Donoghue's effective field theory of quantum gravity is extended to include the interaction of massless particles. The collinear divergences which accompany massless particles are examined first in the context of QED and then in quantum gravity. A result of Weinberg is extended to show how these divergences vanish in the case of gravity. The scattering cross section for hypothetical massless scalar particles is computed first, because it is simpler, and the results are then extended to photons. Some terms in the cross section are shown to correspond to the Aichelburg-Sexl metric surrounding a massless particle and to quantum corrections to that metric. The scattering cross section is also applied to calculate quantum corrections to the bending of starlight, and though small, the result obtained is qualitatively different than in the classical case. Since effective field theory includes the low-energy degrees of freedom which generate collinear divergences, the results presented here will remain relevant in any future quantum theory of gravity.

The central objective of this work is to present an analysis of the asymptotic conformal Killing vectors in asymptotically-flat space-times of general relativity. This problem has been examined by two different methods; in Chapter 5 the asymptotic expansion technique originated by Newman and Unti [31] leads to a solution for asymptotically-flat spacetimes which admit an asymptotically shear-free congruence of null geodesics, and in Chapter 6 the conformal rescaling technique of Penrose [54] is used both to support the findings of the previous chapter and to set out a procedure for solution in the general case. It is pointed out that Penrose's conformal technique is preferable to the use of asymptotic expansion methods, since it can be established in a rigorous manner without leading to the possible convergence difficulties associated with asymptotic expansions. Since the asymptotic conformal symmetry groups of asymptotically flat space-times Are generalisations of the conformal group of Minkowski space-time we devote Chapters 3 and 4 to a study of the flat space case so that the results of later chapters may receive an interpretation in terms of familiar concepts. These chapters fulfil a second, equally important, role in establishing local isomorphisms between the Minkowski-space conformal group, 90(2,4) and SU(2,2). The SO(2,4) representation has been used by Kastrup [61] to give a physical interpretation using space-time gauge transformations. This appears as part of the survey of interpretative work in Chapter 7. The SU(2,2) representation of the conformal group has assumed a theoretical prominence in recent years. through the work of Penrose [9-11] on twistors. In Chapter 4 we establish contact with twistor ideas by showing that points in Minkowski space-time correspond to certain complex skew-symmetric rank two tensors on the SU(2,2) carrier space. These objects are, in Penrose's terminology [91, simple skew-symmetric twistors of valence [J. A particularly interesting aspect of conformal objects in space-time is explored in Chapter 8, where we extend the work of Geroch [16] on multipole moments of the Laplace equation in 3-space to the consideration. of Q tý =0 in Minkowski space-time. This development hinges upon the fact that multipole moment fields are also conformal Killing tensors. In the final chapter some elementary applications of the results of Chapters 3 and 5 are made to cosmological models which have conformal flatness or asymptotic conformal flatness. In the first class here we have 'models of the Robertson-Walker type and in the second class we have the asymptotically-Friedmann universes considered by Hawking [73]. / University of Bradford Research Studenship

