first scientific results are now produced. While the first observing cycles mostly provided mosaics and time series of continuum brightness temperature maps with a cadence of 1-2s, additional receiver bands and polarization capabilities will be offered in the future. Currently, polarization capabilities are offered for selected receiver bands but not yet for solar observing. An overview of the recent development, first scientific results and potential of solar magnetic field measurements with ALMA will be presented.
We discuss selected aspects regarding the magnetic field evolution of solar-type stars. Most of the stars with activity cycles are in the range where the normalized chromospheric Calcium emission increases linearly with the inverse Rossby number. For Rossby numbers below about a quarter of the solar value, the activity saturates and no cycles have been found. For Rossby numbers above the solar value, again no activity cycles have been found, but now the activity goes up again for a major fraction of the stars. Rapidly rotating stars show nonaxisymmetric large-scale magnetic fields, but there is disagreement between models and observations regarding the actual value of the Rossby number where this happens. We also discuss the prospects of detecting the sign of magnetic helicity using various linear polarization techniques both at the stellar surface using the parity-odd contribution to linear polarization and above the surface using Faraday rotation.