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.

Applications of Gauge/Gravity Duality to QCD and Heavy Ion Collisions

The description of quarks and gluons, using the theory of quantum chromodynamics (QCD), has been known for a long time. Nevertheless, many fundamental questions in QCD remain unanswered. This is mainly due to problems in solving the theory at low energies, where the theory is strongly interacting. AdS/CFT is a duality between a specific string theory and a conformal field theory. Duality provides new tools to solve the conformal field theory in the strong coupling regime. There is also some evidence that using the duality, one can get at least qualitative understanding of how QCD behaves at strong coupling. In this thesis, we try to address some issues related to QCD and heavy ion collisions, applying the duality in various ways.

Other Side of This Life : Death, Value, and Social Being in Thomas Pynchon's Fiction

This dissertation analyzes the interrelationship between death, the conditions of (wo)man s social being, and the notion of value as it emerges in the fiction of the American novelist Thomas Pynchon (1937 ). Pynchon s present work includes six novels V. (1963), The Crying of Lot 49 (1966), Gravity s Rainbow (1973), Vineland (1990), Mason & Dixon (1997), Against the Day (2006) and several short stories. Death constitues a central thematic in Pynchon s work, and it emerges through recurrent questions of mortality, suicide, mass destruction, sacrifice, afterlife, entropy, the relationship between the animate and the inanimate, and the limits of representation. In Pynchon, death is never a mere biological given (or event); it is always determined within a certain historical, cultural, and ideological context. Throughout his work, Pynchon questions the strict ontological separation of life and death by showing the relationship between this separation and social power. Conceptual divisions also reflect the relationship between society and its others, and death becomes that through which lines of social demarcation are articulated. Determined as a conceptual and social "other side", death in Pynchon forms a challenge to modern culture, and makes an unexpected return: the dead return to haunt the living, the inanimate and the animate fuse, and technoscientific attempts at overcoming and controlling death result in its re-emergence in mass destruction and ecological damage. The questioning of the ontological line also affects the structuration of Pynchon's prose, where the recurrent narrated and narrative desire to reach the limits of representation is openly associated with death. Textualized, death appears in Pynchon's writing as a sudden rupture within the textual functioning, when the "other side", that is, the bare materiality of the signifier is foregrounded. In this study, Pynchon s cultural criticism and his poetics come together, and I analyze the subversive role of death in his fiction through Jean Baudrillard s genealogy of the modern notion of death from L échange symbolique et la mort (1976). Baudrillard sees an intrinsic bond between the social repression of death in modernity and the emergence of modern political economy, and in his analysis economy and language appear as parallel systems for generating value (exchange value/ sign-value). For Baudrillard, the modern notion of death as negativity in relation to the positivity of life, and the fact that death cannot be given a proper meaning, betray an antagonistic relation between death and the notion of value. As a mode of negativity (that is, non-value), death becomes a moment of rupture in relation to value-based thinking in short, rationalism. Through this rupture emerges a form of thinking Baudrillard labels the symbolic, characterized by ambivalence and the subversion of conceptual opposites.

Drag på parnassen. Två sextiotalsstudier. : Del I: Medelklass med mänskligt ansikte. Medelklassradikalism i fyra romaner av Christer Kihlman, Jarl Sjöblom, Marianne Alopaeus och Ulla-Lena Lundberg. Del II: Modernistdebatten. Sak, person och fält i en finlandssvensk litteraturdebatt år 1965.