The General theory of Relativity was first introduced by Albert Einstein. There have been many attempts to unify General Relativity with the Standard Model of Physics and many of these try to do so by modifying General Relativity slightly. One way to do this is to add a mass to the graviton. Such a theory was proposed by Fierz and Pauli. However, a massive gravity theory suffers from the vDvZ discontinuty where taking the masss of the graviton to zero does not reproduce the results of General Relativity exactly. This can, to some extent, be resolved via the Vainshtein mechanism, where General Relativity can be reproduced within a certain radius from a source, called the Vainshtein radius. Another modification that can be imagined, is to add a second metric. However, doing this results in extra degrees of freedom which manifest as a Boulaware Deser ghost. The bimetric action which avoids the Boulaware Deser ghost was first introduced by Hassan and Rosen in 2011. In this theory, only one of the metrics couples to standard model matter to avoid the ghost. In this scenario, the propagating massless and massive spin-2 modes turn out to be linear combinations of the two metrics, just as in neutrino mixings. In this thesis, we review some works which investigate the oscillations between the massless and massive modes and the implications for gravitational waves. In particular we consider the bounds on the parameters of the theory based on the fact that evidence for such oscillations have not been observed by LIGO. We use a new LIGO result to extend these bounds. We also review an investigation which explores the possibility that the dark matter particle could be the massive particle of bimetric gravity. / Den allmänna relativitetsteorin introducerades först av Albert Einstein.Många har försökt förena allmän relativitetsteori med partikelfysikensstandardmodell och många av dessa försök gör detta genom att lägga tillen massa för gravitonen. En sådan teori föreslogs av Fierz och Pauli.Massiv gravitation lider dock av vDvZ-diskontinuiteten där gränsen närgravitonmassan går mot noll inte reproducerar allmän relativitetsteori.Detta kan, till viss del, lösas genom Vainshteinmekanismen, där allmänrelativitetsteori kan reproduceras inom ett visst avstånd från källan,kallat Vainshteinradien. En annan modifikation som kan komma på fråga äratt lägga till en andra metrik. Att göra detta leder dock till nyafrihetsgrader som yttrar sig som ett Boulaware-Deser-spöke. Denbimetriska verkan som undviker Boulaware-Deser-spöket introduceradesförst av Hassan och Rosen år 2011. I denna teori kopplar enbart en avmetrikerna till standardmodellen vilket gör att spöket kan undvikas. Idetta scenario visar sig det masslösa och det massivapropagationsegentillstånden vara linjärkombinationer av de tvåmetrikerna i analogi med neutrinoblandning. I detta arbete går vi igenomnågra arbete som undersöker oscillationerna mellan de två metrikerna ochimplikationerna för gravitationsvågor. Speciellt kommer vi att betraktade begränsningar som finns på teoriparametrarna baserat på det faktumatt LIGO inte observerat några bevis för sådana oscillationer. Vianvänder också nya LIGO-resultat för att utöka dessa begränsningar. Vidiskutera också möjligheten att mörk materia skulle kunna bestå av denmassiva gravitonen i bimetrisk gravitation.

In this thesis, we consider three aspects of black holes. First, we examine a black hole boosted through a uniform magnetic field. We find that it can acquire an electric charge, just as a spinning black hole in an ambient magnetic field can, though the gravito-electrodynamics upstage naive arguments about screening electric fields in determining the value of the charge accrued. We study the chaotic behavior of the charged particles via their fractal basin boundaries. Second, we study the vanishing of Love numbers for black holes from a geometric perspective and connect it to the existence of quasinormal modes in de Sitter space. Behind each phenomenon is a ladder structure with a geometric/representation-theoretic origin which makes it possible to connect the asymptotic behavior of solutions at different boundaries. Third, we model the formation of a black hole in dRGT massive gravity in a de Sitter background with a collapsing homogeneous and pressureless ball of dust or ``star''. We focus on several choices of parameters corresponding to models of interest. We compute the position of the apparent horizon where it crosses the surface of the star, the Ricci curvature at the boundary, and the finite correction to the curvature of the apparent horizon due to the graviton mass. We argue that our collapsing solutions cannot be matched to a static, spherically symmetric vacuum solution at the star's surface, providing further evidence that physical black hole solutions in massive gravity are likely time-dependent.

String theory imposes slight modifications to Einstein's equations of general relativity (GR). In (4), the authors claim that the gravitational field equations in empty space, which in GR are just R [subscript greek letters mu nu ] = 0, should hold one extra term which is first order in the string constant [alpha'] and proportional to the Riemann curvature tensor squared. They do admit, however, that this simple modification is just schematic. In (1) the authors use modified equations which are coupled to the dilation field. We show that equations given in (4) do not admit an isotropic solution; justification of these equations would require sacrificing isotropy. We thus investigate the consequences of the coupled equations from (1) and the black-hole solution they give there. We calculate the additional perihelion precession of Mercury, the added deflection of photons by the sun, and the extra gravitational redshift which should be present if these equations hold. We determine that additional effects due to string theory in each of these cases are quite minuscule.

No description available.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Earth and Planetary Science, 1980. / Microfiche copy available in Archives and Science. / Includes bibliographical references. / by Thomas Marshall Eubanks. / M.S.

We begin by reviewing special and general relativity in such a way as to smoothly transition into current research. We present the variational formalism of general relativity as well as the extension into the palatini formalism. This allows us to develop a theory on a metric affine manifold rather than the standard manifold in general relativity. We present a generalized action intended to replace the Einstein Hilbert action in general relativity and derive some consequences thereof. The modified field equations are derived by varying this action using the Palatini approach. The corresponding differential equations are solved thereby establishing the equivalence between the modified action and the standard action with a cosmological constant. Furthermore the metric due to a spherically symmetric distribution of mass is found and applied in calculating the bending of light in the curved space. It is deduced that no difference between the modified action and the original Einstein Hilbert action is observed thereby implying that the experiment involving the bending of light around the sun in 1919 in no way distinguishes between our modification and the original approach by Einstein and Hilbert.

