Denna uppsats tar upp två filosofers argumentation kring konflikten mellan Presentism och denspeciella relativitetsteorin: D. H. Mellor och Theodore Sider. Utifrån detta ges ett försvar avPresentism i ljuset av speciella relativitetsteorin och Mellor´s och Sider´s argument. Försvaretgår ut på att visa att denna konflikt inte innebär inkompatibilitet. Möjligheten att försvaraPresentism genom att påpeka olika tolkningar av speciella relativitetsteorin som empirisktlikvärdiga ges.

<p>This thesis presents a brief review of gravitation and cosmology, and then gives an overview of the theory of cosmological perturbations; subsequently some applications are discussed, such as large-scale structure formation. Cosmological perturbations are here presented both in the Newtonian paradigm and in two di¤erent relativistic approaches. The relativistic approaches are (i) the metric approach, where small variations of the metric tensor are considered, and (ii) the covariant approach, which focusses on small variations of the curvature. Dealing with these two approaches also involves addressing the gauge problem –how to map an idealized world model into a more accurate world model.</p>

<p>In this thesis we study multipole moments of axisymmetric spacetimes. Using the recursive definition of the multipole moments of Geroch and Hansen we develop a method for computing all multipole moments of a stationary axisymmetric spacetime without the use of a recursion. This is a generalisation of a method developed by Herberthson for the static case.</p><p>Using Herberthson’s method we also develop a method for finding a static axisymmetric spacetime with arbitrary prescribed multipole moments, subject to a specified convergence criteria. This method has, in general, a step where one has to find an explicit expression for an implicitly defined function. However, if the number of multipole moments are finite we give an explicit expression in terms of power series.</p> / Note: The two articles are also available in the pdf-file. Report code: LiU-TEK-LIC-2006:4.

This thesis presents a brief review of gravitation and cosmology, and then gives an overview of the theory of cosmological perturbations; subsequently some applications are discussed, such as large-scale structure formation. Cosmological perturbations are here presented both in the Newtonian paradigm and in two di¤erent relativistic approaches. The relativistic approaches are (i) the metric approach, where small variations of the metric tensor are considered, and (ii) the covariant approach, which focusses on small variations of the curvature. Dealing with these two approaches also involves addressing the gauge problem –how to map an idealized world model into a more accurate world model.

This is a thesis on general relativity. It analyzes dynamical properties of Einstein's field equations in cosmology and in the vicinity of spacetime singularities in a number of different situations. Different techniques are used depending on the particular problem under study; dynamical systems methods are applied to cosmological models with spatial homogeneity; Hamiltonian methods are used in connection with dynamical systems to find global monotone quantities determining the asymptotic states; Fuchsian methods are used to quantify the structure of singularities in spacetimes without symmetries. All these separate methods of analysis provide insights about different facets of the structure of the equations, while at the same time they show the relationships between those facets when the different methods are used to analyze overlapping areas. The thesis consists of two parts. Part I reviews the areas of mathematics and cosmology necessary to understand the material in part II, which consists of five papers. The first two of those papers uses dynamical systems methods to analyze the simplest possible homogeneous model with two tilted perfect fluids with a linear equation of state. The third paper investigates the past asymptotic dynamics of barotropic multi-fluid models that approach a `silent and local' space-like singularity to the past. The fourth paper uses Hamiltonian methods to derive new monotone functions for the tilted Bianchi type II model that can be used to completely characterize the future asymptotic states globally. The last paper proves that there exists a full set of solutions to Einstein's field equations coupled to an ultra-stiff perfect fluid that has an initial singularity that is very much like the singularity in Friedman models in a precisely defined way. / <p>Status of the paper "Perfect Fluids and Generic Spacelike Singularities" has changed from manuscript to published since the thesis defense.</p>

