A mathematical introduction to Kerr black holes

Lo scopo della tesi è descrivere i buchi neri di Kerr. Dopo aver introdotto tutti gli strumenti matematici necessari quali tensori, vettori di Killing e geodetiche, enunceremo la metrica di Kerr, il teorema no-hair e il frame-dragging. In seguito, a partire dalla metrica di Kerr, calcoleremo e descriveremo le ergosfere, gli orizzonti degli eventi e il moto dei fotoni nel piano equatoriale.

Black holes in the Milky Way Galaxy

Extremely strong observational evidence has recently been found for the presence of black holes orbiting a few relatively normal stars in our Milky Way Galaxy and also at the centers of some galaxies. The former generally have masses of 4–16 times the mass of the sun, whereas the latter are “supermassive black holes” with millions to billions of solar masses. The evidence for a supermassive black hole in the center of our galaxy is especially strong.

The nature of LINER galaxies: Ubiquitous hot old stars and rare accreting black holes

Context. Galaxies, which often contain ionised gas, sometimes also exhibit a so-called low-ionisation nuclear emission line region (LINER). For 30 years, this was attributed to a central mass-accreting supermassive black hole (more commonly known as active galactic nucleus, AGN) of low luminosity, making LINER galaxies the largest AGN sub-population, which dominate in numbers over higher luminosity Seyfert galaxies and quasars. This, however, poses a serious problem. While the inferred energy balance is plausible, many LINERs clearly do not contain any other independent signatures of an AGN. Aims. Using integral field spectroscopic data from the CALIFA survey, we compare the observed radial surface brightness profiles with what is expected from illumination by an AGN. Methods. Essential for this analysis is a proper extraction of emission lines, especially weak lines, such as Balmer H beta lines, which are superposed on an absorption trough. To accomplish this, we use the GANDALF code, which simultaneously fits the underlying stellar continuum and emission lines. Results. For 48 galaxies with LINER-like emission, we show that the radial emission-line surface brightness profiles are inconsistent with ionisation by a central point-source and hence cannot be due to an AGN alone. Conclusions. The most probable explanation for the excess LINER-like emission is ionisation by evolved stars during the short but very hot and energetic phase known as post-AGB. This leads us to an entirely new interpretation. Post-AGB stars are ubiquitous and their ionising effect should be potentially observable in every galaxy with the gas present and with stars older than ~1 Gyr unless a stronger radiation field from young hot stars or an AGN outshines them. This means that galaxies with LINER-like emission are not a class defined by a property but rather by the absence of a property. It also explains why LINER emission is observed mostly in massive galaxies with old stars and little star formation.

Heavily obscured AGN: an ideal laboratory to study the early co-evolution of galaxies and black holes

Obscured AGN are a crucial ingredient to understand the full growth history of super massive black holes and the coevolution with their host galaxies, since they constitute the bulk of the BH accretion. In the distant Universe, many of them are hosted by submillimeter galaxies (SMGs), characterized by a high production of stars and a very fast consumption of gas. Therefore, the analysis of this class of objects is fundamental to investigate the role of the ISM in the early coevolution of galaxies and black holes. We present a multiwavelength study of a sample of six obscured X-ray selected AGN at z>2.5 in the CDF-S, detected in the far-IR/submm bands. We performed the X-ray spectral analysis based on the 7Ms Chandra dataset, which provides the best X-ray spectral information currently available for distant AGN. We were able to place constraints on the obscuring column densities and the intrinsic luminosities of our targets. Moreover, we built up the UV to FIR spectral energy distributions (SEDs) by combining the broad-band photometry from CANDELS and the Herschel catalogs, and analyzed them by means of an SED decomposition technique. Therefore, we derived important physical parameters of both the host galaxy and the AGN. In addition, we obtained, through an empirical calibration, the gas mass in the host galaxy and assessed the galaxy sizes in order to estimate the column density associated with the host ISM. The comparison of the ISM column densities with the values measured from the X-ray spectral analysis pointed out that the contribution of the host ISM to the obscuration of the AGN emission can be substantial, ranging from ~10% up to ~100% of the value derived from the X-ray spectra. The absorption may occur at different physical scales in these sources and, in particular, the medium in the host galaxy is an ingredient that should be taken into account, since it may have a relevant role in driving the early co-evolution of galaxies with their black holes.

