= Sean M. Carroll
{c}
{tag=Physicist}
{wiki}
<Sean M. Carroll> develops and teaches the geometric account of <gravity> in <general relativity>. His 1997 lecture notes connect <differential geometry> to <Einstein field equations> and applications in <gravitational radiation>, <black holes> and <cosmology>.
A central example is the <covariant derivative>: differentiating the coordinate components of a <vector field> alone does not produce another tensor. An additional <affine connection> term accounts for the changing coordinate basis. This construction allows physical equations to retain their meaning when coordinates change, supplying the mathematical foundation for the later gravitational applications.<Lecture Notes on General Relativity by Sean M. Carroll>[Chapters 2–3: manifolds, tensor transformations, connection and covariant differentiation]{ref}
\Image[https://commons.wikimedia.org/wiki/Special:Redirect/file/Sean_Carroll_2017.jpg?width=260]
{title=Portrait of <Sean M. Carroll>}
{description=Sgerbic; colour correction and sharpening by OttRider. https://creativecommons.org/licenses/by-sa/4.0/[CC BY-SA 4.0], via Wikimedia Commons.}
{source=https://commons.wikimedia.org/wiki/File:Sean_Carroll_2017.jpg}
{width=260}
Back to article page