The objective of my dissertation Pull (or Draught, or Moves) at the Parnassus , is to provide a deeper understanding of Nordic Middle Class radicalism of the 1960 s as featured in Finland-Swedish literature. My approach is cultural materialist in a broad sense; social class is regarded a crucial aspect of the contents and contexts of the novels and literary discussions explored. In the first volume, Middle Class With A Human Face , novels by Christer Kihlman, Jarl Sjöblom, Marianne Alopaeus, and Ulla-Lena Lundberg, respectively, are read from the points of view of place, emotion, and power. The term "cryptotope" is used to designate the hidden places found to play an important role in all of these four narratives. Also, the "chronotope of the provincial small town", described by Mikhail Bakhtin in 1938, is exemplified in Kihlman s satirical novel, as is the chronotope of of war (Algeria, Vietnam) in those of Alopaeus and Lundberg s. All the four novels signal changes in the way general "scripts of emotions", e.g. jealousy, are handled and described. The power relations in the novels are also read, with reference to Michel Foucault. As the protagonists in two of them work as journalists, a critical discussion about media and Bourgeois hegemony is found; the term "repressive legitimation" is created to grasp these patterns of manipulation. The Modernist Debate , part II of the study, concerns a literary discussion between mainly Finland-Swedish authors and critics. Essayist Johannes Salminen (40) provided much of the fuel for the debate in 1963, questioning the relevance to contemporary life of the Finland-Swedish modernist tradition of the 1910 s and 1920 s. In 1965, a group of younger authors and critics, including poet Claes Andersson (28), followed up this critique in a debate taking place mainly in the newspaper Vasabladet. Poets Rabbe Enckell (62), Bo Carpelan (39) and others defended a timeless poetry. This debate is contextualized and the changing literary field is analyzed using concepts provided by sociologist Pierre Bourdieu. In the thesis, the historical moment of Middle Class radicalism with a human face is regarded a temporary luxury that new social groups could afford themselves, as long as they were knocking over the statues and symbols of the Old Bourgeoisie. This is not to say that all components of the Sixties strategy have lost their power. Some of them have survived and even grown, others remain latent in the gene bank of utopias, waiting for new moments of change.

"Han är en trollkarl. Alla skriver laudatur som går på hans lektioner" : en studie om elevernas uppfattningar om orsakerna till toppresultat i svenska i tre finska gymnasier

Tämä pro gradu -tutkielma on tehty osana Svenska i toppen -projektia, joka alkoi syksyllä 2008 Pohjoismaisten kielten ja pohjoismaisen kirjallisuuden laitoksella. Tutkimuksen tavoitteena on selvittää, mitkä tekijät vaikuttavat lukiolaisten näkökulmasta hyvien tulosten saavuttamiseen ruotsin ylioppilaskirjoituksissa kolmessa suomenkielisessä lukiossa, jotka sijaitsevat Turun, Tampereen ja Joensuun seuduilla. Lisäksi tavoitteena on selvittää, miten maantieteelliset tekijät vaikuttavat opiskelijoiden ruotsin kielen osaamiseen sekä mitä eroja on keskipitkän ja pitkän ruotsin oppimäärän opiskelijoiden asenteissa kieltä kohtaan. Tutkielman aineistona on kolme ryhmähaastattelua, joihin on osallistunut 14 lukiolaista, 11 tyttöä ja 3 poikaa. Haastattelut on tehty joulukuussa 2008 sekä tammi- ja maaliskuussa 2009. Haastatteluissa on käytetty strukturoitua kyselylomaketta, jossa kysytään opiskelijoiden näkemyksiä ruotsin opiskelusta. Tutkimusmenetelmänä on kvalitatiivinen tutkimusote, jossa on piirteitä kolmesta eri menetelmästä: tapaustutkimuksesta, etnografisesta tutkimuksesta sekä temaattisesta analyysistä. Tärkeimpänä teoriataustana on ruotsi toisena kielenä -tutkimus, oppiminen sosiokonstruktivistisena ilmiönä sekä motivaatiotutkimus. Tarkastelen kielenoppijaa luokkahuoneessa sosiaalisena osallistujana omassa oppimisprosessissaan. Oppiminen nähdään kokonaisuutena, johon kuuluu eri osa-alueita, esimerkiksi koulujen käytännöt, yhteisön vaikutus oppimiseen sekä opiskelijan identiteetin muokkautuminen kouluyhteisössä. Motivaatiota tarkastelen kielenoppimisen näkökulmasta, ja se koostuu erilaisista dynaamisista vaiheista, esimerkiksi tavoitteiden asettamisesta oppimisprosessin alussa, valintojen tekemisestä sekä motivaation ylläpitämisestä oppimisprosessin kuluessa. Tutkimuksen tulokset osoittavat, että suurin yksittäinen syy menestykseen opiskelijoiden näkökulmasta on opettaja, joka omalla toiminnallaan voi merkittävästi parantaa opiskelijoiden oppimisedellytyksiä. Työhön panostaminen, opiskelijoiden yksilöllinen kohtaaminen myös luokkahuoneen ulkopuolella ja esimerkiksi omien oppimateriaalien valmistaminen ovat opettajaan liittyviä tekijöitä, jotka voivat nostaa opiskelijoiden motivaatiota huomattavasti. Myös lukion maantieteellisellä sijainnilla on vaikutusta. Paikkakunnilla, joilla ruotsin kieltä käytetään vähän, korostuu opettajan rooli kielellisen oppimisympäristön luomisessa. Keskipitkän ja pitkän ruotsin opiskelijoiden välillä ei tutkimuksessa ilmene eroja asenteissa kieltä kohtaan.

