2 edition of **On the Einstein tensors of spherically symmetric space-times** found in the catalog.

On the Einstein tensors of spherically symmetric space-times

Hyoichiro Takeno

- 110 Want to read
- 31 Currently reading

Published
**1969**
in Hiroshima
.

Written in English

- Hyperspace.,
- Space and time.,
- Calculus of tensors.

**Edition Notes**

Statement | Hyoichiro Takeno and Shinʼichi Kitamura. |

Series | Research Institute for Theoretical Physics, Hiroshima University, RRK69-13 |

Contributions | Kitamura, Shin-ichi, 1931- joint author. |

Classifications | |
---|---|

LC Classifications | QA691 .T35 |

The Physical Object | |

Pagination | 25 p. |

Number of Pages | 25 |

ID Numbers | |

Open Library | OL5030386M |

LC Control Number | 73870922 |

Static spherically symmetric spacetimes A metric is said to be stationary if it admits a timelike Killing vector K. It is said to be static if it is stationary and there exists a surface Σ of codimension one which is everywhere orthogonal to K. In a neighborhood of Σ . Once upon a time there was a guy named Albert Einstein. He dabbled (a lot) with physics and with mathematical creatures called “tensors”, which he introduced the following way in his paper The Foundation of the General Theory of Relativity.

the schwarzschild solution and black holes We now move from the domain of the weak-field limit to solutions of the full nonlinear Einstein's equations. With the possible exception of Minkowski space, by far the most important such solution is that discovered by Schwarzschild, which describes spherically symmetric vacuum spacetimes. There is only one plane symmetric static vacuum solution of Einstein field equations. In section 3 we find all the cylindrically symmetric static vacuum solutions. Most of the spacetimes obtained in section 3 are new in the literature. Section 4 consist on the calculation of spherically symmetric static vacuum solution.

It is shown that the results of the paper by Contreras et al. [Contreras, G., Nunez, L. A., Percoco, U. "Ricci Collineations for Non-degenerate, Diagonal and Spherically Symmetric Ricci Tensors" () Gen. Rel. Grav. 32, ] concerning the Ricci Collineations in spherically symmetric space-times with non-degenerate and diagonal Ricci tensor do not cover all possible cases. Vacuum, Einstein–Maxwell and pure radiation ﬁelds Timelike orbits Spacelike orbits Generalized Birkhoﬀ theorem Spherically- and plane-symmetric ﬁelds Dust solutions Perfect ﬂuid solutions with plane, spherical or pseudospherical symmetry Some basic.

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The general line element for a static space times with maximal symmetric transverse spaces can be written as ds 2 = e A(r) dt 2 −e B(r) dr 2 −r 2 (dθ 2 +f 2.

The classification of symmetric second‐rank tensors in Minkowski space and its application to the Einstein tensor is reviewed. It is shown that, for spherically symmetric metrics, the Einstein tensor always has a spacelike double eigenvector; and the possible types of Einstein tensor that this degeneracy allows are by: This book describes the basic solutions of Einstein's equations with a particular emphasis on what they mean, both geometrically and physically.

Concepts such as big bang and big crunch-types of singularities, different kinds of horizons and gravitational waves, are described in the context of the particular space-times in which they naturally Cited by: A family (not the most general) of spherically symmetric space‐times which admit geodesic correspondences is given by H.

Takeno, The Theory of Spherically Symmetric Space‐Times, Sci. Rep. Res. Inst. Theoret. Phys., Hiroshima University, No.

5 (), p. Cited by: We assume a realistic barotropic equation of state. Equilibria of the spherically symmetric Einstein–Euler equations are given by the Tolman–Oppenheimer–Volkoff equations, and time-periodic solutions around the equilibrium of the linearized equations can be considered.

Our aim is to find true solutions near these time-periodic by: The classification of symmetric second-rank tensors in Minkowski space and its application to the Einstein tensor is reviewed. It is shown that, for spherically symmetric metrics, the Einstein.

Einstein's theory of general relativity is a theory of gravity and, as in the earlier Newtonian theory, much can be learnt about the character of gravitation and its effects by investigating particular idealised examples. This book describes the basic solutions of Einstein's equations with a particular emphasis on what they mean, both geometrically and physically.

