einstein tensor वाक्य
उदाहरण वाक्य
मोबाइल
- Thus another name for the Einstein tensor is the " trace-reversed Ricci tensor ".
- The left hand side, the Einstein tensor, can be thought of as a kind of average curvature.
- To get physical results, we can either turn to perturbation methods or linear approximations of the Einstein tensor.
- We have got about half the material we need to formulate the Einstein equations, namely, the Einstein tensor.
- Now that we have postulated the metric tensor, we have a lot of algebra to do in order to arrive at the Einstein tensor.
- Then, each set of tensor elements may be symbollically coded, until one finally has got symbollic expressions for all 4 x 4 = 16 components of the Einstein tensor.
- On the left-hand side is the Einstein tensor, a specific divergence-free combination of the Ricci tensor R _ { \ mu \ nu } and the metric.
- This implies that the curvature of space ( represented by the Einstein tensor ) is directly connected to the presence of matter and energy ( represented by the stress energy tensor ).
- In the special case of a locally inertial reference frame near a point, the first derivatives of the metric tensor vanish and the component form of the Einstein tensor is considerably simplified:
- The EFE describe how mass and energy ( as represented in the stress energy tensor ) are related to the curvature of space-time ( as represented in the Einstein tensor ).
- The Einstein tensor is built up from the metric tensor and its partial derivatives; thus, the EFE are a system of ten partial differential equations to be solved for the metric.
- In the above field equations, G ^ { \ alpha \ beta } is the Einstein tensor, computed uniquely from the vacuum regions ", which contain no matter or nongravitational fields.
- Adding a " constant " to the right-hand side of the Einstein equations will effect a change in the Einstein tensor, and thus also in the curvature properties of space-time.
- But in the Brans Dicke theory, the Einstein tensor is determined partly by the immediate presence of mass-energy and momentum, and partly by the long-range scalar field \ phi \,.
- Where "'\ kappa "'is a constant, and the Einstein tensor on the left side of the equation is equated to the stress energy tensor representing the energy and momentum present in the spacetime.
- First published by Einstein in 1915 as a tensor equation, the EFE equate local spacetime curvature ( expressed by the Einstein tensor ) with the local energy and momentum within that spacetime ( expressed by the stress energy tensor ).
- The special case of n = 4 dimensions in physics ( 3 space, 1 time ) gives G \,, the trace of the Einstein tensor, as the negative of R \,, the Ricci tensor's trace.
- Then we need only ensure that the divergences vanish ( i . e . that the second Maxwell equation is satisfied for a " source-free " field ) and that the electromagnetic stress-energy matches the Einstein tensor.
- It is a matter of pure mathematics that, in any metric theory, the Riemann tensor can always be written as the sum of the Weyl curvature ( or " conformal curvature tensor " ) plus a piece constructed from the Einstein tensor.
- In differential geometry, the "'Einstein tensor "'( named after Albert Einstein; also known as the "'trace-reversed Ricci tensor "') is used to express the curvature of a pseudo-Riemannian manifold.
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