Self-Similar Spacetime Geometries / Homothetic Motions

  1. Cahill M E, A H Taub: Spherically Symmetric Similarity Solutions of the Einstein Field Equations for a Perfect Fluid, Commun. Math. Phys. 21 (1971), 1
    NB: (+ - - -).
  2. Carr B J, S W Hawking: Black Holes in the Early Universe, Mon. Not. R. Astron. Soc. 168 (1974), 399
  3. Eardley D M: Self-Similar Spacetimes: Geometry and Dynamics, Commun. Math. Phys. 37 (1974), 287
    NB: Mainly treats the example of a spacelike $H_{3}$ transitive on 3-surfaces.
  4. Rosquist K, R T Jantzen: Spacetimes with a Transitive Similarity Group, Class. Quantum Grav. 2 (1985), L129
  5. Wainwright J: Self-Similar Solutions of Einstein's Equations, in Galaxies, Axisymmetric Systems and Relativity, Ed. M A H MacCallum, (Cambridge: Cambridge University Press, 1985)
  6. Collins C B, J M Lang: Singularities in Self-Similar Spacetimes, Class. Quantum Grav. 3 (1986), 1143
  7. Hsu L, J Wainwright: Self-Similar Spatially Homogeneous Cosmologies: Orthogonal Perfect Fluid and Vacuum Solutions, Class. Quantum Grav. 3 (1986), 1105
    NB: Provides all OSH solutions of the EFE with perfect fluid source (incl. vacuum), which admit a simply transitive $H_{4}$.
  8. Jantzen R T, K Rosquist: Exact Power Law Metrics in Cosmology, Class. Quantum Grav. 3 (1986), 281
  9. 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.
  10. Hewitt C G, J Wainwright, S W Goode: Qualitative Analysis of a Class of Inhomogeneous Self-Similar Cosmological Models, Class. Quantum Grav. 5 (1988), 1313
    NB: Dynamical systems analysis of dynamical equilibrium states of diagonal $G_{2}$ perfect fluid class with $p(\mu) = (\gamma-1)\,\mu$, I: compact state space.
  11. Hewitt C G, J Wainwright, M Glaum: Qualitative Analysis of a Class of Inhomogeneous Self-Similar Cosmological Models: II, Class. Quantum Grav. 8 (1991), 1505
    NB: Dynamical systems analysis of dynamical equilibrium states of diagonal $G_{2}$ perfect fluid class with $p(\mu) = (\gamma-1)\,\mu$, II: non-compact state space.
  12. McIntosh C B G, J D Steele: All Vacuum Bianchi I Metrics with a Homothety, Class. Quantum Grav. 8 (1991), 1173
  13. Steele J D: Simply-Transitive Homothety Groups, Gen. Rel. Grav. 23 (1991), 811
  14. da Costa J, E G L R Vaz: Vaccum Type N Space-Times Admitting Homothetic Vector Fields With Isolated Fixed Points, Gen. Rel. Grav. 24 (1992), 745
  15. Uggla C: Inhomogeneous Self-Similar Cosmological Models, Class. Quantum Grav. 9 (1992), 2287
    NB: $H_{3}$ transitive on timelike 3-surfaces; reduction of EFE to system of ODEs; Hamiltonian formulation; $p(\mu) = (\gamma-1)\,\mu$.
  16. Carr B J, A Koutras: Self-Similar Perturbations of a Kantowski-Sachs Model, Astrophys. J. 405 (1993), 34
    NB: Self-similar KS solution has $\gamma < 2/3$, violation of SEC.
  17. Ponce de Leon J: Self-Similar Symmetry in General Relativity, Gen. Rel. Grav. 25 (1993), 865
    NB: Spherically symmetric example given; imperfect fluid with $q^{a} = 0$. Also shearfree case discussed.
  18. Nilsson U, C Uggla: Spatially Self-Similar Locally Rotationally Symmetric Perfect Fluid Models, Class. Quantum Grav. 13 (1996), 1601. Also: Preprint gr-qc/9511064.
  19. Coley A A: Kinematic Self-Similarity, Class. Quantum Grav. 14 (1997), 87. Also: Preprint gr-qc/9610061.
  20. Goliath M, U S Nilsson, C Uggla: Spatially Self-Similar Spherically Symmetric Perfect-Fluid Models, Class. Quantum Grav. 15 (1998), 167. Also: Preprint gr-qc/9811064.
  21. Goliath M, U S Nilsson, C Uggla: Timelike Self-Similar Spherically Symmetric Perfect-Fluid Models, Class. Quantum Grav. 15 (1998), 2841. Also: Preprint gr-qc/9811065.
  22. Carr B J, A A Coley: Self-Similarity in General Relativity (Topical Review), Class. Quantum Grav. 16 (1999), R31. Also: Preprint gr-qc/9806048.
  23. Wainwright J, M J Hancock, C Uggla: Asymptotic Self-Similarity Breaking at Late Times in Cosmology, Class. Quantum Grav. 16 (1999), 2577. Also: Preprint gr-qc/9812010.
  24. Carr B J, A A Coley: A Complete Classification of Spherically Symmetric Perfect Fluid Similarity Solutions, Phys. Rev. D 62 (2000), 044023. Also: Preprint gr-qc/9901050.
  25. Carr B J, A A Coley, M Goliath, U S Nilsson, C Uggla: Critical Phenomena and a New Class of Self-Similar Spherically Symmetric Perfect-Fluid Solutions, Phys. Rev. D 61 (2000), 081502. Also: Preprint gr-qc/9901031.

Selected References
Last revision: Thu, 24-8-2000 (This page is under construction)