| 1. |
- Jonsson, Rickard, 1973
(författare)
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A covariant formalism of spin precession with respect to a reference congruence
- 2006
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Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 23:1, s. 37-59
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Tidskriftsartikel (refereegranskat)abstract
- We derive an effectively three-dimensional relativistic spin precession formalism. The formalism is applicable to any spacetime where an arbitrary timelike reference congruence of worldlines is specified. We employ what we call a stopped spin vector which is the spin vectorthat we would get if we momentarily make a pure boost of the spin vector to stop it relative to the congruence. Starting from the Fermi transport equation for the standard spin vector we derive a corresponding transport equation for the stopped spin vector. Employing a spacetime transport equation for a vector along a worldline, corresponding to spatial parallel transport with respect to the congruence, we can write down a precession formula for a gyroscope relative to the local spatial geometry defined by the congruence. This general approach has already been pursued by Jantzen et al (see e.g. Jantzen R T, Carini P and Bini D 1992 Ann. Phys. 215 1-50), but the algebraic form of our respective expressions differs. We are also applying the formalism to a novel type of spatial parallel transport introduced in Jonsson (2006 Class. Quantum Grav. 23 1), as well as verifying the validity of the intuitive approach of aforthcoming paper (Jonsson 2006 forthcoming) where gyroscope precession is explained entirely as a double Thomas type of effect. We also present the resulting formalism in explicit three-dimensional form (using the boldface vector notation), and give examples of applications.
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| 2. |
- Jonsson, Rickard, 1973
(författare)
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An intuitive approach to inertial forces and the centrifugal force paradox in general relativity
- 2006
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Ingår i: American Journal of Physics. - : American Association of Physics Teachers (AAPT). - 0002-9505 .- 1943-2909. ; 74:10, s. 905-916
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Tidskriftsartikel (refereegranskat)abstract
- As the velocity of a rocket in a circular orbit near a black hole increases, the outwardly directed rocket thrust must increase to keep the rocket in its orbit. This feature might appear paradoxical from a Newtonian viewpoint, but we show that it follows naturally from the equivalence principle together with special relativity and a few general features of black holes. We also derive a general relativistic formalism of inertial forces for reference frames with acceleration and rotation. The resulting equation relates the real experienced forces to the time derivative of the speed and the spatial curvature of the particle trajectory relative to the reference frame. We show that an observer who follows the path taken by a free (geodesic) photon will experience a force perpendicular to the direction of motion that is independent of the observer's velocity. We apply our approach to resolve the submarine paradox, which regards whether a submerged submarine in a balanced state of rest will sink or float when given a horizontal velocity if we take relativistic effects into account. We extend earlier treatments of this topic to include spherical oceans and show that for the case of the Earth the submarine floats upward if we take the curvature of the ocean into account.
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| 3. |
- Jonsson, Rickard, 1973, et al.
(författare)
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Generalizing optical geometry
- 2006
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Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 23:1, s. 61-76
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Tidskriftsartikel (refereegranskat)abstract
- We show that by employing the standard projected curvature as a measure of spatial curvature, we can make a certain generalization of optical geometry (Abramowicz M A and Lasota J-P 1997 Class. Quantum Grav. A 14 23-30). This generalization applies to any spacetime that admits a hypersurface orthogonal shearfree congruence of worldlines. This is a somewhat larger class of spacetimes than the conformally static spacetimes assumed in standard optical geometry. In the generalized optical geometry, which in the generic case is time dependent, photons move with unit speed along spatial geodesics and the sideways force experienced by a particle following a spatially straight line is independent of the velocity. Also gyroscopes moving along spatial geodesics do not precess (relative to the forward direction). Gyroscopes that follow a curved spatial trajectory precess according to a very simple law of three-rotation. We also present an inertial force formalism in coordinate representation for this generalization. Furthermore, we show that by employing a new sense of spatial curvature (Jonsson R 2006 Class. Quantum Grav. 23 1)) closely connected to Fermat's principle, we can make a more extensive generalization of optical geometry that applies to arbitrary spacetimes. In general this optical geometry will be time dependent, but still geodesic photons move with unit speed and follow lines that are spatially straight in the new sense. Also, the sideways experienced (comoving) force on a test particle following a line that is straight in the new sense will be independent of the velocity.
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| 4. |
- Jonsson, Rickard, 1973
(författare)
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Gravity Illustrated. Spacetime Edition
- 2004
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis deals with essentially four different topics within general relativity: pedagogical techniques for illustrating curved spacetime, inertial forces, gyroscope precession and optical geometry. Concerning the pedagogical techniques, I investigate two distinctly different methods, the dual and the absolute method. In the dual scheme, I start from the geodesic equation in a 1+1 static, diagonal, Lorentzian spacetime, such as the Schwarzschild radial line element. I then find another metric, with Euclidean signature, which produces the same geodesics x(t). This geodesically equivalent dual metric can be embedded in ordinary Euclidean space. Freely falling particles correspond to straight lines on the embedded surface. In the absolute scheme, I start from an arbitrary Lorentzian spacetime with a given field of timelike four-velocities uμ. I then perform a coordinate transformation to the local Minkowski system comoving with the given four-velocity at every point. In the local system the sign of the spatial part of the metric is flipped to create a new metric of Euclidean signature. For the particular case of two dimensions we may embed this absolute geometry as a curved surface. The method is well suited for visualizing gravitational time dilation, cosmological expansion and black holes. Concerning inertial forces, gyroscope precession and optical geometry, the general framework is based on the introduction of a congruence of reference worldlines in an arbitrary spacetime. This allows us to describe the local motion and acceleration of particles in terms of the speed relative to the congruence, the time derivative of the speed and the spatial curvature (project down along the reference congruence) of the corresponding worldline. I present two papers concerning inertial forces in this framework, one formal and one intuitive. I also present two papers concerning gyroscope precession, again one formal and one intuitive. In particular I illustrate how one can explain gyroscope precession in an arbitrary stationary spacetime as a double Thomas precession effect. Introducing a novel type of spatial curvature measure for the worldline of a test particle, we present a natural way of generalizing the theory of optical geometry to include arbitrary spacetimes. The generalized optical geometry allows us to do optical geometry across the horizon of a black hole.