Despite the many successes of the current standard model of cosmology on the largest physical scales, it relies on two phenomenologically motivated constituents, cold dark matter and dark energy, which account for approximately 95% of the energy-matter content of the universe. From a more fundamental point of view, however, the introduction of a dark energy (DE) component is theoretically challenging and extremely fine-tuned, despite the many proposals for its dynamics. On the other hand, the concept of cold dark matter (CDM) also suffers from several issues such as the lack of direct experimental detection, the question of its cosmological abundance and problems related to the formation of structure on small scales. A perhaps more natural solution might be that the gravitational interaction genuinely differs from that of general relativity, which expresses itself as either one or even both of the above dark components. Here we consider different possibilities on how to constrain hypothetical modifications to the gravitational sector, focusing on the subset of tensor-vector-scalar (TeVeS) theory as an alternative to CDM on galactic scales and a particular class of chameleon models which aim at explaining the coincidences of DE. Developing an analytic model for nonspherical lenses, we begin our analysis with testing TeVeS against observations of multiple-image systems. We then approach the role of low-density objects such as cosmic filaments in this framework and discuss potentially observable signatures. Along these lines, we also consider the possibility of massive neutrinos in TeVeS theory and outline a general approach for constraining this hypothesis with the help of cluster lenses. This approach is then demonstrated using the cluster lens A2390 with its remarkable straight arc. Presenting a general framework to explore the nonlinear clustering of density perturbations in coupled scalar field models, we then consider a particular chameleon model and highlight the possibility of measurable effects on intermediate scales, i.e. those relevant for galaxy clusters. Finally, we discuss the prospects of applying similar methods in the context of TeVeS and present an ansatz which allows to cast the linear perturbation equations into a more convenient form.

Cette thèse se consacre premièrement à certains aspects de la définition de charges conservées en relativité générale pour les espaces asymptotiquement plats à l’infini spatial. À l’aide de la dualité gravitationnelle, présente au niveau linéarisé, on étudie également l’existence de charges topologiques, magnétiques, ainsi que leurs contributions aux superalgèbres dans les théories de supergravité N = 1 et N = 2 à quatre dimensions. La thèse est divisée en trois parties.<p>Dans la première partie, les espaces asymptotiquement plats à l’infini spatial sont décrits à l’aide d’une généralisation de la métrique de type Beig-Schmidt. La construction de charges à partir de l’étude des équations du mouvement et de la classification de tenseurs symétriques et de divergences nulles nous permet de démontrer l’unicité des charges de Poincaré pour l’ansatz non-généralisé en présence de conditions de parité. L’équivalence des charges de Ashtekar- Hansen et Mann-Marolf est ainsi revisitée. Dans le cas d’un ansatz généralisé, une régulation de la forme symplectique divergente, à l’aide de contre-termes rajoutés à l’action de Mann-Marolf, nous donne la possibilité de considérer un espace des phases sans conditions de parité, tout en gardant un principe variationnel bien défini. Le groupe asymptotique comprend alors, en plus des charges de Poincaré où les charges de Lorentz ne sont plus asymptotiquement linéaires, des charges non-triviales associées aux supertranslations et aux transformations logarithmiques.<p>Dans la deuxième partie, on étudie la dualité gravitationnelle et la définition de charges magnétiques en gravitation linéarisée. On revisite la dualité et on montre qu’une dualisation sur les indices de Lorentz facilite la compréhension de celle-ci. Les dix charges de Poincaré ainsi que leurs duales magnétiques sont alors exprimées en termes d’intégrales de surface. Nous illustrons ensuite nos résultats à travers l’étude des sources de certaines solutions électriques et de leur duales magnétiques. Les solutions électriques envisagées sont :les trous noirs de type Schwarzschild et de type Kerr ainsi que les ondes de chocs de type pp.<p>Dans la dernière partie, on établit la supersymétrie des espaces de type Taub-NUT lorentzien chargés électriquement et magnétiquement dans la supergravité N = 2. Motivé par l’existence d’une égalité BPS, on entreprend alors une recherche sur l’inclusion de la charge NUT dans l’algèbre de supersymétrie. Grâce à une complexification de la forme de Witten-Nester, cette contribution de la charge NUT à la superalgèbre est comprise comme une déformation topologique, symétrique, au crochet antisymétrique des super-charges. Ce résultat est alors appliqué à la superalgèbre N = 1 à travers l’étude des ondes de chocs de type pp.<p> / Doctorat en Sciences / info:eu-repo/semantics/nonPublished