Description Of General Relativity Research Articles

Understanding Curved Spacetime

According to general relativity (GR), we live in a four-dimensional curved universe. Since the human mind cannot visualize those four dimensions, a popular analogy compares the universe to a two-dimensional rubber sheet distorted by massive objects. This analogy is often used when teaching GR to upper secondary and undergraduate physics students. However, physicists and physics educators criticize the analogy for being inaccurate and for introducing conceptual conflicts. Addressing these criticisms, we analyze the rubber sheet analogy through systematic metaphor analysis of textbooks and research literature, and present an empirical analysis of upper secondary school students’ use and understanding of the analogy. Taking a theoretical perspective of embodied cognition allows us to account for the relationship between the experiential and sensory aspects of the metaphor in relation to the abstract nature of spacetime. We employ methods of metaphor and thematic analysis to study written accounts of small groups of 97 students (18–19 years old) who worked with a collaborative online learning environment as part of their regular physics lessons in five classes in Norway. Students generated conceptual metaphors found in the literature as well as novel ones that led to different conceptions of gravity than those held by experts in the field. Even though most students showed awareness of some limitations of the analogy, we observed a conflict between students’ embodied understanding of gravity and the abstract description of GR. This conflict might add to the common perception of GR being counterintuitive. In making explicit strengths and weaknesses of the rubber sheet analogy and learners’ conceptual difficulties, our results offer guidance for teaching GR. More generally, these findings contribute to the epistemological implications of employing specific scientific metaphors in classrooms.

General relativity in the radial gauge: Reduced phase space and canonical structure

Firstly, we present a reformulation of the standard canonical approach to spherically symmetric systems in which the radial gauge is imposed. This is done via the gauge unfixing technique, which serves as the exposition in the context of the radial gauge. Secondly, we apply the same techniques to the full theory, without assuming spherical symmetry, resulting in a reduced phase space description of general relativity. The canonical structure of the theory is analyzed.

General relativity as a two-dimensional CFT

The tree-level scattering amplitudes of general relativity (GR) encode the full nonlinearity of the Einstein field equations. Yet remarkably compact expressions for these amplitudes have been found which seem unrelated to a perturbative expansion of the Einstein–Hilbert action. This suggests an entirely different description of GR which makes this on-shell simplicity manifest. Taking our cue from the tree-level amplitudes, we discuss how such a description can be found. The result is a formulation of GR in terms of a solvable two-dimensional conformal field theory (CFT), with the Einstein equations emerging as quantum consistency conditions.

Double null hamiltonian dynamics and the gravitational degrees of freedom

In this paper we review the Hamiltonian description of General Relativity using a double null foliation. We start by looking at the 2+2 version of geometrodynamics and show the role of the conformal 2-structure of the 2-metric in encoding (through the shear) the 2 gravitational degrees of freedom. In the second part of the paper we consider instead a canonical analysis of a double null 2+2 Hamiltonian description of General Relativity in terms of self-dual 2-forms and the associated SO(3) connection variables. The algebra of first class constraints is obtained and forms a Lie algebra that consists of two constraints that generate diffeomorphisms in the two surface, a constraint that generates diffeomorphisms along the null generators and a constraint that generates self-dual spin and boost transformations.

GENERAL DESCRIPTION OF DIRAC SPIN–ROTATION EFFECT WITH RELATIVISTIC FACTOR

The Mashhoon rotation–spin coupling is studied by means of the parallelism description of general relativity. The relativistic rotational tetrad is exploited which results in the Minkowski metric, and the torsion axial-vector and Dirac spin coupling will give the Mashhoon rotation–spin term. For the high speed rotating cases, the tangent velocity constructed by the angular velocity Ω multiplying the distance r may exceed over the speed of light c, i.e. Ωr ≥ c, which will make the relativistic factor γ infinity or imaginary. In order to avoid this "meaningless" difficulty occurring in γ factor, we choose to make the rotation non-uniform and position-dependent in a particular way, and then we find that the new rotation–spin coupling energy expression is consistent with the previous results in the low speed limit.

A particle-grid method for general relativistic hydrodynamics: I. Formalism and test applications

The author describes a particle-grid method for the numerical solution of Einstein's equations coupled to a perfect fluid, and apply it to the test problems of spherical pressureless collapse and shock tubes in Minkowski spacetime. The method is a generalization of the collision-dominated particle-in-cell technique widely used in multidimensional Newtonian hydrodynamics problems. In the formalism described here, using the Arnowitt-Deser-Misner (ADM) 3+1 description of general relativity, the metric and fluid 4-velocity components are evaluated on the grid and are then interpolated to the particles. A subsequent movement of the particles simulates fluid advection. The applications to Tolman-Bondi spacetimes (Oppenheimer-Snyder collapse in particular) and to relativistic shocks in flat spacetime indicate that the method can produce good results.

An application of the Multi-Grid method to the construction of initial data for Brill Waves

A linear constraint equation arising from the 3+1 description of general relativity has been solved using both a standard Successive-Over-Relaxation (SOR) scheme and a Multi-Grid (MG) algorithm. In a comparison of computer timings we show that MG can reach a specified convergence criterion nearly 10 times faster than SOR for grids of ∼ 64 × 64 zones, where this factor increases with grid size. In addition it is shown that iterating to a specified convergence criterion can result in wasted work since the truncation error of the solution can be reached well before such a criterion is satisfied. Since MG provides estimates of the solution errors we can assess the minimal amoun of work required to solve the problem. Then it is found that our equation can be solved on a 256 × 256 zones grid using MG in approximately the same time as SOR would need for a ∼ 25 × 25 zones grid if a usual convergence criterion were employed.