References
- R. Penrose, The geometry of impulsive gravitational waves, in General Relativity, Papers in Honour of J. L. Synge, L. O'Raifeartaigh, ed., Clarendon Press, Oxford, 1972, pp. 101–115.
- Aichelburg , PC and Balasin , H . 1997 . Generalized symmetries of impulsive gravitational waves . Class. Quant. Grav. , 14 : A31 – A41 .
- Grosser , M , Kunzinger , M , Oberguggenberger , M and Steinbauer , R . 2001 . Geometric Theory of Generalized Functions, Mathematics and its Applications , Vol. 537 , Dordrecht : Kluwer Academic .
- E. Erlacher, Inversion of Colombeau generalised functions, preprint (2010).
- Kunzinger , M and Steinbauer , R . 1999 . A note on the Penrose junction conditions . Class. Quant. Grav. , 16 : 1255 – 1264 .
- Steinbauer , R . 2000 . Distributional methods in general relativity , Ph.D. thesis University of Vienna . Available at http://www.mat.univie.ac.at/~stein/research/PhD/PhD.pdf
- Kunzinger , M and Steinbauer , R . 1999 . A rigorous solution concept for geodesic and geodesic deviation equations in impulsive gravitational waves . J. Math. Phys. , 40 : 1479 – 1489 .
- Penrose , R . 1968 . Twistor quantization and curved space-time . Int. J. Theor. Phys. , 1 : 61 – 99 .
- Aichelburg , PC and Sexl , RU . 1971 . On the gravitational field of a massless particle . J. Gen. Rel. Grav. , 2 : 303 – 312 .
- Balasin , H and Nachbagauer , H . 1995 . The ultrarelativistic Kerr-geometry and its energy-momentum tensor . Class. Quant. Grav. , 12 : 707 – 713 .
- Loustó , CO and Sánchez , N . 1989 . The ultrarelativistic limit of the Kerr-Newman geometry and particle scattering at the Planck scale . Phys. Lett. B , 232 : 462 – 466 .
- Podolský , J and Griffths , JB . 1998 . Boosted static multipole particles as sources of impulsive gravitational waves . Phys. Rev. D , 58 : 124024
- Verlinde , H and Verlinde , E . 1993 . High-energy scattering in Quantum gravity . Class. Quant. Grav. , 10 : 175 – 184 .
- De Haro , S . 1998 . Planckian scattering and black holes . J. High Energy Phys. , 10 : 51 – 66 .
- Podolský , J and Vesely , K . 1998 . Continuous coordinates for all impulsive pp-waves . Phys. Lett. A , 241 : 145 – 147 .
- Dray , T and 't Hooft , G . 1985 . The gravitational shockwave of a massless particle . Nucl. Phys. B , 253 : 173 – 188 .
- Steinbauer , R . 1998 . Geodesics and geodesic deviation for impulsive gravitational waves . J. Math. Phys. , 39 : 2201 – 2212 .
- Ferrari , V , Pendenza , P and Veneziano , G . 1988 . Beam like gravitational waves and their geodesics . J. Gen. Rel. Grav. , 20 : 1185 – 1191 .
- Balasin , H . 1997 . Geodesics for impulsive gravitational waves and the multiplication of distributions . Class. Quant. Grav. , 14 : 455 – 462 .
- Hajek , O . 1985 . Book Review: Differential systems involving impulses . Bull. Am. Math. Soc. , 12 : 272 – 279 .
- Steinbauer , R . 1997 . The ultrarelativistic Reissner-Nordstrøm field in the Colombeau algebra . J. Math. Phys. , 38 : 1614 – 1622 .
- Colombeau , JF . 1984 . New Generalized Functions and Multiplication of Distributions , Amsterdam : North-Holland .
- Colombeau , JF . 1985 . Elementary Introduction to New Generalized Functions , Amsterdam : North-Holland .
- Oberguggenberger , M . 1992 . Multiplication of Distributions and Applications to Partial Differential Equations, Pitman Research Notes in Mathematics , Vol. 259 , Harlow , , UK : Longman .
- Steinbauer , R and Vickers , JA . 2006 . The use of generalized functions and distributions in general relativity . Class. Quant. Grav. , 23 : R91 – R114 .
- R. Steinbauer and J.A. Vickers, On the Geroch-Traschen class of metrics, Class. Quant. Grav. 26 (2009), pp. 065001, 19.
- Erlacher , E . 2007 . Local existence results in algebras of generalised functions , Ph.D. thesis University of Vienna . Available at http://www.mat.univie.ac.at/~diana/uploads/publication47.pdf
- Madsen , I and Tornehave , J . 1997 . From Calculus to Cohomology , Cambridge : Cambridge University Press .
- Gale , D and Nikaido , H . 1965 . The Jacobian matrix and global univalence of mappings . Math. Ann. , 159 : 81 – 93 .