The host galaxies and black holes of typical z~0.5-1.4 AGNs

We study the stellar and star formation properties of the host galaxies of 58 X-ray-selected AGNs in the GOODS portion of the Chandra Deep Field South (CDF-S) region at z ~ 0.5-1.4. The AGNs are selected such that their rest-frame UV to near-infrared spectral energy distributions (SEDs) are dominated by stellar emission; i.e., they show a prominent 1.6 μm bump, thus minimizing the AGN emission "contamination." This AGN population comprises approximately 50% of the X-ray-selected AGNs at these redshifts. We find that AGNs reside in the most massive galaxies at the redshifts probed here. Their characteristic stellar masses (M_* ~ 7.8 × 10^10 and M_* ~ 1.2 × 10^11 M_☉ at median redshifts of 0.67 and 1.07, respectively) appear to be representative of the X-ray-selected AGN population at these redshifts and are intermediate between those of local type 2 AGNs and high-redshift (z ~ 2) AGNs. The inferred black hole masses (M_BH ~ 2 × 10^8 M_☉) of typical AGNs are similar to those of optically identified quasars at similar redshifts. Since the AGNs in our sample are much less luminous (L_2–10 keV < 10^44 erg s^−1) than quasars, typical AGNs have low Eddington ratios (η ~ 0.01-0.001). This suggests that, at least at intermediate redshifts, the cosmic AGN "downsizing" is due to both a decrease in the characteristic stellar mass of typical host galaxies and less efficient accretion. Finally, there is no strong evidence in AGN host galaxies for either highly suppressed star formation (expected if AGNs played a role in quenching star formation) or elevated star formation when compared to mass-selected (i.e., IRAC-selected) galaxies of similar stellar masses and redshifts.

State sum models for quantum gravity

This paper reviews the construction of quantum field theory on a 4-dimensional spacetime by combinatorial methods, and discusses the recent developments in the direction of a combinatorial construction of quantum gravity.

Geometrical measurements in three-dimensional quantum gravity

A set of observables is described for the topological quantum field theory which describes quantum gravity in three space-time dimensions with positive signature and positive cosmological constant. The simplest examples measure the distances between points, giving spectra and probabilities which have a geometrical interpretation. The observables are related to the evaluation of relativistic spin networks by a Fourier transform.

Effects of spin on high-energy radiation from accreting black holes

Observations of jets in X-ray binaries show a correlation between radio power and black hole spin. This correlation, if confirmed, points toward the idea that relativistic jets may be powered by the rotational energy of black holes. In order to examine this further, we perform general relativistic radiative transport calculations on magnetically arrested accretion flows, which are known to produce powerful jets via the Blandfordâ Znajek (BZ) mechanism. We find that the X-ray and γ-ray emission strongly depend on spin and inclination angle. Surprisingly, the high-energy power does not show the same dependence on spin as the BZ jet power, but instead can be understood as a redshift effect. In particular, photons observed perpendicular to the spin axis suffer little net redshift until originating from close to the horizon. Such observers see deeper into the hot, dense, highly magnetized inner disk region. This effect is largest for rapidly rotating black holes due to a combination of frame dragging and decreasing horizon radius. While the X-ray emission is dominated by the near horizon region, the near-infrared (NIR) radiation originates at larger radii. Therefore, the ratio of X-ray to NIR power is an observational signature of black hole spin.

Next-to-soft radiative corrections in QCD and quantum gravity

The origin of divergent logarithmic contributions to gauge theory cross sections arising from soft and collinear radiation is explored and a general prescription for tackling next-to-soft logarithms is presented. The NNLO Abelian-like contributions to the Drell-Yan K-factor are reproduced using this generalised prescription. The soft limit of gravity is explored where the interplay between the eikonal phase and Reggeization of the graviton is explained using Wilson line techniques. The Wilson line technique is then implemented to treat the set of next-to-soft contributions arising from dressing external partons with a next-to-soft Wilson line.

