DOCSLIB.ORG

Research Article Conformal Mappings in Relativistic Astrophysics

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Research Article Conformal Mappings in Relativistic Astrophysics Hindawi Publishing Corporation Journal of Applied Mathematics Volume 2013, Article ID 196385, 12 pages http://dx.doi.org/10.1155/2013/196385 Research Article Conformal Mappings in Relativistic Astrophysics S. Hansraj, K. S. Govinder, and N. Mewalal Astrophysics and Cosmology Research Unit, School of Mathematics, University of KwaZulu-Natal, Private Bag X54001, Durban 4000, South Africa Correspondence should be addressed to K. S. Govinder; [email protected] Received 1 March 2013; Accepted 10 June 2013 Academic Editor: Md Sazzad Chowdhury Copyright © 2013 S. Hansraj et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We describe the use of conformal mappings as a mathematical mechanism to obtain exact solutions of the Einstein field equations in general relativity. The behaviour of the spacetime geometry quantities is given under a conformal transformation, and the Einstein field equations are exhibited for a perfect fluid distribution matter configuration. The field equations are simplified andthenexact static and nonstatic solutions are found. We investigate the solutions as candidates to represent realistic distributions of matter. In particular, we consider the positive definiteness of the energy density and pressure and the causality criterion, as well as the existence of a vanishing pressure hypersurface to mark the boundary of the astrophysical fluid. 1. Introduction By considering the case of a uniform density sphere, Schwarzschild [3]foundauniqueinteriorsolution.However, The gravitational evolution of celestial bodies may be mod- the problem of finding all possible solutions for a nonconstant eled by the Einstein field equations. These are a system of energy density is still an open problem. Since the system of ten highly coupled partial differential equations expressing field equations is underdetermined, one of the geometric or an equivalence between matter and geometry. The equations dynamical variables must be specified at the outset. This free- are extremely difficult to solve in general and so simpler cases dom of choice renders it impractical to determine all possible have to be treated to gain an understanding into how certain solutions. A comprehensive review of the static spherically typesofmatterbehaveundertheinfluenceofthegravitational symmetric fluid sphere has been compiled by Delgaty and field. For example, the most studied configuration of a matter Lake [4]. Recent work by Fodor [5], Martin and Visser [6], distribution is that of a static spherically symmetric perfect Lake [7], Boonserm et al. [8], and Rahman and Visser [9], fluid. The assumption of spherical symmetry has the effect of whichresuscitatedanideafirstproposedbyWyman[10], reducing the field equations to a system of three equations in reported algorithms for finding all possible exact solutions. four unknowns if the matter is neutral. While this is a severe, However, each prescription required an integration or two but reasonable, restriction, even in this case not all solutions which may be intractable in practice given that a certain to the system of field equations have been found. Work on variablehadtobeselectedinsomeadhocfortuitousway. this problem has been ongoing since the first exact solution In any event, even if solutions to the field equations are appeared in 1916 when Karl Schwarzschild published his found, they have to satisfy certain physical requirements to solution for a vacuum (matter free), and, to the present, this be considered candidates for realistic matter. Finch and Skea exterior solution continues to be used to model phenomena [11] studied over 100 exact solutions and have found that only such as black holes. This solution is unique, and, moreover, about16satisfythemostelementaryphysicalrequirements. Birkhoff [1] showed that the solution is independent of It should be remarked that the importance of some of the whether the sphere is static or not. In other words, the so called requirements for physical plausibility is debatable Schwarzschild exterior solution [2] is simply a consequence given that the gravitational processes inside a star may not be of the spherical geometry. From this theorem also follows accurately determined. the conclusion that pulsating fluid spheres do not generate If spherical symmetry is maintained and if, in addition, gravitational waves. the matter distribution contained charge, then the Einstein 2 Journal of Applied Mathematics field equations must be supplemented by Maxwell’s equations Table 1 which incorporate the effects of the electromagnetic field. (1) =0 X is a Killing vector These Einstein-Maxwell equations constitute a set of six field (2) ; =0≠ X is a homothetic Killing vector equations in