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Wepresent the theory as a number of postulates about a mathematical model for spacetime.
In §3.1 we introduce the mathematical model and in §3.2 the first two postulates, local causality and local energy conservation. These postulates are common to both special and general relativity, and thus may be regarded as tested by the many experiments that have been performed to check the former. In §3.3 we derive the equations of the matter fields and obtain the energy–momentum tensor from a Lagrangian.
The third postulate, the field equations, is given in §3.4. This is not so well established experimentally as the first two postulates, but we shall see that any alternative equations would seem to have one or more undesirable properties, or else require the existence of extra fields which have not yet been detected experimentally.
The mathematical model we shall use for spacetime, i.e. the collection of all events, is a pair (ℳ, g) where ℳ is a connected four-dimensional Hausdorff C∞ manifold and g is a Lorentz metric (i.e. a metric of signature + 2) on ℳ.
We present multi-wavelength data and analysis, including new FUV AstroSat/UVIT observations of the spiral galaxy UGC 10420 ($z=0.032$), a member of the cluster Abell 2199. UGC 10420 is present on the edge of the X-ray emitting region of the cluster at a distance of ${\sim} 680$ kpc from the centre. The far-ultraviolet (FUV) data obtained by the AstroSat mission show intense knots of star formation on the leading edge of the galaxy, accompanied by a tail of the same on the diametrically opposite side. Our analysis shows that the images of the galaxy disc in the optical and mid-infrared are much smaller in size than that in the FUV. While the broadband optical colours of UGC 10420 are typical of a post-starburst galaxy, the star formation rate (SFR) derived from a UV-to-IR spectral energy distribution is at least a factor of nine higher than that expected for a star-forming field galaxy of similar mass at its redshift. A careful removal of the contribution of the diffuse intracluster gas shows that the significant diffuse X-ray emission associated with the interstellar medium of UGC 10420 has a temperature, $T_X = 0.24^{+0.09}_{-0.06}$ keV (0.4–2.0 keV) and luminosity, $L_X = 1.8\pm{0.9}\times 10^{40}$ erg s$^{-1}$, which are typical of the X-ray emission from late-type spiral galaxies. Two symmetrically placed X-ray hot spots are observed on either sides of an X-ray weak nucleus.
Our analysis favours a scenario where the interaction of a galaxy with the hot intracluster medium of the cluster, perturbs the gas in the galaxy causing starburst in the leading edge of the disc. On the other hand, the turbulence thus developed may also push some of the gas out of the disc. Interactions between the gas ejected from the galaxy and the intracluster medium can then locally trigger star formation in the wake of the galaxy experiencing ram-pressure stripping. Our data however does not rule out the possibility of a flyby encounter with a neighbouring galaxy, although no relevant candidates are observed in the vicinity of UGC 10420.
Pulsar wind nebulae (PWN) are fascinating systems and archetypal sources for high-energy astrophysics in general. Due to their vicinity, brightness, to the fact that they shine at multi-wavelengths, and especially to their long-living emission at gamma rays, modelling their properties is particularly important for the correct interpretation of the visible Galaxy. A complication in this respect is the variety of properties and morphologies they show at different ages. Here, we discuss the differences among the evolutionary phases of PWN, how they have been modeled in the past and what progresses have been recently made. We approach the discussion from a phenomenological, theoretical (especially numerical) and observational point of view, with particular attention to the most recent results and open questions about the physics of such intriguing sources.
Active galactic nuclei (AGN) have been observed as far as redshift $z \sim 7$. They are crucial in investigating the early Universe as well as the growth of supermassive black holes at their centres. Radio-loud AGN with their jets seen at a small viewing angle are called blazars and show relativistic boosting of their emission. Thus, their apparently brighter jets are easier to detect in the high-redshift Universe. DES J014132.4–542749.9 is a radio-luminous but X-ray weak blazar candidate at $z = 5$. We conducted high-resolution radio interferometric observations of this source with the Australian Long Baseline Array at $1.7$ and $8.5$ GHz. A single, compact radio-emitting feature was detected at both frequencies with a flat radio spectrum. We derived the milliarcsecond-level accurate position of the object. The frequency dependence of its brightness temperature is similar to that of blazar sources observed at lower redshifts. Based on our observations, we can confirm its blazar nature. We compared its radio properties with those of two other similarly X-ray-weak and radio-bright AGN, and found that they show very different relativistic boosting characteristics.