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Gravitational waves and massless particle fields
| Content Provider | Semantic Scholar |
|---|---|
| Author | Holten, J. W. Van |
| Copyright Year | 1999 |
| Abstract | These notes address the planar gravitational wave solutions of general relativity in empty space-time, and analyze the motion of test particles in the gravitational wave field. Next we consider related solutions of the Einstein equations for the gravitational field accompanied by long-range wave fields of scalar, spinor and vector type, corresponding to massless particles of spin s = (0, 1 2 , 1). The motion of test masses in the combined gravitational and scalar, spinor or vector wave fields is discussed. ∗ Work performed as part of the research program of the Foundation for Fundamental Research of Matter (FOM). 1 Planar gravitational waves a. Planar wave solutions of the Einstein equations Planar gravitational wave solutions of the Einstein equations have been known since a long time [1]-[3]. In the following I discuss unidirectional solutions of this type, propagating along a fixed light-cone direction; thus the fields depend only on one of the light-cone co-ordinates (u, v), here taken transverse to the x-y-plane: u = ct− z, v = ct+ z. (1) Such gravitational waves can be described by space-time metrics gμνdx dx = − dudv −K(u, x, y)du + dx + dy = − cdτ, (2) or similar solutions with the roles of v and u interchanged. If the space-time is asymptotically minkowskian. With the metric (2), the connection co-efficients become Γ v uu = K,u, Γ x uu = 1 2 Γ v xu = 1 2 K,x, Γ y uu = 1 2 Γ v yu = 1 2 K,y. (3) All other components vanish. The corresponding Riemann tensor has non-zero components Ruxux = − 1 2 K,xx, Ruyuy = − 1 2 K,yy, Ruxuy = Ruyux = − 1 2 K,xy. (4) The only non-vanishing component of the Ricci tensor then is Ruu = − 1 2 (K,xx +K,yy) ≡ − 1 2 ∆transK. (5) Here the label trans refers to the transverse (x, y)-plane, with the z-axis representing the longitudinal direction. In complex notation ζ = x+ iy, ζ̄ = x− iy, (6) the Einstein equations in vacuo become Rμν = 0 ⇔ K,ζζ̄ = 0. (7) The general solution of this equation reads K(u, ζ, ζ̄) = f(u; ζ) + f̄(u; ζ) = ∞ |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://arxiv.org/pdf/gr-qc/9906026v1.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/gr-qc/9906026v2.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Arabic numeral 0 Axis vertebra Emoticon Note (document) Optic axis of a crystal Solutions Source-to-source compiler Spinor Transverse wave notation |
| Content Type | Text |
| Resource Type | Article |