four unknowns. In this case, the problem is =0≠ simplerasnowtwoofthematterorgeometricalquantities (3) ; ; X is a special conformal Killing vector =0̸ must be chosen at the beginning and the remaining four (4) ; X is a nonspecial conformal Killing vector will follow from the integration of the field equations. A detailed collection of the two-variable choices that have been considered has been achieved by Ivanov [12]. The caveat is approach has to do with the fact that the existence of confor- that, although there is an extra degree of freedom, finding mal Killing vectors is known to simplify the field equations— physically palatable solutions is extremely rare. Addition- in other words, they involve a geometric constraint. This is in ally,itisrequiredthattheexactsolutionfortheinterior opposition to an algebraic constraint which may be imposed, be matched with the unique exterior solution for charged for example, by demanding that the eigenvectors of the Weyl spheres according to Reissner [13] and Nordstrom [14]. The tensor have certain preferred alignments. This gives rise to the solution of Hansraj and Maharaj [15]intheformofBessel Petrov [21] classification scheme which in reality is a result in functions of half integer order was shown to satisfy ele- pure mathematics applicable to any Lorentzian manifold. In mentary physical requirements. Other matter configurations our approach, the procedure is aided by the Defrise-Carter include radiation and rotation. In each case a unique exterior [22] theorem which specifies how conformal Killing vectors solution has been found—the exterior metric for a radiating become Killing vectors under conformal transformations. star is credited to Vaidya [16], while an exterior metric for The theorem states the following: suppose that a manifold (, ) a rotating sphere was constructed by Kerr [17]. While in the g is neither conformally flat nor conformally related to case of radiating spheres many interior solutions have been a generalised plane wave. Then, a Lie algebra of conformal found, this is not the case for a rotating sphere. The problem Killing vectors on with respect to g can be regarded as a of finding a solution to the Einstein field equations that Lie algebra of Killing vectors with regard to some metric on incorporate rotations is still unsolved problem in classical conformally related to g [23]. general relativity. The benefit of utilising this approach is that we may utilise The mathematical approach described earlier often relies a known exact solution of the Einstein field equations and on choosing functional forms for some of the variables that then solve the associated conformally related equations. This eventually allow for the integration of the entire system of is because the conformal Einstein tensor splits neatly into the differential equations. Fortunately, the analysis is simplified original Einstein tensor and a conformally related part. So, by the fact that a single master equation holds the key to for example, if one begins with a vacuum seed solution, then unlocking the whole system. This master equation may be it is known that the Einstein tensor is zero and so only the interpreted as a second-order linear differential equation conformal part must now be considered in conjunction with (see Duorah and Ray [18], Durgapal and Bannerji [19], and a perfect fluid energy momentum tensor. Such solutions are Finch and Skea [20]) or as a first-order Ricatti equation referred to as conformally Ricci-flat spacetimes. This scheme (for example, see Lake [7]andFodor[5]). Once a solution has yielded useful results. A pioneering work on this method is found, then the physical and geometric quantities must was conducted by van den Bergh [24, 25], and, recently be established and checked for physical plausibility. An Castejon-Amenedo´ and Coley [26]andHansrajetal.[27] alternative approach is to impose some physical constraints a found new classes of exact solutions that were nonstatic. In priori, for example, to prescribe an equation of state relating fact, the fluid congruences were found to be accelerating, the pressure and energy density. However, the drawback of shearing, and expanding, which is a category of solution types this approach is that the field equations may not be solvable. that is rare. Hansraj [28] analysed the conjecture of van den Only a few solutions of this kind have been reported in the Bergh [24] that perfect fluid spacetimes can be found by using literature. Interestingly, the charged analogue of the Finch- the nonconformally flat Schwarzschild exterior solution. It Skea [20] stars reported by Hansraj and Maharaj [15]turned was proved that all such
Load more

Recommended publications
  • Gravitational Decoupling in Higher Order Theories
