killing vector वाक्य
उदाहरण वाक्य
मोबाइल
- It turns out that the most general pp-wave spacetime has only one Killing vector field, the null geodesic congruence k = \ partial _ v.
- In the usual coordinates, outside the Killing horizon, the Killing vector field \ partial / \ partial t is timelike, whilst inside it is spacelike.
- When the energy-momentum tensor represents an electromagnetic field, a Killing vector field does " not necessarily " preserve the electric and magnetic fields.
- While general space-times lack a finite-parameter time-translation symmetry, stationary space-times have such a symmetry, known as a Killing vector.
- They have argued that static stars must have " static �ther " solutions, which means that the �ther points in the direction of a timelike Killing vector.
- Killing vector field whose integral curves are closed spacelike curves ( circles, in fact ), which moreover degenerate to zero length closed curves on the axis R = 0.
- Here, it is useful to know that any Killing vectors which may be present will ( in the case of a vacuum solution ) automatically satisfy the curved spacetime Maxwell equations.
- However this is difficult to reconcile with static black holes, as at the event horizon there are no timelike Killing vectors available and so the black hole solutions cannot have static �thers.
- Indeed, in the Cartesian chart we can readily find ten linearly independent Killing vector fields, generating respectively one parameter subgroups of time translation, three spatials, three rotations and three boosts.
- In connection with this, it may be shown that " every Killing vector field is a matter collineation " ( by the Einstein field equations, with or without cosmological constant ).
- While the focus here has been on energy, analogue definitions for global momentum exist; given a field of angular Killing vectors and following the Komar technique, one can also define global angular momentum.
- In connection with this, it may be shown that " every Killing vector field is a matter collineation " ( by the Einstein field equations ( EFE ), with or without cosmological constant ).
- Equivalently, a plane-wave is a pp-wave with at least a five-dimensional Lie algebra of Killing vector fields X, including X = \ partial _ v and four more which have the form
- A Killing vector field is uniquely determined by specifying the values of the vector field and its first covariant derivative ( equivalently, specifying X and F ) at any point ( for every connected component ) of M.
- It can be shown that the G�del solution is, up to local isometry, the " only " perfect fluid solution of the Einstein field equation admitting a five-dimensional Lie algebra of Killing vectors.
- It was customary to represent black hole horizons via stationary solutions of field equations, i . e ., solutions which admit a time-translational Killing vector field everywhere, not just in a small neighborhood of the black hole.
- For example, Killing vector fields may be used to classify spacetimes, as there is a limit to the number of global, smooth Killing vector fields that a spacetime may possess ( the maximum being 10 for 4-dimensional spacetimes ).
- For example, Killing vector fields may be used to classify spacetimes, as there is a limit to the number of global, smooth Killing vector fields that a spacetime may possess ( the maximum being 10 for 4-dimensional spacetimes ).
- We can restate this by saying that our symmetry group includes as three-dimensional subgroups examples of Bianchi types I, III and VIII . Four of the five Killing vectors, as well as the curvature tensor, do not depend upon the coordinate y.
- In particular, the three spatial Killing vector fields have exactly the same form as the three nontranslational Killing vector fields in a spherically symmetric chart on E 3; that is, they exhibit the notion of arbitrary Euclidean rotation about the origin or spherical symmetry.
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