Volume B, number 1 PItYSICS LETTERS 20 March SPHERICALLY SYMMETRIC SOLUTIONS OF EINSTEIN-MAXWELL THEORY WITH A GAUSS-BONNET TERM D.L. WILTSHIRE Department of Applied Mathematics and Theoretical Physics, Universi(r' of Cambridge, Silver Street, Cambridge CB3 9E IV, UK Received 19 December The low energy expansion of supersymmetric string theory Cited by: As a symmetric order-2 tensor, the Einstein tensor has 10 independent components in a 4-dimensional space.

It follows that the Einstein field equations are a set of 10 quasilinear second-order partial differential equations for the metric tensor.

Box he Stress-Energy Tensor for a Perfect Fluid in Its Rest LIF T Box quation Reduces to Equation E Box luid Dynamics from Conservation of Four-Momentum F the Einstein ﬁeld equation, a tensorial equation which takes the form Gµν = 8πTµν, Gµν is an Einstein’s tensor which is symmetric and vanishes when spacetime is ﬂat, Tµν is the so-called energy-momentum tensor which can be thought of as a source for the gravitational ﬁeld.

It is a. The general spherically symmetric line element for a perfect fluid source is specified in comoving coordinates and the kinematical quantities are obtained in § The nonvanishing components of the connection coefficients, the Ricci tensor, Ricci scalar and the Einstein tensor are explicitly calculated.

In § the energy-momentum. Lecture Symmetries, spherically-symmetric spacetimes Yacine Ali-Ha moud There are two regimes where GR has known analytic solutions: either in the weak-gravity regime, which we have studied so far, or in the case of highly symmetric spacetimes, on which we will now focus.

The notion of symmetry is conveyed by Killing vector elds (see. (2) A spherically symmetric spacetime has a 3-parameter group of spacelike Killing vector fields that satisfy the properties of the Lie group SO(3), which describes rotations in 3-dimensional space. As noted, these definitions are coordinate-independent; they define invariant geometric properties of the spacetime.

By exploiting the null tetrad formalism of Jogia and Griffiths and the technique of differential forms on a non-Riemannian space-time, non-static conformally flat, Petrov-type D, spherically symmetric solutions of the Einstein–Cartan field equations; when Weyssenhoff fluid is the source of curvature and spin, are : L.N.

Katkar, D.R. Phadatare. Symmetries of static, spherically symmetric space‐times Article (PDF Available) in Journal of Mathematical Physics 28(5) May with 43 Reads How we measure 'reads'.

18 The Origin of Orbits in Spherically Symmetric Space-Time The following line element [11] is a representation of a spherically symmetric space-time: ds2 = −mc2dt2 +ndr2 +r2dΩ2 () where dΩ2 is the inﬁnitesimal volume element in spherical polar coordinates.

() is not the most general line element possible mathematically for. This solution gives the geometry of spacetime for a spherically symmetric static mass distribution. The famous Schwarzschild singularity is discussed briefly.

This is followed in chapter 6 by a more in-depth discussion, using various tools from differential geometry, of the stress-energy-momentum by: I've been studying gravity with a dynamical preferred frame, namely one in which the preferred frame is set by the existence of a unit time-like vector field called the "aether".

I've been using this. Geodesics in spherically symmetric spacetimes Particle geodesics in a Schwarzschild spacetime Deflection of light by the Sun Falling into a black hole Questions References 6 Tensors and geometry Covariant derivatives Basic properties of covariant derivatives Riemann and Ricci.

Spacetime symmetries are features of spacetime that can be described as exhibiting some form of role of symmetry in physics is important in simplifying solutions to many problems.

Spacetime symmetries are used in the study of exact solutions of Einstein's field equations of general ime symmetries are distinguished from internal symmetries.We discuss the static, spherically symmetric Einstein-spinor field system in the possible presence of various spinor field nonlinearities.

We take into account that the spinor field energy-momentum tensor (EMT) has in general some off-diagonal components, whose vanishing due to the Einstein equations substantially affects the form of the spinor field itself and the space-time geometry.case of a spherically symmetrical static perfect fluid Einstein's equa tions, which consist of the simultaneous solution of several second order non-linear differential equations, have been reduced to the solu tion of a single second order linear equation.

For many cases a power series solution is applicable and relatively straightforward.