    S S symmetry Article Gravitational Decoupling in Higher Order Theories Joseph Sultana Department of Mathematics, Faculty of Science, University of Malta, MSD 2080 Msida, Malta; [email protected] Abstract: Gravitational decoupling via the Minimal Geometric Deformation (MGD) approach has been used extensively in General Relativity (GR), mainly as a simple method for generating exact anisotropic solutions from perfect fluid seed solutions. Recently this method has also been used to generate exact spherically symmetric solutions of the Einstein-scalar system from the Schwarzschild vacuum metric. This was then used to investigate the effect of scalar fields on the Schwarzschild black hole solution. We show that this method can be extended to higher order theories. In particular, we consider fourth order Einstein–Weyl gravity, and in this case by using the Schwarzschild metric as a seed solution to the associated vacuum field equations, we apply the MGD method to generate a solution to the Einstein–Weyl scalar theory representing a hairy black hole solution. This solution is expressed in terms of a series using the Homotopy Analysis Method (HAM). Keywords: Einstein–Weyl gravity; gravitational decoupling; black holes 1. Introduction Obtaining exact physically relevant solutions of Einstein’s field equations is by no means a straightforward task. The spherically symmetric perfect fluid analytic solutions of Einstein’s equations have been derived and analyzed in detail [1,2]. However, as soon as Citation: Sultana, J. Gravitational one relaxes the assumption of a perfect fluid source and considers more realistic sources, Decoupling in Higher Order Theories. then the problem of finding analytic solutions becomes intractable.
    [Show full text]
  • Axisymmetric Spacetimes in Relativity
    9, tr' Axisymmetric Spacetimes in Relativity S. P. Drake Department of Physics and Mathematical Physics îåäi,î31 tÏfåi" Australia 22 July 1998 ACKNO\MTEDGEMENTS It is an unfortunate fact that only my name Soes on this thesis' This is not the work of one person, it is an accumulation of the labor of many' AII those who have helped me in ways that none of us could image should be acknowledged, but how. None of this would have been possible were it not for the wisdom and guidance of my supervisor Peter Szekeres. I have often pondered over the difficulty of supervising students. It must be heart-bleaking to watch as students make necessary mistakes. Patience I'm sure must be the key' So for his wisdom, patience and kindness I am deeply indebted to Peter Szekeres. Without the love and support of my family this thesis would never have begun, much less been completed, to them I owe my life, and all that comes with it. It would take too long to write the names of all those I wish to thank. Those who are special to me, have helped me through so much over the years will receive the thanks in Person. I would like to the department of physics here at Adelaide where most of my thesis work was done. I would like to thank the department of physics at Melbourne university, where I did my undergraduate degree and began my PhD. I would like to thank the university of Padova for there hospitality dur- ing my stay there.
    [Show full text]
  • General Relativistic Static Fluid Solutions with Cosmological Constant
    General Relativistic Static Fluid Solutions with Cosmological Constant Diplomarbeit von Christian G. B¨ohmer aus Berlin eingereicht bei der Mathematisch-Naturwissenschaftlichen Fakult¨at der Universit¨at Potsdam arXiv:gr-qc/0308057v3 4 Feb 2006 durchgefuhrt¨ am Max-Planck-Institut fur¨ Gravitationsphysik - Albert-Einstein-Institut - in Golm unter Anleitung von Prof. Dr. Bernd G. Schmidt Contents 1 Introduction 3 2 Cosmological TOV equation 7 2.1 TheCosmologicalConstant . 7 2.2 Remarks on the Newtonian limit . 8 2.3 TOV-Λequation ......................... 8 2.4 Schwarzschild-anti-de Sitter and Schwarzschild-de Sitter so- lution ............................... 11 2.5 Newtonianlimits ......................... 13 2.5.1 Limit of Schwarzschild-anti-de Sitter and Schwarzschild- deSittermodels ..................... 13 2.5.2 Limit of the TOV-Λ equation . 13 3 Solutions with constant density 15 3.1 Spatial geometry of solutions . 16 3.2 Solutions with negative cosmological constant . 17 3.2.1 Stellar models with spatially hyperbolic geometry . 18 3.2.2 Joining interior and exterior solution . 20 3.2.3 Stellar models with spatially Euclidean geometry . 22 3.2.4 Stellar models with spatially spherical geometry . 24 3.3 Solutions with vanishing cosmological constant . 27 3.4 Solutions with positive cosmological constant . 28 3.4.1 Stellar models with spatially spherical geometry . 28 3.4.2 Solutions with exterior Nariai metric . 31 3.4.3 Solutions with decreasing group orbits at the boundary 33 3.4.4 Decreasing solutions with two regular centres . 35 3.4.5 The Einstein static universe . 37 3.4.6 Increasing solutions with two regular centres . 38 3.4.7 Solutions with geometric singularity .
