Ernst denklemi

Ernst denklemi, matematik'te doğrusal-olmayan bir kısmi diferansiyel denklem'dir. ==Adı== Ünlü fizikçi Frederick J. ErnstLisans-Fizik, Princeton Üniversitesi ve Doktora-Fizik, University of Wisconsin–Madison (Doktora Tezi: The Wave Functional Description of Elementary Particles with Application to Nucleon Structure); 1964 - 1969: Yardımcı Doçent, 1969 - 1980: Doçent, 1980 - 1987: Professör, Hepsi Fizik-Illinois Institute of Technology; 1987'den sonra Matematik-Kısmî Türevsel Denklemler ve Fizik-Genel Görelilik Kuramı Profesörü, Clarkson University Potsdam, New York. 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== * === 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 == Kategori:Genel görelilik Kategori:Kısmi diferansiyel denklemler