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| 5. |
- Jonsson, Rickard, 1973
(författare)
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Gyroscope precession in special and general relativity from basic principles
- 2007
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Ingår i: American Journal of Physics. - : American Association of Physics Teachers (AAPT). - 0002-9505 .- 1943-2909. ; 75:5, s. 463-471
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Tidskriftsartikel (refereegranskat)abstract
- In special relativity a gyroscope that is suspended in a torque-free manner will precess as it is moved along a curved path relative to an inertial frame S. We explain this effect, which is known as Thomas precession, by considering a real grid that moves along with the gyroscope, and that by definition is not rotating as observed from its own momentary inertial rest frame. From the basic properties of the Lorentz transformation we deduce how the form and rotation of the grid (and hence the gyroscope) will evolve relative to S. As an intermediate step we consider how the grid would appear if it were not length contracted along the direction of motion. We show that the uncontracted grid obeys a simple law of rotation. This law simplifies the analysis of spin precession compared to more traditional approaches based on Fermi transport. We also consider gyroscope precession relative to an accelerated reference frame and show that there are extra precession effects that can be explained in a way analogous to the Thomas precession. Although fully relativistically correct, the entire analysis is carried out using three-vectors. By using the equivalence principle the formalism can also be applied to static spacetimes in general relativity. As an example, we calculate the precession of a gyroscope orbiting a static black hole. (C) 2007 American Association of Physics Teachers.
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| 6. |
- Jonsson, Rickard, 1973
(författare)
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Inertial forces and the foundations of optical geometry
- 2006
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Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 23:1, s. 1-36
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Tidskriftsartikel (refereegranskat)abstract
- Assuming a general timelike congruence of worldlines as a reference frame, we derive a covariant general formalism of inertial forces in general relativity. Inspired by the works of Abramowicz et al (see e.g. Abramowicz and Lasota 1997 Class. Quantum Grav. 14 A23-30), we also study conformal rescalings of spacetime and investigate how these affect the inertial force formalism. While many ways of describing spatial curvature of a trajectory have been discussed in papers prior to this, one particular prescription (which differs from the standard projected curvature when the reference congruence is shearing), appears novel. For the particular case of a hypersurface-forming congruence, using a suitable rescaling of spacetime, we show that a geodesic photon always follows a line that is spatially straight with respect to the new curvature measure. This fact is intimately connected to Fermat's principle, and allows for a certain generalization of the optical geometry as will be further pursued in a companion paper (Jonsson and Westman 2006 Class. Quantum Grav. 23 61). For the particular case when the shear tensor vanishes, we present the inertial force equation in a three-dimensional form (using the bold-face vector notation), and note how similar it is to its Newtonian counterpart. From the spatial curvature measures that we introduce, we derive corresponding covariant differentiations of a vector defined along a spacetime trajectory. This allows us to connect the formalism of this paper to that of Jantzen and co-workers (see e.g. Bini et al 1997 Int. J. Mod. Phys. D 6 143-98).
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| 7. |
- Jonsson, Rickard, 1971-, et al.
(författare)
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Making the threatening other laughable : Ambiguous performances of urban vernaculars in Swedish media
- 2020
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Ingår i: Language & Communication. - : Elsevier BV. - 0271-5309 .- 1873-3395. ; 71, s. 1-15
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Tidskriftsartikel (refereegranskat)abstract
- The threatening young man who speaks Rinkeby Swedish has become a culturally recognizable ‘figure of personhood’ (Agha, 2007) of linguistic and ethnic otherness in Sweden. Drawing upon Billig's theory of humour, we illustrate how this characterological persona is not monolithic; nor does it remain uncontested but is constantly being (re)negotiated in the media. By drawing attention to those humorous performances that rhetorically make fun of entrenched stereotypes, the article explores the subversive, as well as disciplinary, potentials of this kind of humour. Read together, the examples in this article indicate that the ‘exemplary speaker’ (Androutsopoulos, 2016) of Swedish contemporary urban vernaculars can be laughed at and with but cannot easily be fixed into a unified homogenous figure.
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| 8. |
- Jonsson, Rickard, 1973
(författare)
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Optical geometry across the horizon
- 2006
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Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 23:1, s. 77-89
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Tidskriftsartikel (refereegranskat)abstract
- In a recent paper (Jonsson and Westman 2006 Class. Quantum Grav. 23 61), a generalization of optical geometry, assuming a non-shearing reference congruence, is discussed. Here we illustrate that this formalism can be applied to (a finite four-volume) of any spherically symmetric spacetime. In particular we apply the formalism, using a non-static reference congruence, to do optical geometry across the horizon of a static black hole. While the resulting geometry in principle is time dependent, we can choose the reference congruence in such a manner that an embedding of the geometry always looks the same. Relative to the embedded geometry the reference points are then moving. We discuss the motion of photons, inertial forces and gyroscope precession in this framework.
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| 9. |
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| 10. |
- Jonsson, Rickard, et al.
(författare)
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Youth language
- 2020
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Ingår i: Routledge handbook of linguistic ethnography ed. by Karin Tusting. - London : Routledge. - 9781138938168
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Bokkapitel (refereegranskat)
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