Spacetime and Geometry: An Introduction to General Relativity

By S. Carroll. 2003

2,200 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/db55ed6b64d35509854623f6d57ca3529bc57c85

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Citations in the corpus

Teaching general relativity to undergraduates (2012, unknown): “…PHYSICS-FIRST INTERTWINED + ACTIVE-LEARNING ADJUSTED MATH-FIRST GRADUATE Wald, 1984 Misner, Thorne, & Wheeler, 1973 Weinberg, 1972 Ryder, 2009 Carroll, 2004 Schutz, 1985 Ohanian & Ruffini, 1994 Cheng, 2005 Moore, 2012 Hartle, 2003 Henriksen, 2011 Taylor & Wheeler, 2000 Schutz, 2003 DELAY IN…”
Torsion-balance tests of the weak equivalence principle (2012, background): “General relativity describes gravity in non-uniform fields, so modern statements of the equivalence principle attempt to generalize by requiring uniformity only for some small region [133, 22, 99].”
Cosmological backgrounds of gravitational waves (2018, background): “The rest of this section is based on [25] (see also [26]), which presents the flat space-time limit of Bardeen’s cosmological gauge-invariant perturbation theory [27].”
Mechanical systems in the quantum regime (2011, background): “When the masses and velocities of the objects involved are made smaller and smaller, the relativistic corrections eventually vanish and one obtains the classical laws of motion [1].”
Beyond the Cosmological Standard Model (2014, unknown): “the result of coherent de ections of light by mass concentrations. For the metric of eq. (10.20), the rst order perturbation to a photon trajectory is given by (generalizing for example eq. (7.72) of [952]): d2x(1) d2 = q2r~ ?( + ) ; (10.44) where qis the norm of the tangent vector along the unpertu”
Theoretical Aspects of Massive Gravity (2011, background): “Conventions for the curvature tensors, covariant derivatives and Lie derivatives are those of Carroll [36].”
Regular black hole metrics and the weak energy condition (2014, background): “The regular black hole may also be characterized by energy conditions [9, 10] that the corresponding energy-momentum tensor should satisfy.”
Generalized Uncertainty Principle: Approaches and Applications (2014, unknown): “For example, the metric field of Reissner black hole [101] is given as ds(2) = − ( 1− 2G r + GQ r2 ) dt(2) + ( 1− 2G r + GQ r2 ) dr(2) + r(2)dΩ(2).”
Gravitational wave background from reheating after hybrid inflation (2007, unknown): “The energy-momentum tensor of the GW is given by [40]”
Necessary and sufficient conditions for big bangs, bounces, crunches, rips, sudden singularities and extremality events (2005, background): “However, over the last few years, the zoo of cosmological singularities considered in the literature has become considerably more extensive, with “big rips” and “sudden singularities” added to the mix, as well as renewed interest in non-singular cosmological events such as “bounces” and…”