    [Show full text]
  • Generalized Relativistic Anisotropic Compact Star Models by Gravitational Decoupling
    Eur. Phys. J. C (2019) 79:85 https://doi.org/10.1140/epjc/s10052-019-6602-1 Regular Article - Theoretical Physics Generalized relativistic anisotropic compact star models by gravitational decoupling S. K. Maurya1,a, Francisco Tello-Ortiz2,b 1 Department of Mathematics and Physical Science, College of Arts and Science, University of Nizwa, Nizwa, Sultanate of Oman 2 Departamento de Física, Facultad de ciencias básicas, Universidad de Antofagasta, Casilla 170, Antofagasta, Chile Received: 29 November 2018 / Accepted: 15 January 2019 / Published online: 29 January 2019 © The Author(s) 2019 Abstract In this work we have extended the Maurya-Gupta main ingredient of this scheme is to add an extra source to isotropic fluid solution to Einstein field equations to an aniso- the energy momentum tensor of a spherically symmetric and tropic domain. To do so, we have employed the gravitational static spacetime through a dimensionless constant β decoupling via the minimal geometric deformation approach. m = ˜ m + βθm, The present model is representing the strange star candidate Tn Tn n (1) LMC X-4. A mathematical, physical and graphical analy- ˜ m sis, shown that the obtained model fulfills all the criteria where Tn represents a perfect fluid matter distribution and θ m to be an admissible solution of the Einstein field equations. n is the extra source which encodes the anisotropy and Specifically, we have analyzed the regularity of the metric can be formed by scalar, vector or tensor fields. It is worth ˜ m potentials and the effective density, radial and tangential pres- mentioning that Tn does not necessarily should corresponds sures within the object, causality condition, energy condi- to a perfect fluid, in fact it can describes, for example, an tions, equilibrium via Tolman–Oppenheimer–Volkoff equa- anisotropic fluid, a charged fluid, etc.
    [Show full text]
  • An Algorithm to Generate Anisotropic Rotating Fluids with Vanishing Viscosity
    An algorithm to generate anisotropic rotating fluids with vanishing viscosity Stefano Viaggiu∗1,2,3 1Dipartimento di Fisica Nucleare, Subnucleare e delle Radiazioni, Universit´adegli Studi Guglielmo Marconi, Via Plinio 44, I-00193 Rome, Italy 2Dipartimento di Matematica, Universit`adi Roma “Tor Vergata”, Via della Ricerca Scientifica, 1, I-00133 Roma, Italy. 3INFN, Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Via Cintia Edificio 6, 80126 Napoli, Italy. December 31, 2018 Abstract Starting with generic stationary axially symmetric spacetimes de- pending on two spacelike isotropic orthogonal coordinates x1, x2, we build anisotropic fluids with and without heat flow but with wanish- ing viscosity. In the first part of the paper, after applying the trans- formation x1 J(x1), x2 F (x2)(with J(x1), F (x2) regular func- → → 1 2 1 2 tions) to general metrics coefficients gab(x , x ) gab(J(x ), F (x )) → with Gx1x2 = 0, being Gab the Einstein’s tensor, we obtain that 1 2 G˜x1x2 = 0 Gx1x2 (J(x ), F (x )) = 0. Therefore, the transformed arXiv:1811.00769v2 [gr-qc] 27 Dec 2018 → spacetime is endowed with an energy-momentum tensor Tab with ex- pression gabQi + heat term (where gab is the metric and Qi ,i =1..4 are functions depending on the physical parameters of the{ fluid),} i.e. without viscosity and generally with a non-vanishing heat flow. We show that after introducing suitable coordinates, we can obtain in- terior solutions that can be matched to the Kerr one on spheroids or Cassinian ovals, providing the necessary mathematical machinery. In the second part of the paper we study the equation involving the heat flow and thus we generate anisotropic solutions with vanishing ∗[email protected] and [email protected] 1 heat flow.