Quantum fluctuations and thermal dissipation in higher derivative gravity

In this paper, based on the AdS(2)/CFT1 prescription, we explore the low frequency behavior of quantum two point functions for a special class of strongly coupled CFTs in one dimension whose dual gravitational counterpart consists of extremal black hole solutions in higher derivative theories of gravity defined over an asymptotically AdS spacetime. The quantum critical points thus described are supposed to correspond to a very large value of the dynamic exponent (z -> infinity). In our analysis, we find that quantum fluctuations are enhanced due to the higher derivative corrections in the bulk which in turn increases the possibility of quantum phase transition near the critical point. On the field theory side, such higher derivative effects would stand for the corrections appearing due to the finite coupling in the gauge theory. Finally, we compute the coefficient of thermal diffusion at finite coupling corresponding to Gauss Bonnet corrected charged Lifshitz black holes in the bulk. We observe an important crossover corresponding to z = 5 fixed point. (C) 2015 The Author. Published by Elsevier B.V.

Noncommutative Quantum Field Theories and UV/IR Mixing

Our present-day understanding of fundamental constituents of matter and their interactions is based on the Standard Model of particle physics, which relies on quantum gauge field theories. On the other hand, the large scale dynamical behaviour of spacetime is understood via the general theory of relativity of Einstein. The merging of these two complementary aspects of nature, quantum and gravity, is one of the greatest goals of modern fundamental physics, the achievement of which would help us understand the short-distance structure of spacetime, thus shedding light on the events in the singular states of general relativity, such as black holes and the Big Bang, where our current models of nature break down. The formulation of quantum field theories in noncommutative spacetime is an attempt to realize the idea of nonlocality at short distances, which our present understanding of these different aspects of Nature suggests, and consequently to find testable hints of the underlying quantum behaviour of spacetime. The formulation of noncommutative theories encounters various unprecedented problems, which derive from their peculiar inherent nonlocality. Arguably the most serious of these is the so-called UV/IR mixing, which makes the derivation of observable predictions especially hard by causing new tedious divergencies, to which our previous well-developed renormalization methods for quantum field theories do not apply. In the thesis I review the basic mathematical concepts of noncommutative spacetime, different formulations of quantum field theories in the context, and the theoretical understanding of UV/IR mixing. In particular, I put forward new results to be published, which show that also the theory of quantum electrodynamics in noncommutative spacetime defined via Seiberg-Witten map suffers from UV/IR mixing. Finally, I review some of the most promising ways to overcome the problem. The final solution remains a challenge for the future.

On gravitational fields of stars in f(R) gravity theories

Einstein's general relativity is a classical theory of gravitation: it is a postulate on the coupling between the four-dimensional, continuos spacetime and the matter fields in the universe, and it yields their dynamical evolution. It is believed that general relativity must be replaced by a quantum theory of gravity at least at extremely high energies of the early universe and at regions of strong curvature of spacetime, cf. black holes. Various attempts to quantize gravity, including conceptually new models such as string theory, have suggested that modification to general relativity might show up even at lower energy scales. On the other hand, also the late time acceleration of the expansion of the universe, known as the dark energy problem, might originate from new gravitational physics. Thus, although there has been no direct experimental evidence contradicting general relativity so far - on the contrary, it has passed a variety of observational tests - it is a question worth asking, why should the effective theory of gravity be of the exact form of general relativity? If general relativity is modified, how do the predictions of the theory change? Furthermore, how far can we go with the changes before we are face with contradictions with the experiments? Along with the changes, could there be new phenomena, which we could measure to find hints of the form of the quantum theory of gravity? This thesis is on a class of modified gravity theories called f(R) models, and in particular on the effects of changing the theory of gravity on stellar solutions. It is discussed how experimental constraints from the measurements in the Solar System restrict the form of f(R) theories. Moreover, it is shown that models, which do not differ from general relativity at the weak field scale of the Solar System, can produce very different predictions for dense stars like neutron stars. Due to the nature of f(R) models, the role of independent connection of the spacetime is emphasized throughout the thesis.

VACUUM POLARIZATION EFFECTS ON QUASINORMAL MODES IN ELECTRICALLY CHARGED BLACK HOLE SPACE-TIMES

We investigate the influence of vacuum polarization of quantum massive fields on the scalar sector of quasinormal modes in spherically symmetric black holes. We consider the evolution of a massless scalar field on the space-time corresponding to a charged semiclassical black hole, consisting of the quantum-corrected geometry of a Reissner-Nordstrom black hole dressed by a quantum massive scalar field in the large mass limit. Using a sixth order WKB approach we find a shift in the quasinormal mode frequencies due to vacuum polarization.