On generalized torsion two-forms in general relativity: a result of null tetrad formalism

1981 ◽  
Vol 5 (6) ◽  
pp. 481-487
Author(s):  
Roberto Cianci
Keyword(s):  
General Relativity ◽  
Tetrad Formalism ◽  
Null Tetrad

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.

Asymptotically flat spaces in asymptotically null-spherical coordinates

1970 ◽  
Vol 320 (1542) ◽  
pp. 349-368 ◽  
Keyword(s):  
Flat Space ◽  
Riemann Tensor ◽  
Polar Coordinates ◽  
Field Equations ◽  
Simple Criterion ◽  
Tetrad Formalism ◽  
Metric Tensor ◽  
Asymptotically Flat ◽  
Null Tetrad ◽  
Gravitational Fields

The behaviour of asymptotically flat gravitational fields in the framework of general relativity is studied by the use of tetrad formalism. For this, a system of coordinates u , r , θ and ɸ is used, such that at spatial infinity u = const, is a null hypersurface and r , θ and ɸ reduce to the usual spherical polar coordinates. A set of four vectors (a tetrad) is also chosen with the only restriction that they are everywhere null. The metric tensor and the four vectors are expanded in inverse powers of r ; the rotation coefficients and the tetrad components of the Riemann tensor are then calculated in a similar expansion; and the first two terms in the expansion beyond their values for a flat space are retained. The field equations in these approximations are derived explicitly and their effect on the expansion of the tetrad components of the Riemann tensor is studied; and the total energy and linear momentum are examined. In this paper three main results are derived: (i) the form of the peeling theorem in the above-mentioned coordinates for an arbitrary null tetrad; (ii) the generalized expression for the news function of the field; (iii) a simple criterion for recognizing certain classes of non-radiating fields.

Tetrad formalism and reference frames in general relativity

2006 ◽  
Vol 37 (1) ◽  
pp. 104-134 ◽  
Author(s):  
A. F. Zakharov ◽  
V. A. Zinchuk ◽  
V. N. Pervushin
Keyword(s):  
General Relativity ◽  
Reference Frames ◽  
Tetrad Formalism

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.

The Hawking mass for an ellipsoidal surface

2020 ◽  
Vol 35 (11) ◽  
pp. 2050073
Author(s):  
Rehana Rahim ◽  
Khalid Saifullah
Keyword(s):  
General Relativity ◽  
Schwarzschild Spacetime ◽  
Null Tetrad ◽  
Ellipsoidal Surface ◽  
Quasilocal Mass

The mass of a system in general relativity cannot be defined locally. Thus, one defines mass at quasilocal level. There are many definitions of quasilocal mass. One of them is the Hawking mass. In this paper, we determine the Hawking mass for ellipsoidal 2-surface for a non-Schwarzschild spacetime. In order to do this, we first determine a null tetrad and then compute the Hawking mass. The results are presented graphically also.

Perturbations of space-times in general relativity

1974 ◽  
Vol 341 (1624) ◽  
pp. 49-74 ◽  
Keyword(s):  
General Relativity ◽  
Gauge Invariance ◽  
Separation Of Variables ◽  
Tetrad Formalism ◽  
Gauge Invariant ◽  
Gravitational Fields ◽  
Coupled Equations ◽  
Definition Of ◽  
Natural Way ◽  
Perturbation Equations

A definition of perturbations of space-times in general relativity is proposed. The definition leads in a natural way to a concept of gauge invariance, and to an extension of a lemma of Sachs (1964). Coupled equations governing linearized perturbations of certain tetrad components of scalar, electromagnetic, and gravitational fields are derived by the use of Geroch, Held & Penrose’s (1973) version of the tetrad formalism of Newman & Penrose (1962). It is shown that these perturbations are gauge invariant if and only if the unperturbed space-time is vacuum of algebraic type {22} or, equivalently, if and only if the perturbation equations decouple. Finally the maximal subclass of type {22} space-times for which the decoupled perturbation equations can be solved by separation of variables is found. This class comprises all the nonaccelerating type {22} space-times, including that of Kerr, thus elucidating earlier results of Bardeen & Press (1972) and Teukolsky (1973).

Sign in / Sign up

Export Citation Format

Share Document