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:

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

Kullanım amacı

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

Bibliyografya

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

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