    [Show full text]
  • Invariant Construction of Cosmological Models Erik Jörgenfelt
    Invariant Construction of Cosmological Models Erik Jörgenfelt Spring 2016 Thesis, 15hp Bachelor of physics, 180hp Department of physics Abstract Solutions to the Einstein field equations can be constructed from invariant objects. If a solution is found it is locally equivalent to all solutions constructed from the same set. Here the method is applied to spatially-homogeneous solutions with pre-determined algebras, under the assumption that the invariant frame field of standard vectors is orthogonal on the orbits. Solutions with orthogonal fluid flow of Bianchi type III are investigated and two classes of orthogonal dust (zero pressure) solutions are found, as well as one vacuum energy solution. Tilted dust solutions with non-vanishing vorticity of Bianchi types I–III are also investigated, and it is shown that no such solution exist given the assumptions. Sammanfattning Lösningar till Einsteins fältekvationer kan konstrueras från invarianta objekt. Om en lösning hittas är den lokalt ekvivalent till alla andra lösningar konstruerade från samma mängd. Här appliceras metoden på spatialt homogena lösningar med förbestämda algebror, under anta- gandet att den invarianta ramen med standard-vektorer är ortogonal på banorna. Lösningar med ortogonalt fluidflöde av Bianchi typ III undersöks och två klasser av dammlösningar (noll tryck) hittas, liksom en vakum-energilösning. Dammlösningar med lut och noll-skild vorticitet av Bianchi typ I–III undersöks också, och det visas att inga sådana lösningar existerar givet antagandena. Contents 1 Introduction 1 2 Preliminaries 3 2.1 Smooth Manifolds...................................3 2.2 The Tangent and Co-tangent Bundles........................4 2.3 Tensor Fields and Differential Forms.........................6 2.4 Lie Groups......................................
    [Show full text]
  • Full Abstract Booklet
    21st International Conference on General Relativity and Gravitation Columbia University in the City of New York July 10th - 15th, 2016 ii Contents Session A1 1 A group theoretic approach to shear-free radiating stars (Gezahegn Zewdie Abebe)................................... 1 Separable metrics and radiating stars (Gezahegn Zewdie Abebe) . 1 Lie point symmetries, vacuum Einstein equations, and Ricci solitons (Mo- hammad Akbar).............................. 2 Open Access Non-Linear Electrodynamics Gedanken Experiment for Mod- ified Zero Point Energy and Planck's Constant, h Bar, in the Begin- ning of Cosmological Expansion, So h(Today) = h(Initial). (Andrew Beckwith) ................................. 2 Solving the Einstein-Maxwell Equations for the Propagation of Relativistic Energy during Kasner and other Anisotropic Early-Universe Models (Brett Bochner).............................. 3 Ergosphere of the Born-Infeld black hole (Nora Breton)........... 3 Elastic waves in spherically symmetric elastic spacetimes (Irene Brito,Jaume Carot, and Estelita Vaz)......................... 3 Cylindrically symmetric inhomogeneous dust collapse (Irene Brito, M. F. A. Da Silva, Filipe C. Mena and N. O. Santos)............ 4 Did GW150914 produce a rotating gravastar? (Cecilia Chirenti) . 4 The Inverse spatial Laplacian of spherically symmetric backgrounds (Karan Fernandes) ................................ 4 Coordinate families for the Schwarzschild geometry based on radial timelike geodesics (Tehani Finch)......................... 5 Rotating black hole
    [Show full text]
  • Symmetries in General Relativity
