#metric_tensor — Public Fediverse posts

I wondered what the metric tensor of #GR says about a point in space. I was disappointed to learn the coefficients are somewhat arbitrary, as they depend on the coordinate system.

But it does tell the speed of light as measured by an observer far away from gravitational sources. And:

1. This is a physical value (invariant).
2. It is dependent on direction.

Don't miss the links in

https://blog.miamao.de/blog/Speed_of_Light_from_Metric.html

if you get confused.

#metric_tensor #physics #generalRelativity

The geometry of data: the missing metric tensor and the Stein score [Part II]
https://blog.christianperone.com/2024/11/the-geometry-of-data-part-ii/
#ycombinator #data_manifold #differential_geometry #diffusion_models #machine_learning #manifold #metric_tensor #riemannian_manifold #score_based_generative_models