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By A Grothendieck

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10) With the exception of the static limit (α = 0), ω0± = 0 for all x > 0. The real zeros of the argument of the square-root, specify x I and x I I . Figure 4 is a plot of x I and x I I versus α. It can be shown analytically, or seen from figure 4 that in the Schwarzschild limit (α = 0) x I and x I I occur at the same distance, x I = x I I = 1/3. As α decreases x I (r I increases) and x I I increases (r I I decreases) until α = 1 at which point x I = 1/4 and x I I = 1. 3. NON-KEPLERIAN RINGS In this section we show that, under certain conditions, stable rings of matter form about compact stellar objects.

Indeed the effect we are discussing is sensitive to the rotation parameter α. The space outside a radiating source is filled with photons. In this case, the stress energy tensor of dust (non interacting matter) in the presence of a photon field is Tαβ = ρd u α u β + Pp gαβ , (24) P1: GXB General Relativity and Gravitation (GERG) pp639-gerg-453454 November 15, 2002 56 11:13 Style file version May 27, 2002 Drake where u α is the four velocity of the dust, ρd is its density and Pp is the photon pressure.

J. Phys. A 30, 4327–4336. [10] Iliev, B. Z. (1998). J. Phys. A 31, 1287–1296. [11] Iliev, B. Z. (1998). J. Geometry Phys. 24, 209–222. [12] Hartley, D. (1995). Class. Quantum Grav. 12 L103–L105. [13] Manoff, S. (1996). Int. J. Mod. Phys. A 11, 3849–3874. [14] Manoff, S. (1998). Class. Quantum Grav. 15, 465–477. P1: GXB General Relativity and Gravitation (GERG) pp639-gerg-453452 November 15, 2002 11:12 On the Existence of a Gyroscope in Spaces with Affine Connections and Metrics [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] Style file version May 27, 2002 33 Manoff, S.

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A general theory of fibre spaces with structure sheaf by A Grothendieck

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