A2: Mathematical relativity and other progress in classical gravity theory—a session report

Review Article
Part of the following topical collections:
  1. The First Century of General Relativity: GR20/Amaldi10


We report on selected oral contributions to the A2 session “Mathematical relativity and other progress in classical gravity theory” of “The 20th International Conference on General Relativity and Gravitation (GR20)” in Warsaw.


Mathematical general relativity Evolution problems Black holes 


  1. 1.
    Andersson, L., Mars, M., Metzger, J., Simon, W.: The time evolution of marginally trapped surfaces. Class. Quantum Gravity 26(14), 085018 (2009)Google Scholar
  2. 2.
    Andersson, L., Mars, M., Simon, W.: Local existence of dynamical and trapping horizons. Phys. Rev. Lett. 95, 111102 (2005). arXiv:gr-qc/0506013 Google Scholar
  3. 3.
    Andersson, L., Mars, M., Simon, W.: Stability of marginally outer trapped surfaces and existence of marginally outer trapped tubes. Adv. Theor. Math. Phys. 12, 853–888 (2008). arXiv:0704.2889 [gr-qc]
  4. 4.
    Andréasson, H., Kunze, M., Rein, G.: Existence of axially symmetric static solutions of the Einstein–Vlasov system. Commun. Math. Phys. 308, 23–47 (2011)ADSCrossRefMATHGoogle Scholar
  5. 5.
    Andréasson, H., Kunze, M., Rein, G.: Rotating, stationary, axially symmetric spacetimes with collisionless matter. Commun. Math. Phys. in press (2013)Google Scholar
  6. 6.
    Aretakis, S.: Nonlinear instability of scalar fields on extremal black holes. Phys. Rev. D 87, 084052 (2013). arXiv:1304.4616 [gr-qc]
  7. 7.
    Aretakis, S.: A note on instabilities of extremal black holes under scalar perturbations from afar. Class. Quantum Gravity 30(11), 095010 (2013). arXiv:1212.1103 [gr-qc]
  8. 8.
    Bizoń, P., Chmaj, T., Schmidt, B.G.: Critical behavior in vacuum gravitational collapse in 4+1 dimensions. Phys. Rev. Lett. 95, 071102 (2005). arXiv:gr-qc/0506074 Google Scholar
  9. 9.
    Bizoń, P., Rostworowski, A.: On weakly turbulent instability of anti-de Sitter space. Phys. Rev. Lett. 107, 031102 (2011). arXiv:1104.3702 [gr-qc]Google Scholar
  10. 10.
    Breitenlohner, P., Forgács, P., Maison, D.: Gravitating monopole solutions II. Nucl. Phys. B 442, 126–156 (1995)ADSCrossRefMATHGoogle Scholar
  11. 11.
    Christodoulou, D.: The instability of naked singularities in the gravitational collapse of a scalar field. Ann. Math. 149(2), 183–217 (1999)Google Scholar
  12. 12.
    Chruściel, P.T.: Semi-global existence and convergence of solutions of the Robinson–Trautman (2-dimensional Calabi) equation. Commun. Math. Phys. 137, 289–313 (1991)ADSCrossRefMATHGoogle Scholar
  13. 13.
    Chruściel, P.T., Lopes Costa, J.: On uniqueness of stationary black holes. Astérisque 321, 195–265 (2008). arXiv:0806.0016v2 [gr-qc]Google Scholar
  14. 14.
    Chruściel, P.T., Lopes Costa, J., Heusler, M.: Stationary black holes: uniqueness and beyond. Living Rev. Rel. 15(7) (2012). arXiv:1205.6112 [gr-qc]Google Scholar
  15. 15.
    Chruściel, P.T., Galloway, G., Solis, D.: Topological censorship for Kaluza–Klein space-times. Ann. H. Poincaré 10, 893–912 (2009). arXiv:0808.3233 [gr-qc]Google Scholar
  16. 16.
    Chruściel, P.T., Galloway, G.J., Pollack, D.: Mathematical general relativity: a sampler. Bull. Am. Math. Soc. (N.S.) 47, 567–638 (2010). arXiv:1004.1016 [gr-qc]Google Scholar
  17. 17.
    Chruściel, P.T., Paetz, T.T.: Solutions of the vacuum Einstein equations with initial data on past null infinity. Class. Quantum Grav. 30, 2350237 (2013). arXiv:1307.0321 [gr-qc]
  18. 18.
    Dafermos, M., Holzegel, G.: On the nonlinear stability of higher dimensional triaxial Bianchi-IX black holes. Adv. Theor. Math. Phys. 10(4), 503–523 (2006)CrossRefMATHMathSciNetGoogle Scholar
  19. 19.
    Dilts, J.: The Einstein constraint equations on compact manifolds with boundary (2013). arXiv:1310.2303 [gr-qc]
  20. 20.
    Figueras, P., Murata, K. Reall, H.S.: Black hole instabilities and local Penrose inequalities. Class. Quantum Gravity 28(22), 225030 (2011). arXiv:1107.5785 [gr-qc]
  21. 21.
    Friedrich, H.: On the global existence and the asymptotic behavior of solutions to the Einstein–Maxwell–Yang–Mills equations. J. Diff. Geom. 34, 275–345 (1991)MATHMathSciNetGoogle Scholar
  22. 22.
    Friedrich, H.: Einstein equations and conformal structure: existence of anti-de-Sitter-type space–times. J. Geom. Phys. 17, 125–184 (1995)ADSCrossRefMATHMathSciNetGoogle Scholar
  23. 23.
    Friedrich, H.: The Taylor expansion at past time-like infinity (2013). arXiv:1306.5626
  24. 24.
