Ernst denklemi

Ünlü fizikçi Frederick J. Ernst tarafından bulunmuş olduğundan, "Ernst denklemi" olarak adlandırılmıştır.Sağ tarafında Birinci dereceden kısmî türevler içeren ve doğrusal olmayan terimleri olan  bir denklemdir. Çözümü aranan u karmaşık fonksiyonunun gerçel kısmı R(u), denklemin sol tarafındaki İkinci dereceden kısmî türevlerin çarpımı halinde belirdiğinden, denklemin her iki tarafı da doğrusal-olmayan (non-linear) terimler ihtivâ etmektedir. Denklem aşağıdaki şekilde verilmektedir:Einstein alan denklemlerinin noksansız çözümlerini elde etmek için kullanılan doğrusal olmayan bir kısmi türevsel denklemdir.1971: Frederick J. Ernst, Exterior-Algebraic Derivation of Einstein Field Equations Employing a Generalized Basis1974: Frederick J. Ernst, Complex potential formulation of the axially symmetric gravitational field problem1975: Frederick J. Ernst, Erratum: Complex potential formulation of the axially symmetric gravitational field problem1975: John E. Economou & Frederick J. Ernst, Weyl conform tensor of =2 Tomimatsu–Sato spinning mass gravitational field1978: Frederick J. Ernst, Coping with different languages in the null tetrad formulation of general relativity1978: Frederick J. Ernst & I. Hauser, Field equations and integrability conditions for special type N twisting gravitational fields1978: Isidore Hauser & Frederick J. Ernst, On the generation of new solutions of the Einstein–Maxwell field equations1979: (Erratum) Coping with different languages in the null tetrad formulation of general relativity1980: Isidore Hauser & Frederick J. Ernst, A homogeneous Hilbert problem for the Kinnersley–Chitre transformations of electrovac space-times1980: Isidore Hauser & Frederick J. Ernst, A homogeneous Hilbert problem for the Kinnersley–Chitre transformations1982: Dong-sheng Guo & Frederick J. Ernst, Electrovac generalization of Neugebauer's N = 2 solution of the Einstein vacuum field equations1983: Y. Chen, Dong-sheng Guo & Frederick J. Ernst, Charged spinning mass field involving rational functions1987: Frederick J. Ernst, Alberto Garcia D & Isidore Hauser, Colliding gravitational plane waves with noncollinear polarization. I1987: Frederick J. Ernst, Alberto Garcia D & Isidore Hauser, Colliding gravitational plane waves with noncollinear polarization. II1988: Frederick J. Ernst, Alberto Garcia D & Isidore Hauser, Colliding gravitational plane waves with noncollinear polarization. III1989: Wei Li & Frederick J. Ernst, A family of electrovac colliding wave solutions of Einstein's equations1989: Isidore Hauser & Frederick J. Ernst, Initial value problem for colliding gravitational plane waves. I1989: Isidore Hauser & Frederick J. Ernst, Initial value problem for colliding gravitational plane waves. II1990: Isidore Hauser & Frederick J. Ernst, Initial value problem for colliding gravitational plane waves. III1991: Wei Li, Isidore Hauser & Frederick J. Ernst, Colliding gravitational plane waves with noncollinear polarizations1991: Wei Li, Isidore Hauser & Frederick J. Ernst, Colliding gravitational waves with Killing–Cauchy horizons1991: Wei Li, Isidore Hauser & Frederick J. Ernst, Colliding wave solutions of the Einstein–Maxwell field equations1991: Isidore Hauser & Frederick J. Ernst, Initial value problem for colliding gravitational plane waves. IV1991: Wei Li, Isidore Hauser & Frederick J. Ernst, Nonimpulsive colliding gravitational waves with noncollinear polarizations