Ernst denklemi

Ernst denklemi, matematik'te doğrusal-olmayan bir kısmi diferansiyel denklem'dir.

Adı
Ünlü fizikçi Frederick J. Ernst tarafından bulunmuş olduğundan, "Ernst denklemi" olarak adlandırılmıştır.

Ernst denklemi
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:

Kullanım amacı
Einstein alan denklemlerinin noksansız çözümlerini elde etmek için kullanılan doğrusal olmayan bir kısmi türevsel denklemdir.

Bibliyografya

İlgili yayınlar

Journal of Mathematical Physics  mecmuasında 

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

Kaynakça 

Genel görelilik
Kısmi diferansiyel denklemler