Advanced General Relativity Notes

These lecture notes are intended as a guide to Graduate level readers that are already familiar with basic General Relativity. They present in a concise way some advanced concepts and problems encountered in the study of gravitation. In these notes are covered: Alternates forms of the Schwarzschild Black Hole solution, including the classic Kruskal extension; An account of the building of Conformal, Carter-Penrose, diagrams; A discussion of Birkhoff Theorem; A discussion of tools for Geodesics and congruences, including Energy Conditions; A discussion of Horizons and an approach to some of the singularity theorems; An exploration of the Kerr Black Hole solution properties, including the Penrose Process and Black Hole Thermodynamics; A discussion of the Eckart and Israel-Stewart Relativistic Thermodynamics; A discussion of Tetrads in Relativity, in Einstein-Cartan theory and in Newman-Penrose formalism; An explicitation of calculations on Geodesics approach from Hamilton-Jacobi Formalism; A derivation from Least action of the equation of Motion of a top in Relativity, the M.P.D. equationsComment: 164pp, 40figs. Lecture notes for Graduates with GR1 knowledge. Feedback appreciate

Dark Energy-Dark Matter Interaction and the Violation of the Equivalence Principle from the Abell Cluster A586

We show that the Abell Cluster A586 exhibits evidence of the interaction between dark matter and dark energy and argue that this interaction implies a violation of the Equivalence Principle. This violation is found in the context of two different models of dark energy-dark matter interaction. We also argue, based on the spherical symmetry of the Abell Cluster A586 that skewness is not the most general quantity to test the Equivalence Principle

The impact of nebular emission on the broadband fluxes of high-redshift galaxies

A substantial fraction of the light emitted from young or star-forming galaxies at ultraviolet to near-infrared wavelengths comes from the ionized interstellar medium in the form of emission lines and a nebular continuum. At high redshifts, star formation rates are on average higher and stellar populations younger than in the local Universe. Both of these effects act to boost the impact of nebular emission on the overall spectrum of galaxies. Even so, the broadband fluxes and colours of high-redshift galaxies are routinely analyzed under the assumption that the light observed originates directly from stars. Here, we assess the impact of nebular emission on broadband fluxes in Johnson/Cousins BVRIJHK, Sloan Digital Sky Survey griz and Spitzer IRAC/MIPS filters as a function of observed redshift (up to z=15) for galaxies with different star formation histories. We find that nebular emission may account for a non-negligible fraction of the light received from high-redshift galaxies. The ages and masses inferred for such objects through the use of spectral evolutionary models that omit the nebular contribution are therefore likely to contain systematic errors. We argue that a careful treatment of the nebular component will be essential for the interpretation of the rest-frame ultraviolet-to-infrared properties of the first galaxies formed, like the ones expected to be detected with the James Webb Space Telescope.Comment: 5 pages, 3 figures, accepted for publication in ApJ

Merger as Intermittent Accretion

The Self-Similar Secondary Infall Model (SSIM) is modified to simulate a merger event. The model encompass spherical versions of tidal stripping and dynamical friction that agrees with the Syer & White merger paradigm's behaviour. The SSIM shows robustness in absorbing even comparable mass perturbations and returning to its original state. It suggests the approach to be invertible and allows to consider accretion as smooth mass inflow merging and mergers as intermittent mass inflow accretion.Comment: letter accepted by A&A 29/09/08, 4 pages, colour figure

Black holes and Galactic density cusps -- I. Radial orbit cusps and bulges

In this paper, we study the distribution functions that arise naturally during self-similar radial infall of collisionless matter. Such matter may be thought of either as stars or as dark matter particles. If a rigorous steady state is assumed, then the system is infinite and is described by a universal distribution function given the self-similar index. The steady logarithmic potential case is exceptional and yields the familiar Gaussian for an infinite system with an inverse-square density profile. We show subsequently that for time-dependent radial self-similar infall, the logarithmic case is accurately described by the Fridmann and Polyachenko distribution function. The system in this case is finite but growing. We are able to embed a central mass in the universal steady distribution only by iteration, except in the case of massless particles. The iteration yields logarithmic corrections to the massless particle case and requires a `renormalization' of the central mass. A central spherical mass may be accurately embedded in the Fridmann and Polyachenko growing distribution however. Some speculation is given concerning the importance of radial collisionless infall in actual galaxy formation.Comment: 10 pp, 3 fig

Chandrasekhar's Dynamical Friction and non-extensive statistics

The motion of a point like object of mass $M$ passing through the background potential of massive collisionless particles ($m << M$) suffers a steady deceleration named dynamical friction. In his classical work, Chandrasekhar assumed a Maxwellian velocity distribution in the halo and neglected the self gravity of the wake induced by the gravitational focusing of the mass $M$. In this paper, by relaxing the validity of the Maxwellian distribution due to the presence of long range forces, we derive an analytical formula for the dynamical friction in the context of the $q$-nonextensive kinetic theory. In the extensive limiting case ($q = 1$), the classical Gaussian Chandrasekhar result is recovered. As an application, the dynamical friction timescale for Globular Clusters spiraling to the galactic center is explicitly obtained. Our results suggest that the problem concerning the large timescale as derived by numerical $N$-body simulations or semi-analytical models can be understood as a departure from the standard extensive Maxwellian regime as measured by the Tsallis nonextensive $q$-parameter.Comment: 16pp 5 figs, revised and extended version of arXiv:1202.1873 . Accepted for publication by JCA

Lyman Alpha Emitters in the Hierarchically Clustering Galaxy Formation

We present a new theoretical model for the luminosity functions (LFs) of Lyman alpha (Lya) emitting galaxies in the framework of hierarchical galaxy formation. We extend a semi-analytic model of galaxy formation that reproduces a number of observations for local and high-z galaxies, without changing the original model parameters but introducing a physically-motivated modelling to describe the escape fraction of Lya photons from host galaxies (f_esc). Though a previous study using a hierarchical clustering model simply assumed a constant and universal value of f_esc, we incorporate two new effects on f_esc: extinction by interstellar dust and galaxy-scale outflow induced as a star formation feedback. It is found that the new model nicely reproduces all the observed Lya LFs of the Lya emitters (LAEs) at different redshifts in z ~ 3-6. Especially, the rather surprisingly small evolution of the observed LAE Lya LFs compared with the dark halo mass function is naturally reproduced. Our model predicts that galaxies with strong outflows and f_esc ~ 1 are dominant in the observed LFs. This is also consistent with available observations, while the simple universal f_esc model requires f_esc << 1 not to overproduce the brightest LAEs. On the other hand, we found that our model significantly overpredicts LAEs at z > 6, and absorption of Lya photons by neutral hydrogen in intergalactic medium (IGM) is a reasonable interpretation for the discrepancy. This indicates that the IGM neutral fraction x_HI rapidly evolves from x_HI << 1 at z < 6 to a value of order unity at z ~ 6-7, which is broadly consistent with other observational constraints on the reionization history.Comment: 14 pages, 7 figures, 1 table; accepted to ApJ; the html abstract is replaced to match the accepted version, the .ps and .pdf files are strictly identical between the 2nd and the 3rd version