Locally Rotationally Symmetric Models (LRS)

1. Lema\^{\i}tre G: L'Univers en Expansion, Ann. Soc. Sci. Bruxelles I A 53 (1933), 51 [in French]
   English translation: Gen. Rel. Grav. 29 (1997), 641
2. Tolman R C: Effect of Inhomogeneity in Cosmological Models, Proc. Nat. Acad. Sci. U.S. 20 (1934), 69
3. Bondi H: Spherically Symmetric Models in General Relativity, Mon. Not. R. Astron. Soc. 107 (1947), 410
4. Ellis G F R: Dynamics of Pressure-Free Matter in General Relativity, J. Math. Phys. 8 (1967), 1171
5. Stewart J M, G F R Ellis: Solutions of Einstein's Equations for a Fluid which Exhibits Local Rotational Symmetry, J. Math. Phys. 9 (1968), 1072
6. Ellis G F R, M A H MacCallum: A Class of Homogeneous Cosmological Models, Commun. Math. Phys. 12 (1969), 108
7. Wainwright J: A Class of Algebraically Special Perfect Fluid Space-Times, Commun. Math. Phys. 17 (1970), 42
8. Eardley D, E Liang, R Sachs: Velocity-Dominated Singularities in Irrotational Dust Cosmologies, J. Math. Phys. 13 (1972), 99
   NB: Introduces the notion of "velocity-dominated" (initial) singularities; employs as examples for analysing the singularity structure the exact solutions for plane symmetric and spherically symmetric expanding dust models (LRS class II); fairly technical.
9. King A R, G F R Ellis: Tilted Homogeneous Cosmological Models, Commun. Math. Phys. 31 (1973), 209
10. MacCallum M A H: Cosmological Models from a Geometric Point of View, in Cargèse Lectures in Physics Vol 6, Ed. E Schatzman, (New York: Gordon and Breach, 1973), 61
11. Collins C B, J Wainwright: Role of Shear in General-Relativistic Cosmological and Stellar Models, Phys. Rev. D 27 (1983), 1209
    NB: For a perfect fluid subject to the EFE it is assumed that i) $\Theta \neq 0$, ii) $\omega = 0$, iii) $\sigma = 0$ and iv) $p=p(\mu)$, $(\mu+p) \neq 0$. It follows that any solution is locally either a) FLRW ($G_{6}$ case), b) planar symmetric, tilted SH of Type-V (LRS class II with $K = 0$) or its "temporally homogeneous" counterpart ($G_{4}$ case), or c) spherically symmetric, spatially inhomogeneous (LRS class II with $K > 0$) ($G_{3}$ case). Cases b) and c) have $\dot{u} \neq 0$. Imposing a globally physically reasonable equation of state only seems to leave the FLRW case. This work renders a lot of (later) papers on shearfree perfect fluids uninteresting from a physical point of view.
12. Stephani H: A New Interior Solution of Einstein's Field Equations for a Spherically Symmetric Perfect Fluid in Shear-Free Motion, J. Phys. A: Math. Gen. 16 (1983), 3529
13. Matravers D R, D L Vogel, M S Madsen: Helium Formation in a Bianchi Type V Cosmological Model with Tilt, Class. Quantum Grav. 1 (1984), 407
    NB: LRS, asymptotically like $k=-\,1$ FLRW.
14. Goode S W, J Wainwright: Characterization of Locally Rotationally Symmetric Space-Times, Gen. Rel. Grav. 18 (1986), 315
    NB: Characterisation in terms of canonical null and orthonormal frames for EFE with perfect fluid or electromagnetic field source.
15. Madsen M S, D R Matravers: Structure of the Initial Singularity in LRS Bianchi Type-V Models, Class. Quantum Grav. 3 (1986), 541
16. Collins C B, J M Lang: A Class of Self-Similar Perfect-Fluid Spacetimes, and a Generalisation, Class. Quantum Grav. 4 (1987), 61
    NB: Restriction to homotheties orthogonal to the matter fluid flow, LRS geometry.
17. Senovilla J M M: New LRS Perfect-Fluid Cosmological Models, Class. Quantum Grav. 4 (1987), 1449
18. Coley A A, B O J Tupper: Spherically Symmetric Spacetimes Admitting Inheriting Conformal Vector Fields, Class. Quantum Grav. 7 (1990), 2195
19. Anninos P, R A Matzner, T Rothman, M P Ryan jr: How does Inflation Isotropize the Universe?, Phys. Rev. D 43 (1991), 3821
    NB: investigation of the behaviour in the tilt angle for a one-dimensional spatially inhomogeneous $\phi$ field in a LRS Type-V spacetime (related to a $k=-\,1$ FLRW background); classical results, no quantum fluctuations taken into account. Q: How does matter know which way to move at the end of a de Sitter inflationary phase? "Finally, the investigation shows, once again, the necessity of carrying out computations in nonstandard cosmological models to verify the utility of inflation."
