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Geodesics are introduced and the geodesic equation analysed for the geometries introduced in chapter 2, using variation principles of classical mechanics. Geodesic motino on a sphere is described as well as the Coriolis effect and the Sagnac effect. Newtonian gravity is derived as the non-relativistic limit of geodesic motion in space-time. Geodesics in an expanding universe and heat death is described. Geodesics in Schwarzschild space-time are treated in detail: the precession of the perihelion of Mercury; the bending of light by the Sun; Shapiro time delay; black holes and the event horizon. Gravitational waves and gravitational lensing are also covered.
Newton's Universal Law of Gravitation is compared and contrasted to Coulomb’s Law and the differences highlighted. Tides are discussed, and the Equivalence Principle and how it leads to the notion of curved space-times is explained.
Investigating rare and new objects have always been an important direction in astronomy. Cataclysmic variables (CVs) are ideal and natural celestial bodies for studying the accretion process of semi-detached binaries with accretion processes. However, the sample size of CVs must increase because a lager gap exists between the observational and the theoretical expanding CVs. Astronomy has entered the big data era and can provide massive images containing CV candidates. CVs as a type of faint celestial objects, are highly challenging to be identified directly from images using automatic manners. Deep learning has rapidly developed in intelligent image processing and has been widely applied in some astronomical fields with excellent detection results. YOLOX, as the latest YOLO framework, is advantageous in detecting small and dark targets. This work proposes an improved YOLOX-based framework according to the characteristics of CVs and Sloan Digital Sky Survey (SDSS) photometric images to train and verify the model to realise CV detection. We use the Convolutional Block Attention Module to increase the number of output features with the feature extraction network and adjust the feature fusion network to obtain fused features. Accordingly, the loss function is modified. Experimental results demonstrate that the improved model produces satisfactory results, with average accuracy (mean average Precision at 0.5) of 92.0%, Precision of 92.9%, Recall of 94.3%, and $F1-score$ of 93.6% on the test set. The proposed method can efficiently achieve the identification of CVs in test samples and search for CV candidates in unlabeled images. The image data vastly outnumber the spectra in the SDSS-released data. With supplementary follow-up observations or spectra, the proposed model can help astronomers in seeking and detecting CVs in a new manner to ensure that a more extensive CV catalog can be built. The proposed model may also be applied to the detection of other kinds of celestial objects.
Einsteins field equations are derived and discussed. It is argued that the Einstein tensor is proportional to the energy-momentum tensor and the constant of proportionality is derived by demanding that Newton’s Universal Law of gravitation be recovered in the non-relativistic limit. The modification of Einstein's equations when a cosmological constant is introduced is also presented.
In this chapter some empty space solutions of Einstein's are presented. The form of the Ricci tensor for a general spherical spherically symmetric static metric is given, from which the Schwarzschild solution is derived. Gravitational waves are presented as a solution of Einstein’s equations in empty space in a linear approximation.
The mathematics required to analyse higher dimensional curved spaces and space-times is developed in this chapter. General coordinate transformations, tangent spaces, vectors and tensors are described. Lie derivatives and covariant derivatives are motivated and defined. The concepts of parallel transport and a connection is introduced and the relation between the Levi-Civita connection and geodesics is elucidated. Christoffel symbols the Riemann tensor are defined as well as the Ricci tensor, the Ricci scalar and the Einstein tensor, and their algebraic and differential properties are described (though technical details of the derivationa of the Rimeann tensor are let to an appendix).
The concept to the metric is introduced. Various geometries, both flat and curved, are described including Euclidean space; Minkowski space-time; spheres; hyperbolic planes and expanding space-times. Lorentz transformations and relativistic time dilation in flat space-time is discussed as well as gravitational red-shift and the Global Positioning System. Hubble expansion and the cosmological red-shift are also explained.
Gamma-ray bursts (GRBs) and double neutron star merger gravitational-wave events are followed by afterglows that shine from X-rays to radio, and these broadband transients are generally interpreted using analytical models. Such models are relatively fast to execute, and thus easily allow estimates of the energy and geometry parameters of the blast wave, through many trial-and-error model calculations. One problem, however, is that such analytical models do not capture the underlying physical processes as well as more realistic relativistic numerical hydrodynamic (RHD) simulations do. Ideally, those simulations are used for parameter estimation instead, but their computational cost makes this intractable. To this end, we present DeepGlow, a highly efficient neural network architecture trained to emulate a computationally costly RHD-based model of GRB afterglows, to within a few percent accuracy. As a first scientific application, we compare both the emulator and a different analytical model calibrated to RHD simulations, to estimate the parameters of a broadband GRB afterglow. We find consistent results between these two models, and also give further evidence for a stellar wind progenitor environment around this GRB source. DeepGlow fuses simulations that are otherwise too complex to execute over all parameters, to real broadband data of current and future GRB afterglows.
The International VLBI Service for Geodesy and Astrometry (IVS) regularly provides high-quality data to produce Earth Orientation Parameters (EOP), and for the maintenance and realisation of the International Terrestrial and Celestial Reference Frames, ITRF and ICRF. The first iteration of the celestial reference frame (CRF) at radio wavelengths, the ICRF1, was adopted by the International Astronomical Union (IAU) in 1997 to replace the FK5 optical frame. Soon after, the IVS began official operations and in 2009 there was a significant increase in data sufficient to warrant a second iteration of the CRF, ICRF2. The most recent ICRF3, was adopted by the IAU in 2018. However, due to the geographic distribution of observing stations being concentrated in the Northern hemisphere, CRFs are generally weaker in the South due to there being fewer Southern Hemisphere observations. To increase the Southern Hemisphere observations, and the density, precision of the sources, a series of deep South observing sessions was initiated in 1995. This initiative in 2004 became the IVS Celestial Reference Frame Deep South (IVS-CRDS) observing programme. This paper covers the evolution of the CRDS observing programme for the period 1995–2021, details the data products and results, and concludes with a summary of upcoming improvements to this ongoing project.