Noncommutativity and Some of Its Present-Day Developments

This masters thesis explores some of the most recent developments in noncommutative quantum field theory. This old theme, first suggested by Heisenberg in the late 1940s, has had a renaissance during the last decade due to the firmly held belief that space-time becomes noncommutative at small distances and also due to the discovery that string theory in a background field gives rise to noncommutative field theory as an effective low energy limit. This has led to interesting attempts to create a noncommutative standard model, a noncommutative minimal supersymmetric standard model, noncommutative gravity theories etc. This thesis reviews themes and problems like those of UV/IR mixing, charge quantization, how to deal with the non-commutative symmetries, how to solve the Seiberg-Witten map, its connection to fluid mechanics and the problem of constructing general coordinate transformations to obtain a theory of noncommutative gravity. An emphasis has been put on presenting both the group theoretical results and the string theoretical ones, so that a comparison of the two can be made.

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.

Homoclinic Splitting without Trees

We study a Hamiltonian describing a pendulum coupled with several anisochronous oscillators, giving a simple construction of unstable KAM tori and their stable and unstable manifolds for analytic perturbations. When the coupling takes place through an even trigonometric polynomial in the angle variables, we extend analytically the solutions of the equations of motion, order by order in the perturbation parameter, to a large neighbourhood of the real line representing time. Subsequently, we devise an asymptotic expansion for the splitting (matrix) associated with a homoclinic point. This expansion consists of contributions that are manifestly exponentially small in the limit of vanishing gravity, by a shift-of-countour argument. Hence, we infer a similar upper bound for the splitting itself. In particular, the derivation of the result does not call for a tree expansion with explicit cancellation mechanisms.

Komplexa tal - vad är det?

Komplexa tal har traditionellt undervisats i de finländska gymnasierna som en valbar kurs. Denna situation har förändrats i och med de nya läroplanerna som tagits i bruk senast hösten 2005. Den nya, striktare läroplanen ger inte lika stora valmöjligheter för skolorna att bestämma undervisningsstoffet, inte ens för de valbara kurserna, och därför har många gymnasier varit tvungna att sluta undervisa om komplexa tal. För att fortsättningsvis ge en möjlighet för gymnasieelever att studera komplexa tal finns detta kompendium. Kompendiet fyller två syften. I de gymnasier där komplexa tal fortfarande finns med i läroplanen kan kompendiet användas som läromedel på ifrågavarande kurs. Kompendiet torde vara önskat eftersom det inte existerar något modernt, finlandssvenskt läromedel där de komplexa talen tas upp. Kompendiets andra, huvudsakliga syfte är att finnas till att ge en möjlighet för de elever, som inte går ett gymnasium där komplexa tal undervisas, att på egen hand lära sig grunder om komplexa tal. Kunskap om utvidgandet av talområdet från reella talen till komplexa hör till matematisk allmänbildning, och är till stor nytta om man är intresserad av att fortsätta studera matematik eller naturvetenskaper efter gymnasiet. Kompendiet kommer att läggas ut på nätet för att få det lättillgängligt. I det första kapitlet behandlas matematikens uppkomst. Det andra kapitlet är en introduktion till varför man behöver komplexa tal, där gås tal- och mängdlära igenom samtidigt som de i kompendiet använda beteckningarna introduceras. I det tredje kapitlet behandlas de komplexa talen; grundläggande räkneregler, absolutbelopp och argument, komplexa tal i polär form och lösning till högregradsekvationer är centrala begrepp. de Moivers formel är ett av de viktigare målen, även Eulers formel behandlas kort. Problematik med negativa kvadratrötter tas också upp. Det fjärde kapitlet handlar om de komplexa talens intressanta historia. I kompendiet finns rikligt med exempel och övningsuppgifter. Kapitel fem innehåller extra övningsuppgifter och i kapitel sex finns lösningarna till samtliga uppgifter. Trots att kompendiets omfång avsevärt ökas i och med dessa lösningar är det av värde att de finns med för att kompendiets huvudsakliga syfte skall uppfyllas: att eleverna på egen hand skall kunna lära sig stoffet.

