Ernst equation

In mathematics, the Ernst equation is a non-linear partial differential equation, named after the physicist Frederick J. Ernst.

Ernst equation

${\displaystyle \displaystyle \Re (u)(u_{rr}+u_{r}/r+u_{zz})=(u_{r})^{2}+(u_{z})^{2}.}$

It is used to produce exact solutions of Einstein's equations.

References

• Zwillinger, Daniel (1989), Handbook of differential equations, Boston, MA: Academic Press, ISBN 978-0-12-784390-2, MR 977062

Bibliography

In Journal of Mathematical Physics

1. 1971 Frederick J. Ernst, Exterior-Algebraic Derivation of Einstein Field Equations Employing a Generalized Basis
2. 1974 Frederick J. Ernst, Complex potential formulation of the axially symmetric gravitational field problem
3. 1974 Frederick J. Ernst, Weyl conform tensor for stationary gravitational fields
4. 1975 Frederick J. Ernst, Black holes in a magnetic universe
5. 1975 Frederick J. Ernst, Erratum: Complex potential formulation of the axially symmetric gravitational field problem
6. 1975 John E. Economou & Frederick J. Ernst, Weyl conform tensor of =2 Tomimatsu–Sato spinning mass gravitational field
7. 1976 Frederick J. Ernst & Walter J. Wild, Kerr black holes in a magnetic universe
8. 1976 Frederick J. Ernst, New representation of the Tomimatsu–Sato solution
9. 1976 Frederick J. Ernst, Removal of the nodal singularity of the C-metric
10. 1977 Frederick J. Ernst, A new family of solutions of the Einstein field equations
11. 1978 Frederick J. Ernst, Coping with different languages in the null tetrad formulation of general relativity
12. 1978 Frederick J. Ernst & I. Hauser, Field equations and integrability conditions for special type N twisting gravitational fields
13. 1978 Frederick J. Ernst, Generalized C-metric
14. 1978 Isidore Hauser & Frederick J. Ernst, On the generation of new solutions of the Einstein–Maxwell field equations
15. 1979 I. Hauser & Frederick J. Ernst, SU(2,1) generation of electrovacs from Minkowski space
16. Erratum: 1979 Coping with different languages in the null tetrad formulation of general relativity
17. Erratum: 1979 Generalized C metric
18. 1980 Isidore Hauser & Frederick J. Ernst, A homogeneous Hilbert problem for the Kinnersley–Chitre transformations of electrovac space-times
19. 1980 Isidore Hauser & Frederick J. Ernst, A homogeneous Hilbert problem for the Kinnersley–Chitre transformations
20. 1981 Isidore Hauser & Frederick J. Ernst, Proof of a Geroch conjecture
21. 1982 Dong-sheng Guo & Frederick J. Ernst, Electrovac generalization of Neugebauer's N = 2 solution of the Einstein vacuum field equations
22. 1983 Y. Chen, Dong-sheng Guo & Frederick J. Ernst, Charged spinning mass field involving rational functions
23. 1983 Cornelius Hoenselares & Frederick J. Ernst, Remarks on the Tomimatsu–Sato metrics
24. 1987 Frederick J. Ernst, Alberto Garcia D & Isidore Hauser, Colliding gravitational plane waves with noncollinear polarization. I
25. 1987 Frederick J. Ernst, Alberto Garcia D & Isidore Hauser, Colliding gravitational plane waves with noncollinear polarization. II
26. 1988 Frederick J. Ernst, Alberto Garcia D & Isidore Hauser, Colliding gravitational plane waves with noncollinear polarization. III
27. 1989 Wei Li & Frederick J. Ernst, A family of electrovac colliding wave solutions of Einstein's equations
28. 1989 Isidore Hauser & Frederick J. Ernst, Initial value problem for colliding gravitational plane waves. I
29. 1989 Isidore Hauser & Frederick J. Ernst, Initial value problem for colliding gravitational plane waves. II
30. 1990 Isidore Hauser & Frederick J. Ernst, Initial value problem for colliding gravitational plane waves. III
31. 1990 Cornelius Hoenselares & Frederick J. Ernst, Matching pp waves to the Kerr metric
32. 1991 Wei Li, Isidore Hauser & Frederick J. Ernst, Colliding gravitational plane waves with noncollinear polarizations
33. 1991 Wei Li, Isidore Hauser & Frederick J. Ernst, Colliding gravitational waves with Killing–Cauchy horizons
34. 1991 Wei Li, Isidore Hauser & Frederick J. Ernst, Colliding wave solutions of the Einstein–Maxwell field equations
35. 1991 Isidore Hauser & Frederick J. Ernst, Initial value problem for colliding gravitational plane waves. IV
36. 1991 Wei Li, Isidore Hauser & Frederick J. Ernst, Nonimpulsive colliding gravitational waves with noncollinear polarizations
37. 1993 Frederick J. Ernst & Isidore Hauser, On Gürses's symmetries of the Einstein equations