    Friess, J.J., Gubser, S.S., Mitra, I.: Counter-examples to the correlated stability conjecture. Phys. Rev. D 72, 104019 (2005). arXiv:hep-th/0508220
  25. 25.
    Galloway, G.J.: Maximum principles for null hypersurfaces and null splitting theorems. Ann. H. Poincaré 1, 543–567 (2000)CrossRefMATHMathSciNetGoogle Scholar
  26. 26.
    García-Parrado, A.: Bi-conformal vector fields and the local geometric characterization of conformally separable pseudo-Riemannian manifolds. I. J. Geom. Phys. 56(7), 1069–1095 (2006)ADSCrossRefMATHMathSciNetGoogle Scholar
  27. 27.
    García-Parrado, A.: On the characterization of non-degenerate foliations of pseudo-riemannian manifolds with conformally flat leaves. J. Math. Phys. 54(6), 063503 (2013)ADSCrossRefMathSciNetGoogle Scholar
  28. 28.
    Green, S.R., Schiffrin, J.S., Wald, R.M.: Dynamic and thermodynamic stability of relativistic. Perfect Fluid Stars (2013). arXiv:1309.0177 [gr-qc]
  29. 29.
    Gubser, S.S., Mitra, I.: Instability of charged black holes in anti-de Sitter space (2000). arXiv:hep-th/0009126
  30. 30.
    Hollands, S., Wald, R.M.: Stability of black holes and black Branes. Commun. Math. Phys. 321, 629–680 (2013). arXiv:1201.0463 [gr-qc]
  31. 31.
    Holst, M., Meier, C., Tsogtgerel, G.: Non-CMC solutions of the Einstein constraint equations on compact manifolds with apparent horizon boundaries (2013). arXiv:1310.2302 [gr-qc]
  32. 32.
    Jaramillo, J.L.: A note on degeneracy, marginal stability and extremality of black hole horizons. Class. Quantum Gravity 29, 177001 (2012). arXiv:1206.1271 [gr-qc]
  33. 33.
    Jaramillo, J.L.: A Young–Laplace law for black hole horizons (2013). arXiv:1309.6593 [gr-qc]
  34. 34.
    Klainerman, S.: PDE as a unified subject. Geom. Funct. Anal. Special Volume, Part I, 279–315 (2000)Google Scholar
  35. 35.
    Klainerman, S., Rodnianski, I., Szeftel, J.: The bounded \(L^2\) curvature conjecture (2012). arXiv:1204.1767 [math.AP]
  36. 36.
    Kozameh, C., Perez, A., Moreschi, O.: Smooth null hypersurfaces near the horizon in the presence of tails. Phys. Rev. D 87, 064039 (2013)ADSCrossRefGoogle Scholar
  37. 37.
    Kunduri, H.K., Lucietti, J.: Classification of near-horizon geometries of extremal black holes. Living Rev. Relativ. 16, 8 (2013). arXiv:1306.2517 [hep.th]
  38. 38.
    Li, C., Lucietti, J.: Uniqueness of extreme horizons in Einstein–Yang–Mills theory. Class. Quantum Gravity 30, 095017 (2013). arXiv:1302.4616 [hep-th]
  39. 39.
    Lübbe, C., Valiente Kroon, J.A.: Anti de Sitter-like Einstein–Yang–Mills spacetimes, in preparation (2013)Google Scholar
  40. 40.
    Lübbe, C., Valiente Kroon, J.A.: Spherically symmetric Anti-de Sitter-like instein-Yang-Mills (2013). arXiv:1403.2885 [gr-qc]
  41. 41.
    Lucietti, J., Murata, K., Reall, H.S., Tanahashi, N.: On the horizon instability of an extreme Reissner–Nordstróm black hole. JHEP 1303, 035 (2013). arXiv:1212.2557 [gr-qc]
  42. 42.
    Luk, J., Rodnianski, I.: Local propagation of impulsive gravitational waves (2012). arXiv:1209.1130
  43. 43.
    Luk, J., Rodnianski, I.: Nonlinear interaction of impulsive gravitational waves for the vacuum Einstein equations (2013). arXiv:1301.1072
  44. 44.
    Maxwell, D.: Solutions of the Einstein constraint equations with apparent horizon boundaries. Commun. Math. Phys. 253, 561–583 (2005). arXiv:gr-qc/0307117
  45. 45.
    Neugebauer, G., Hennig, J.: Stationary two-black-hole configurations: a non-existence proof. J. Geom. Phys. 62, 613–630 (2012). arXiv:1105.5830 [gr-qc]Google Scholar
  46. 46.
    Nolan, B.C., Winstanley, E.: On the existence of dyons and dyonic black holes in Einstein–Yang–Mills theory. Class. Quantum Gravity 29, 235024 (2012)ADSCrossRefMathSciNetGoogle Scholar
  47. 47.
    Reall, H.S.: Higher dimensional black holes and supersymmetry. Phys. Rev. D 68, 024024 (2003). arXiv:hep-th/0211290
  48. 48.
    Rein, G.: Static solutions of the spherically symmetric Vlasov–Einstein system (1993). arXiv:gr-qc/9304028
  49. 49.
    Ringström, H.: On the Topology and Future Stability of the Universe. Oxford Mathematical Monographs. Oxford University Press, Oxford (2013)CrossRefGoogle Scholar
  50. 50.
    Tafel, J., Jóźwikowski, M.: New solutions of initial conditions in general relativity (2013). arXiv:1312.7819 [gr-qc]
  51. 51.
    Weinberg, E.J.: Black holes with hair (2001). arXiv:gr-qc/0106030

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© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Gravitational PhysicsUniversity of ViennaViennaAustria

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