Special relativity is a subject that attracts interest among students, but there are many things that make students experience it as difficult. As a physics teacher, it is important to both have a solid base of knowledge in physics as well as educational knowledge within the subject. You need to know what students usually struggle with, which parts to focus on to give the students a good understanding of physics, et cetera. This project is a literature study that examines special relativity in four parts. The first part of the project is a historical description of special relativity, summarizing how researchers have concluded the theory of special relativity. It consists of a series of experiments and hypotheses before Einstein tied everything together with his theory of special relativity. Then the central ideas of special relativity are described, with a focus on exercises that describe relativistic phenomena. The ideas covered in this second part are the relativity of simultaneity, time dilation, length contraction and mass and energy equivalence. The third part consists of a summary of current educational research to explore different ways to teach special relativity, according to the educational research. Many students make up their own explanations when presented with a relativistic phenomenon, that matches their Newtonian view in mechanics. It is a challenge to get students to think in a new relativistic way. A common difficulty is to move between different reference systems, which is necessary since relativistic phenomena in movement is only visible when looking at the same movement from different reference system. For the last part of the project, the Swedish curriculum and Swedish textbooks are examined. The section on relativity often begins with what students struggle most with, moving between frames of reference. Before introducing special relativity, it is useful to practice switching between different reference systems in classical mechanics, using Galilean transformations and relative motion. Another idea might be to introduce special relativity with, for example, the equivalence in mass and energy, where students do not encounter the problem with reference systems. / Speciell relativitetsteori är något som väcker nyfikenhet hos elever, men det finns mycket som gör att eleverna upplever det som svårt. Som lärare är det viktigt att ha en gedigen ämneskunskap och mycket didaktisk kunskap. Man måste ha koll på vad eleverna brukar ha svårt för, vilka delar man bör fokusera på för att eleverna ska få en bra grund, med mera. Det här projektet är en litteraturstudie som undersöker speciell relativitetsteori i gymnasieskolan i fyra delar. Första delen i projektet är en historisk beskrivning av speciell relativitetsteori, hur forskare har kommit fram till den speciella relativitetsteorin. Historiebeskrivningen består av en serie experiment och hypoteser innan Einstein knöt ihop säcken med den speciella relativitetsteorin. Sedan beskrivs de centrala idéerna inom relativitetsteori, med fokus på många exempel som beskriver relativistiska fenomen. De delar som behandlas i det här projektet är relativiteten i simultanitet, tidsdilatation, längdkontraktion samt massa- och energiekvivalens. Den tredje delen består av en sammanfattning av modern fysikdidaktisk forskning, för att ta reda på hur man kan undervisa forskningsbaserat inom speciell relativitet. Elever skapar ofta egna förklaringar till relativistiska fenomen, som stämmer bättre överens med en Newtonsk uppfattning. Att få eleverna till ett nytt relativistiskt tankesätt är en utmaning. Det som elever främst har svårt med är att gå mellan olika referenssystem, vilket är nödvändigt för att uppfatta relativistiska fenomen inom rörelse. Till sist undersöks den svenska läroplanen och svenska läroböcker. Ofta börjar avsnittet om relativitetsteori med det elever har som svårast för, att gå mellan olika referenssystem. Innan speciell relativitetsteori introduceras är det bra att öva att gå mellan olika referenssystem inom klassisk mekanik, arbeta med relativ rörelse och Galileitransformationer. En annan idé kan vara att introducera speciell relativitetsteori med till exempel ekvivalensen i massa- och energi, där eleverna inte stöter på det problemet.

In this thesis we investigate the superenergy tensor that was introduced by Chevreton in 1964 as an electromagnetic counterpart to the Bel-Robinson tensor for the gravitational feld. We show that in Einstein-Maxwell spacetimes with a source-free electromagnetic feld, the Chevreton superenergy tensor has many interesting properties. It is a completely symmetric rank-4 tensor and it gives rise to conserved currents for orthogonally transitive 1- and 2-parameter isometry groups. The trace of this tensor is divergence-free and it is related to the Bach tensor. We investigate the implications for when the trace vanishes and we are able to determine the full set of such spacetimes. We use this to treat the problem of Einstein{-Maxwell spacetimes that are conformally related to Einstein spaces and we find new exact solutions with this property.