Eru Ilúvatar : Jumala J.R.R. Tolkienin legendariumissa

The purpose of my research is to inquire into the essence and activity of God in the legendarium of the English philologist and writer J.R.R. Tolkien (1892-1973). The legendarium, composed of Tolkien’s writings related to Middle-earth, was begun when he created two Elvish languages, Quenya based on Finnish, Sindarin based on Welsh. Tolkien developed his mythology inspired by Germanic myths and The Kalevala. It is a fictional ancient history set in our world. The legendarium is monotheistic: God is called Eru ‘The One’ and Ilúvatar ‘Father of All’. Eru is the same as the Christian God, for Tolkien wanted to keep his tales consistent with his faith. He said his works were Christian by nature, with the religious element absorbed into the story and the symbolism. In The Silmarillion, set in the primeval ages of Middle-earth, the theological aspects are more conspicuous, while in The Lord of the Rings, which brings the stories to an end, they are mostly limited to symbolic references. The legendarium is unified by its realistic outlook on creaturely abilities and hope expressing itself as humbly defiant resistance. ”The possibility of complexity or of distinctions in the nature of Eru” is a part of the legendarium. Eru Ilúvatar is Trinitarian, as per Tolkien’s faith. Without contextual qualifiers, Eru seems to refer to God the Father, like God in the Bible. Being the creator who dwells outside the world is attributed to Him. The Holy Spirit is the only Person of the Trinity bestown with names: the Flame Imperishable and the Secret Fire. When Eru creates the material world with His word, He sends the Flame Imperishable to burn at the heart of the world. The Secret Fire signifies the Creative Power that belongs to God alone, and is a part of Him. The Son, the Word, is not directly mentioned, but according to one writing Eru must step inside the world in order to save it from corruption, yet remain outside it at the same time. The inner structure of the legendarium refers to the need for a future salvation. The creative word of Eru, “Eä! Let these things Be!”, probably has a connection with the Logos in Christianity. Thus we can find three “distinctions” in Eru: a Creator who dwells outside the world, a Sustainer who dwells inside it and a Redeemer who shall step inside it. Some studies of Tolkien have claimed that Eru is distant and remote. This seems to hold water only partially. Ilúvatar, the Father of All, has a special relation with the Eruhíni, His Children, the immortal Elves and the mortal Men. He communicates with them directly only through the Valar, who resemble archangels. Nevertheless, only the Children of Eru can fight against evil, because their tragic fortunes turn evil into good. Even though religious activities are scarce among them, the fundamental faith and ultimate hope of the “Free Peoples” is directed towards Eru. He is present in the drama of history as the “Author of the Story”, who at times also interferes with its course through catastrophes and eucatastrophes, ‘good catastrophes’. Eru brings about a catastrophe when evil would otherwise bring good to an end, and He brings about a eucatasrophe when creaturely strength is not sufficent for victory. Victory over corruption is especially connected with mortal Men, of whom the most (or least) insignificant people are the Hobbits. However, because of the “primeval disaster” (that is, fall) of Mankind, ultimate salvation can only remain open, a hope for the far future.