Volume renormalization for conformally compact asymptotically hyperbolic manifolds in dimension four
Shih-Tsai Feng
TL;DR
This paper introduces a new formula for renormalized volume in four-dimensional conformally compact asymptotically hyperbolic manifolds, extending previous results and providing variational insights.
Contribution
It generalizes existing renormalized volume formulas to a broader class of manifolds and derives variational formulas for the functional.
Findings
New renormalized volume formula for 4D conformally compact asymptotically hyperbolic manifolds
Extension of previous formulas by Anderson, Albin, and Chang-Qing-Yang
Variational formulas for the renormalized volume as a functional
Abstract
We derive a new renormalized volume formula for conformally compact asymptotically hyperbolic manifolds in dimension four. The formula generalizes the ones given by Anderson, Albin, and Chang-Qing-Yang for the case of Poincare-Einstein manifolds. We also derive variational formulas for the renormalized seen as a functional on the manifold.
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Geometric Analysis and Curvature Flows · Geometry and complex manifolds