    Symmetries in General Relativity Contents 1. Topics 1205 2. Participants 1207 2.1. ICRANet participants . 1207 2.2. Past collaborators . 1207 2.3. Ongoing collaborations . 1208 2.4. Students . 1208 3. Brief description 1209 3.1. Spacetime splitting techniques in General Relativity . 1209 3.1.1. “1+3” splitting of the spacetime . 1209 3.1.2. Measurement process in general relativity . 1210 3.2. Motion of particles and extended bodies in general relativity . 1210 3.2.1. Test particles . 1211 3.2.2. Spinning test particles . 1212 3.2.3. Particles with both dipolar and quadrupolar structure (Dixon’s model) . 1212 3.2.4. Exact solutions representing extended bodies with quadrupo- lar structure . 1213 3.3. Perturbations . 1213 3.3.1. Curvature and metric perturbations in algebraically spe- cial spacetimes . 1213 3.3.2. Curvature perturbations in type D spacetimes . 1214 3.3.3. Metric perturbations in a Reissner-Nordstrom¨ spacetime 1214 3.3.4. Curvature perturbations due to spinning bodies on a Kerr background . 1215 3.3.5. Metric perturbations due to spinning bodies on a Schwarzschild background . 1215 3.3.6. Gravitational Self-force and Effective-One-Body model: synergies . 1215 3.4. Cosmology . 1216 3.4.1. Mixmaster universe and the spectral index . 1216 3.4.2. Wave equations in de Sitter spacetime . 1216 3.4.3. Fluids obeying non-ideal equations of state . 1216 1203 Contents 4. Publications (2011 { 2016) 1219 A. Spacetime splitting techniques in general relativity 1255 A.1. Observer-orthogonal splitting . 1257 A.1.1. The measurement process . 1258 A.2. Examples . 1259 A.3.
    [Show full text]
  • Arxiv:2006.07418V1 [Gr-Qc]
    Turning a Newtonian analogy for FLRW cosmology into a relativistic problem Valerio Faraoni1, ∗ and Farah Atieh1, † 1Department of Physics and Astronomy, Bishop’s University, 2600 College Street, Sherbrooke, Qu´ebec, Canada J1M 1Z7 A Newtonian uniform ball expanding in empty space constitutes a common heuristic analogy for FLRW cosmology. We discuss possible implementations of the corresponding general-relativistic problem and a variety of new cosmological analogies arising from them. We highlight essential ingredients of the Newtonian analogy, including that the quasilocal energy is always “Newtonian” in the sense that the magnetic part of the Weyl tensor does not contribute to it. A symmetry of the Einstein-Friedmann equations produces another one in the original Newtonian system. I. INTRODUCTION also radial null geodesics, for which the analogous Fried- mann equation provides the empty Milne universe. This A Newtonian analogy is often used to introduce “easy” way to derive an analogy has significant limita- Friedmann-Lemaˆıtre-Robertson-Walker (FLRW) cosmol- tions, which are discussed below. However, it can be ogy to beginners and provide physical intuition (e.g., [1– generalized to many static and spherically symmetric ge- 4]—see [5] for a different version). The analogy is based ometries, producing a host of new cosmological analogies. on a ball of uniform density expanding in empty space The second, and proper, way to address the problem and on conservation of energy for a test particle on the consists of looking for exact solutions of the Einstein surface of this ball. The Newtonian energy conservation equation that are spherically symmetric, time-dependent, equation is formally analogous to the Friedmann equa- and asymptotically flat and are sourced by a ball of per- tion of relativistic cosmology for a universe filled with a fect fluid with uniform density and pressure, expanding perfect fluid with zero pressure (a dust).
