Coping with different languages in the null tetrad formulation of general relativity

1978 ◽  
Vol 19 (2) ◽  
pp. 489-493 ◽  
Author(s):  
Frederick J. Ernst
Keyword(s):  
General Relativity ◽  
Null Tetrad ◽  
Tetrad Formulation

scholarly journals The Riemann-Silberstein vector in the Dirac algebra

2018 ◽  
Vol 65 (1) ◽  
pp. 65 ◽  
Author(s):  
Shahen Hacyan
Keyword(s):  
General Relativity ◽  
Electromagnetic Field ◽  
Explicit Form ◽  
Maxwell Equations ◽  
Compact Form ◽  
Algebraic Representation ◽  
Dirac Algebra ◽  
Null Tetrad ◽  
Covariant Derivatives ◽  
Tetrad Formulation

It is shown that the Riemann-Silberstein vector, defined as ${\bf E} + i{\bf B}$, appears naturally in the $SL(2,C)$ algebraic representation of the electromagnetic field. Accordingly, a compact form of the Maxwell equations is obtained in terms of Dirac matrices, in combination with the null-tetrad formulation of general relativity. The formalism is fully covariant; an explicit form of the covariant derivatives is presented in terms of the Fock coefficients.

Null-tetrad formulation of the Yang-Mills field equations

1978 ◽  
Vol 45 (2) ◽  
pp. 310-334 ◽  
Author(s):  
M. Carmeli ◽  
Ch. Charac ◽  
M. Kaye
Keyword(s):  
Field Equations ◽  
Yang Mills ◽  
Null Tetrad ◽  
Tetrad Formulation ◽  
Mills Field

Tetrad Formulation of Junction Conditions in General Relativity

1967 ◽  
Vol 8 (11) ◽  
pp. 2302-2308 ◽  
Author(s):  
Frank B. Estabrook ◽  
Hugo D. Wahlquist
Keyword(s):  
General Relativity ◽  
Junction Conditions ◽  
Tetrad Formulation

Null-tetrad formulation of dyons

1991 ◽  
Vol 104 (3) ◽  
pp. 337-348 ◽  
Author(s):  
P. S. Bisht ◽  
O. P. S. Negi ◽  
B. S. Rajput
Keyword(s):  
Null Tetrad ◽  
Tetrad Formulation

Gravitational waves in general relativity XI. Cylindrical-spherical waves

1969 ◽  
Vol 313 (1512) ◽  
pp. 83-96 ◽  
Keyword(s):  
General Relativity ◽  
Wave Propagation ◽  
Electromagnetic Wave ◽  
Electromagnetic Wave Propagation ◽  
Null Geodesic ◽  
Riemann Tensor ◽  
Optical Parameters ◽  
Null Tetrad ◽  
Spherical Waves ◽  
Cylindrical Waves

Further properties of a vacuum metric obtained in an earlier paper, representing a spherical-fronted gravitational wave (which, however, possesses cylindrical symmetry) are derived. This metric is constructed by introducing ‘bending terms’ into Rosen’s metric for cylindrical waves. The way the transition occurs from properties characteristic of cylindrical waves to those of spherical waves is examined. The asymptotic behaviour of the optical parameters and the null tetrad components of the Weyl (Riemann) tensor along an outgoing null geodesic is determined. An interpretation of the axial singularity is given by comparison with an analogous feature in classical electromagnetic wave propagation.

scholarly journals Extension Rules of Newman–Janis Algorithm for Rotation Metrics in General Relativity

2020 ◽  
pp. 1-14
Author(s):  
Yu-Ching, Chou
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Kerr Metric ◽  
Tensor Structure ◽  
De Sitter ◽  
Field Equations ◽  
Null Tetrad ◽  
Axisymmetric Solutions ◽  
Metric Function ◽  
De Sitter Metric

Aims: The aim of this study is to extend the formula of Newman–Janis algorithm (NJA) and introduce the rules of the complexifying seed metric. The extension of NJA can help determine more generalized axisymmetric solutions in general relativity.Methodology: We perform the extended NJA in two parts: the tensor structure and the seed metric function. Regarding the tensor structure, there are two prescriptions, the Newman–Penrose null tetrad and the Giampieri prescription. Both are mathematically equivalent; however, the latter is more concise. Regarding the seed metric function, we propose the extended rules of a complex transformation by r2/Σ and combine the mass, charge, and cosmologic constant into a polynomial function of r. Results: We obtain a family of axisymmetric exact solutions to Einstein’s field equations, including the Kerr metric, Kerr–Newman metric, rotating–de Sitter, rotating Hayward metric, Kerr–de Sitter metric and Kerr–Newman–de Sitter metric. All the above solutions are embedded in ellipsoid- symmetric spacetime, and the energy-momentum tensors of all the above metrics satisfy the energy conservation equations. Conclusion: The extension rules of the NJA in this research avoid ambiguity during complexifying the transformation and successfully generate a family of axisymmetric exact solutions to Einsteins field equations in general relativity, which deserves further study.

scholarly journals An Extension of Newman–Janis algorithm for Rotation Metrics in General Relativity

2019 ◽  
Author(s):  
Yu-Ching Chou
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Kerr Metric ◽  
Tensor Structure ◽  
De Sitter ◽  
Null Tetrad ◽  
Complex Transformation ◽  
Static Black Hole ◽  
Metric Function ◽  
De Sitter Metric

The Newman-Janis algorithm is widely known in the solution of rotating black holes in general relativity. By means of complex transformation, the solution of the rotating black hole can be obtained from the seed metric of a static black hole. This study shows that the extended Newman-Janis algorithm must treat the tensor structure and the seed metric function separately. In the tensor structure, there are two prescriptions, the Newman–Penrose null tetrad and the Giampieri prescription. Both are mathematically the same, while the latter is more concise. In the seed metric function, the extended rules of complex transformation are given in the power of r, and the formulaic solution is deduced. Some exact solutions are derived by the extended algorithm, including the Kerr metric, the Kerr–Newman metric, the rotating–de Sitter, the Kerr–de Sitter metric, and the Kerr–Newman–de Sitter metric.

Sign in / Sign up

Export Citation Format

Share Document