Warped geometry
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Template:Expert In physics, warped geometry is a Lorentzian manifold whose metric tensor can be written in form
- <math>ds^2 \, = g_{ab} dy^a dy^b + f(y) g_{ij} dx^i dx^j</math>
Note that the geometry almost decomposes into a Cartesian product of the "y" geometry and the "x" geometry - except that the "x"-part is warped, i.e. it is rescaled by a scalar function of the other coordinates "y". For this reason, the metric of a warped geometry is often called a warped product metric.
Warped geometries are the key building block of Randall-Sundrum models in particle physics.
Warped geometries are useful in that separation of variables can be used when solving partial differential equations over them.