A new look at the Plebański-Demiański family of solutions

International Journal of Modern Physics D

Volumn 15, Issue 3, 2006, Pages 335-369

  Griffiths, J B ^a   Podolsky J ^b  

^a LOUGHBOROUGH UNIVERSITY   (United Kingdom)

^b CHARLES UNIVERSITY   (Czech Republic)

Author keywords

Exact solutions of the Einstein Maxwell equations; Type D space times

Indexed keywords

EID: 33744917803     PISSN: 02182718     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218271806007742     Document Type: Article

References (45)

1. J. F. Plebański and M. Demiański, Rotating charged and uniformly accelerating mass in general relativity, Ann. Phys. (N.Y.) 98, 98-127 (1976).
2. W. Kinnersley, Type D vacuum metrics, J. Math. Phys. 10, 1195-1203 (1969).
3. G. J. Weir and R. P. Kerr, Diverging type-D metrics, Proc. Roy. Soc. A 355, 31-52 (1977).
4. R. Debever and N. Kamran, Coordonnées symétriques et coordonnées isotropes des solutions de type D des équations d'Einstein-Maxwell avec constante cosmologique, Bull. Cl. Sci. Acad. Roy. Belg. 66, 585-599 (1980).
5. K. Ishikawa and T. Miyashita, Classification of Petrov type D empty Einstein spaces with diverging null geodesic congruences, Prog. Theor. Phys. 67, 828-843 (1982).
6. S. W. Hawking and S. F. Ross, Pair production of black holes on cosmic strings, Phys. Rev. Lett. 75, 3382-3385 (1995).
7. R. B. Mann and S. F. Ross, Cosmological production of charged black hole pairs, Phys. Rev. D 52, 2254-2265 (1995).
8. I. S. Booth and R. B. Mann, Cosmological pair production of charged and rotating black holes, Nucl. Phys. B 539, 267-306 (1999).
9. B. Carter, Hamilton-Jacobi and Schrödinger separable solutions of Einstein's equations, Commun. Math. Phys. 10, 280-310 (1968).
10. R. Debever, N. Kamran and R. G. McLenaghan, Exhaustive integration and a single expression for the general solution of the type D vacuum and electrovac field equations with cosmological constant for a nonsingular aligned Maxwell field, J. Math. Phys. 25, 1955-1972 (1984).
11. D. A. García, Electrovac type D solutions with cosmological constant, J. Math. Phys. 25, 1951-1954 (1984).
12. K. Hong and E. Teo, A new form of the C-metric, Class. Quantum Grav. 20, 3269-3277 (2003).
13. K. Hong and E. Teo, A new form of the rotating C-metric, Class. Quantum Grav. 22, 109-117 (2005).
14. J. K. Kowalczyński and J. F. Plebański, Metric and Ricci tensors for a certain class of space-times of type D, Int. J. Theor. Phys. 16, 371-388 (1977) [Erratum, Int. J. Theor. Phys. 17, 388 (1978)].
15. H. Stephani, D. Kramer, M. MacCallum, C. Hoenselaers and E. Herlt, Exact Solutions of Einstein's Field Equations, 2nd edn. (Cambridge University Press, 2003).
16. R. Debever, On type D expanding solutions of Einstein-Maxwell equations, Bull. Soc. Math. Belg. 23, 360-376 (1971).
17. J. Podolský and J. B. Griffiths, Uniformly accelerating black holes in a de Sitter universe, Phys. Rev. D 63, 024006 (2001).
18. D. A. García, and J. F. Plebański, Solutions of type D possessing a group with null orbits as contractions of the seven-parameter solution, J. Math. Phys. 23, 1463-1465 (1982).
19. J. Leroy, Sur une classe d'espaces-temps solutions des equations d'Einstein-Maxwell, Bull. Acad. Roy. Belg. Cl. Sci. 64, 130 (1978).
20. D. A. García and I. H. Salazar, All null orbit type D electrovac solutions with cosmclogical constant, J. Math. Phys. 24, 2498-2503 (1983).
21. R. Debever, N. Kamran and R. G. McLenaghan, A single expression for the general solution of Einstein's vacuum and electrovac field equations with cosmological constant for Petrov type D admitting a non-singular aligned Maxwell field, Phys. Lett. A 93, 399-402 (1983).
