Ernst denklemi

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

Adı

Ünlü fizikçi Frederick J. Ernst^[1] 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:^[2]

\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

Kaynakça

^ Lisans-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.
^ "Weisstein, Eric W, Ernst denklemi, MathWorld--A Wolfram Web". 16 Ağustos 2017 tarihinde kaynağından arşivlendi. Erişim tarihi: 4 Mayıs 2015.

[1] Lisans-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.

[2] "Weisstein, Eric W, Ernst denklemi, MathWorld--A Wolfram Web". 16 Ağustos 2017 tarihinde kaynağından arşivlendi. Erişim tarihi: 4 Mayıs 2015.

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