20. Hewitt C G, J Wainwright: Dynamical Systems Approach to Tilted Bianchi Cosmologies: Irrotational Models of Type V, Phys. Rev. D 46 (1992), 4242
    NB: LRS $G_{3}$.
21. Knutsen H: Physical Properties of an Exact Spherically Symmetric Solution with Shear in General Relativity, Gen. Rel. Grav. 24 (1992), 1297
    NB: Perfect fluid with $\mu > 0$, $p > 0$ in non-comoving coordinates. Imposing dominant energy condition leads to imaginary values of speed of sound. Naked singularity at centre of fluid.
22. Rangarajan R, M Srednicki: Chaotic Dark Matter, Phys. Rev. D 46 (1992), 3350
23. Kitamura S: On Spherically Symmetric Perfect Fluid Solutions with Shear, Class. Quantum Grav. 11 (1994), 195
24. Griffiths J B: A Class of Plane Symmetric Dust Solutions, Gen. Rel. Grav. 27 (1995), 905
    NB: LRS class II ($K = 0$).
25. Kitamura S: On Spherically Symmetric Perfect Fluid Solutions with Shear. II, Class. Quantum Grav. 12 (1995), 827
26. Kitamura S: A Remark on the Invariant Characterization of a Class of Exact Spherically Symmetric Perfect Fluid Solutions with Shear, Class. Quantum Grav. 12 (1995), 1559
27. Knutsen H: On a Class of Spherically Symmetric Perfect Fluid Distributions in Non-Comoving Coordinates, Class. Quantum Grav. 12 (1995), 2817
28. Rendall A D: Crushing Singularities in Spacetimes with Spherical, Plane and Hyperbolic Symmetry, Class. Quantum Grav. 12 (1995), 1517. Also: Preprint gr-qc/9411011.
29. Burnett G A, A D Rendall: Existence of Maximal Hypersurfaces in Some Spherically Symmetric Spacetimes, Class. Quantum Grav. 13 (1996), 111. Also: Preprint gr-qc/9508001.
    NB: Deals with spacetimes possessing a (compact) constant mean curvature $S^{1}\times S^{2}$ Cauchy surface. Technical.
30. van Elst H, G F R Ellis: The Covariant Approach to LRS Perfect Fluid Spacetime Geometries, Class. Quantum Grav. {\bf 13 (1996), 1099. Also: Preprint gr-qc/9510044.
31. van Elst H: Extensions and Applications of 1+3 Decomposition Methods in General Relativistic Cosmological Modelling, PhD thesis, University of London, 1996
32. Herlt E: Spherically Symmetric Nonstatic Perfect Fluid Solutions with Shear, Gen. Rel. Grav. 28 (1996), 919
    NB: Examination of a class of models with $\dot{u}^{a} = 0 \Rightarrow p = p(t)$ in terms of a Lie point symmetry analysis.
33. Jhingan S, P S Joshi, T P Singh: The Final Fate of Spherically Inhomogeneous Dust Collapse: II. Initial Data and Causal Structure of the Singularity, Class. Quantum Grav. 13 (1996), 3057. Also: Preprint gr-qc/9604046.
34. Nilsson U, C Uggla: Spatially Self-Similar Locally Rotationally Symmetric Perfect Fluid Models, Class. Quantum. Grav. 13 (1996), 1601. Also: Preprint gr-qc/9511064.
35. Singh T P, P S Joshi: The Final Fate of Spherically Inhomogeneous Dust Collapse, Class. Quantum Grav. 13 (1996), 559. Also: Preprint gr-qc/9409062.
    NB: LTB. Discusses the possible occurrence of naked singularities.
36. Stephani H, T Wolf: Spherically Symmetric Perfect Fluids in Shear-Free Motion - The Symmetry Approach, Class. Quantum Grav. 13 (1996), 1261
37. Dwivedi I H, P S Joshi: Initial Data and the Final Fate of Inhomogeneous Dust Collapse, Class. Quantum Grav. 14 (1997), 1223. Also: Preprint gr-qc/9612023.
    NB: LTB.
38. Marklund M: Invariant Construction of Solutions to Einstein's Field Equations - LRS Perfect Fluids I, Class. Quantum Grav. 14 (1997), 1267. Also: Preprint gr-qc/9612014.
39. van Elst H, G F R Ellis: Causal Propagation of Geometrical Fields in Relativistic Cosmology, Phys. Rev. D 59 (1999), 024013. Also: Preprint gr-qc/9810058.
40. Marklund M, M Bradley: Invariant Construction of Solutions to Einstein's Field Equations - LRS Perfect Fluids II, Class. Quantum Grav. 16 (1999), 1577. Also: Preprint gr-qc/9808062.
41. Mustapha N, C Hellaby: Clumps into Voids, Preprint astro-ph/0006083
    NB: LTB.

Selected References
Last revision: Sat, 19-8-2000 (This page is under construction)