    [Show full text]
  • Rainich-Type Conditions for Perfect Fluid Spacetimes
    Rainich-type Conditions for Perfect Fluid Spacetimes Synopsis • We describe and illustrate a relatively simple set of new Rainich-type conditions on an n-dimensional spacetime which are necessary and sufficient for it to define a perfect fluid solution of the Einstein field equations [1]. • Procedures are provided which implement these Rainich-type conditions and which reconstruct the perfect fluid from the metric. • These results provide an example of the idea of geometrization of matter fields in general relativity, which is a purely geometrical characterization of matter fields via the Einstein field equations. Analogous commands pertaining to the geometrization of non-null electromagnetic fields are RainichConditions and RainichElectromagneticField. • For a relatively complicated alternative approach using scalar invariants and which is valid in four dimensions, see [2]. • For an alternative approach which treats thermodynamic fluids in four dimensions, see [3]. Theory a a b • Let M, g be an n-dimensional spacetime, n > 2. Let u be a timelike unit vector field, gabu u =K1, and let µ : M/R and p : M/R be functions. The Einstein equations for a perfect fluid take the form 1 R K g R = µ C p u u C p g , ab 2 ab a b ab where Rab is the Ricci tensor of gaband R is the Ricci scalar. Note that a cosmological constant L can be incorporated into these field equations with the substitution µ / µ C L p / p K L . • Geometrization of the perfect fluid is achieved by uncovering necessary and sufficient conditions on the metric g such that a there exists µ, p, u obeying the perfect fluid Einstein equations.
    [Show full text]
  • Matter Models in General Relativity with a Decreasing Number of Symmetries
    Charles University in Prague Faculty of Mathematics and Physics DOCTORAL THESIS Norman Gürlebeck Matter Models in General Relativity with a Decreasing Number of Symmetries Institute of Theoretical Physics Supervisor of the doctoral thesis: Prof. RNDr. Jiří Bičák, DrSc., dr.h.c. Study program: Physics Specialization: Theoretical physics, astronomy and astrophysics Prague, 2011 Acknowledgements First, I am much obliged to my supervisor Jiří Bičák. With his deep understanding of physics, he was a constant help. Additionally, I always enjoyed and benefited from his crash courses in Czech arts and culture. I am greatly indebted to David Petroff. He is a splendid colleague and friend. With his deliberate and candid manner, discussions could take surprising turns providing insights beyond physics. I also thank his family, which received me several times so warmly in their home. I thank Jörg Frauendiener and Tomáš Ledvinka for agreeing to be the reviewers of my thesis. Furthermore, I thank the colleagues at the institute for creating a nice working atmosphere. All of them and especially Tomáš Ledvinka, Otakar Svítek and Martin Žofka had always an open ear for my question and were never short of helpful remarks. I sincerely appreciate the constant work of Jiří Horáček and Oldřich Semerak that kept my funding going like the Grant No. GAUK 22708. I was also financially supported by the Grant No. GAČR 205/09/H033. The friendship of Ivan Pshenichnyuk, Martin Scholtz and of the spaceship crew Otakar Svítek and Martin Žofka was a big support in the last years (even though we did not meet with success in all space missions).
    [Show full text]
  • Approximate Metric for a Rotating Deformed Mass
    International Journal of Astronomy and Astrophysics, 2015, 5, 1-10 Published Online March 2015 in SciRes. http://www.scirp.org/journal/ijaa http://dx.doi.org/10.4236/ijaa.2015.51001 Approximate Metric for a Rotating Deformed Mass Francisco Frutos-Alfaro1, Paulo Montero-Camacho1, Miguel Araya1, Javier Bonatti-González2 1Space Research Center and School of Physics, University of Costa Rica, San José, Costa Rica 2Nuclear Research Center and School of Physics, University of Costa Rica, San José, Costa Rica Email: [email protected] Received 11 February 2015; accepted 1 March 2015; published 4 March 2015 Copyright © 2015 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/ Abstract A new Kerr-like metric with quadrupole moment is obtained by means of perturbing the Kerr spacetime. The form of this new metric is simple as the Kerr metric. By comparison with the exte- rior Hartle-Thorne metric, it is shown that it could be matched to an interior solution. This ap- proximate metric may represent the spacetime of a real astrophysical object with any Kerr rota- tion parameter a and slightly deformed. Keywords Approximate Solutions of Einstein Equations, Kerr Metric, Erez-Rosen Metric, Quadrupole 1. Introduction In 1963, R. P. Kerr [1] proposed a metric that describes a massive rotating object. Since then, a huge amount of papers about the structure and astrophysical applications of this spacetime appeared. Now, it is widely believed that this metric does not represent the spacetime of a rotating astrophysical object.
    [Show full text]