In this thesis we aim to develop new perspectives on the statistical mechanics of black holes using an information geometric approach (Ruppeiner and Weinhold geometry). The Ruppeiner metric is defined as a Hessian matrix on a Gibbs surface, and provides a geometric description of thermodynamic systems in equilibrium. This Ruppeiner geometry exhibits physically suggestive features; a flat Ruppeiner metric for systems with no interactions i.e. the ideal gas, and curvature singularities signaling critical behavior(s) of the system. We construct a flatness theorem based on the scaling property of the black holes, which proves to be useful in many cases. Another thermodynamic geometry known as the Weinhold geometry is defined as the Hessian of internal energy and is conformally related to the Ruppeiner metric with the system’s temperature as a conformal factor.  We investigate a number of black hole families in various gravity theories. Our findings are briefly summarized as follows: the Reissner-Nordström type, the Einstein-Maxwell-dilaton andBTZ black holes have flat Ruppeiner metrics that can be represented by a unique state space diagram. We conjecture that the state space diagram encodes extremality properties of the black hole solution. The Kerr type black holes have curved Ruppeiner metrics whose curvature singularities are meaningful in five dimensions and higher, signifying the onset of thermodynamic instabilities of the black hole in higher dimensions. All the three-parameter black hole families in our study have non-flat Ruppeiner and Weinhold metrics and their associated curvature singularities occur in the extremal limits. We also study two-dimensional black hole families whose thermodynamic geometries are dependent on parameters that determine the thermodynamics of the black hole in question. The tidal charged black hole which arises in the braneworld gravity is studied. Despite its similarity to the Reissner-Nordström type, its thermodynamic geometries are distinctive. / At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 2: Submitted. / Geometry and Physics

Gravitational perturbations can be in the form of scalars, vectors or tensors. This thesis focuses on the evolution of scalar perturbations in cosmology, and interactions between tensor perturbations, in the form of gravitational waves, and plasma waves. The gravitational waves studied in this thesis are assumed to have small amplitudes and wavelengths much shorter than the background length scale, allowing for the assumption of a flat background metric. Interactions between gravitational waves and plasmas are described by the Einstein-Maxwell-Vlasov, or the Einstein-Maxwell-fluid equations, depending on the level of detail required. Using such models, linear wave excitation of various waves by gravitational waves in astrophysical plasmas are studied, with a focus on resonance effects. Furthermore, the influence of strong magnetic field quantum electrodynamics, leading to detuning of the gravitational wave-electromagnetic wave resonances, is considered. Various nonlinear phenomena, including parametric excitation and wave steepening are also studied in different astrophysical settings. In cosmology the evolution of gravitational perturbations are of interest in processes such as structure formation and generation of large scale magnetic fields. Here, the growth of density perturbations in Kantowski-Sachs cosmologies with positive cosmological constant is studied.

Black holes are one of the most interesting objects in the universe, and studying these objects should give exciting results. This research will investigate the General Theory of Relativity, explaining the essence of the theory needed for deriving solutions for a Schwarzschild black hole. This knowledge leads to deriving the equations of motion of a bosonic scalar field around a Schwarzschild black hole. Computing the dynamical evolution of that scalar field, and taking the limit far away from the black hole, gives an approximation derivation of the  Schrödinger equation. This study opens many doors to future research about black holes and scalar fields. / Svarta hål är ett av de mest intressanta objekten i universum, och därför, att studera dessa föremål bör ge spännande resultat.I detta arbete kommer den allmänna relativitetsteorin  att studeras och förklaras med allt som behövs för att härledalösningar för en Schwarzschild svart hål. Denna kunskap leder till att härleda rörelseekvationerna för ett bosoniskt skalärfält runt ett Schwarzschild svart hål.Genom att beräkna den dynamiska utvecklingen av det skalära fältet och ta gränsen långt bort från svarta hålet,så kommer det at ge en approximativ härledning av Schrödinger ekvationen. Den här typen av studier öppnar många dörrar för framtida forskning om svarta hål och skalära fält.