22. D. A. García and A. Macias, Black holes as exact solutions of the Einstein-Maxwell equations of Petrov type D, in Black Holes: Theory and Observation, Lecture Notes in Physics, Vol. 514, eds. F. W. Hehl, C. Kiefer and R. J. K. Metzler (Springer-Verlag, 1998), p. 205.
23. J. F. Plebański, A class of solutions of the Einstein-Maxwell equations, Ann. Phys. (N.Y.) 90, 196-255 (1975).
24. J. B. Griffiths and J. Podolský, Accelerating and rotating black holes, Class. Quantum Grav. 22, 3467-3479 (2005).
25. E. T. Newman, L. A. Tamburino and T. Unti, Empty-space generalization of the Schwarzschild metric, J. Math. Phys. 4, 915-923 (1963).
26. W. B. Bonnor, A new interpretation of the NUT metric in general relativity, Proc. Camb. Phil. Soc. 66, 145-151 (1969).
27. H. Farhoosh and R. L. Zimmerman, Surfaces of infinite red-shift around a uniformly accelerating and rotating particle, Phys. Rev. D 21, 2064-2074 (1980).
28. J. Bičák and V. Pravda, Spinning C metric: Radiative space-time with accelerating, rotating black holes, Phys. Rev. D 60, 044004 (1999).
29. V. Pravda and A. Pravdová, On the spinning C-metric, in Gravitation: Following the Prague Inspiration (A Celebration of the 60th Birthday of J. Bičák), eds. O. Semerák, J. Podolský and M. Žofka (World Scientific, Singapore, 2002), pp. 247-262.
30. J. Podolský and J. B. Griffiths, Accelerating Kerr-Newman black holes in (anti-) de Sitter space-time, Phys. Rev. D 73, 044018 (2006).
31. S. W. Hawking and G. R. F. Ellis, The Large Scale Structure of Space-Time (Cambridge University Press, 1973).
32. J. B. Griffiths and J. Podolský, Global aspects of accelerating and rotating black hole space-times, Class. Quantum Grav. 23, 555-568 (2006).
33. Ó. J. C. Dias and J. P. S. Lemos, Pair of accelerated black holes in an anti-de Sitter background: The AdS C metric, Phys. Rev. D 67, 064001 (2003).
34. Ó. J. C. Dias and J. P. S. Lemos, Pair of accelerated black holes in a de Sitter background: The dS C metric, Phys. Rev. D 67, 084018 (2003).
35. P. Krtouš and J. Podolský, Radiation from accelerating black holes in a de Sitter universe, Phys. Rev. D 68, 024005 (2003).
36. J. Podolský, M. Ortaggio and P. Krtouš, Radiation from accelerated black holes in an anti-de Sitter universe, Phys. Rev. D 68, 124004 (2003).
37. B. Carter, The commutation property of a stationary, axisymmetric system, Commun. Math. Phys. 17, 233-238 (1970).
38. G. W. Gibbons and S. W. Hawking, Cosmological event horizons, thermodynamics, and particle creation, Phys. Rev. D 15, 2738-2751 (1977).
39. V. A. Ruban, Nonsingular Taub-Newman-Unti-Tamburino metrics, Dokl. Acad. Nauk CCCP 204, 1085-1089 (1972)
40. [Sov. Phys. Dokl. 17, 568-571 (1972)].
41. J. Ehlers and W. Kundt, Exact solutions of the gravitational field equations, in Gravitation: An Introduction to Current Research, ed. L. Witten (Wiley, New York, 1962), pp. 49-101.
42. W. Kinnersley, Recent progress in exact solutions, in General Relativity and Gravitation - Proc. GR7, eds. G. Shaviv and J. Rosen (Wiley, 1975), pp. 109-135.
43. J. R. Ray and M. S. Wei, A solution-generating theorem with applications in general relativity, Nuovo Cimento B 42, 151-164 (1977).
44. M. Halilsoy, Interpolation of the Schwarzschild and Bertotti-Robinson solutions, Gen. Relativ. Gravit. 25, 275-280 (1993).
45. M. Ortaggio and J. Podolský, Impulsive waves in electrovac direct product space-times with A, Class. Quantum Grav. 19, 5221-5227 (2002).