General Relativity: With Applications to Astrophysics

By N. Straumann. 2004

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Applications of the Gauss–Bonnet theorem to gravitational lensing (2008, background): “, see [3] p 375) ds(2) = gμνdx dx = − exp[2A(r)]dt(2) + exp[2B(r)]dr(2) + r(2) ( dθ(2) + sin(2) θdφ(2) )”
Gravitational lensing (2010, background): “Many approaches to gravitational lensing exist, some of them heuristic, whereas others rather formal mathematically; see [358, 423, 425, 466, 492] for examples.”
A NEW MULTI-DIMENSIONAL GENERAL RELATIVISTIC NEUTRINO HYDRODYNAMIC CODE FOR CORE-COLLAPSE SUPERNOVAE. I. METHOD AND CODE TESTS IN SPHERICAL SYMMETRY (2010, background): “…choice for the basis four-vectors of such a frame in terms of the coordinate derivatives ∂t , ∂r , ∂θ , and ∂ϕ (see Hawking & Ellis 1973; Misner et al. 1973; Straumann 2004 for this notation) is given by e0 = α−1W ∂t + W (φ−2vr − α−1βr )∂r , (22) e1 = α−1vrW ∂t + W (φ−2 − α−1βrvr )∂r , (23) e2 =…”