- #1
Tony Stark
- 51
- 2
I Have been reading hartle's book on Gr which states that basis four vectors point in x,y,z,t coordinate axes. So are they similar to the coordinate axis of Cartesian plane.
Tony Stark said:are they similar to the coordinate axis of Cartesian plane
Basis vectors in general relativity are a set of vectors used to define a coordinate system within a curved space. They are used to express the position and movement of objects within this space.
In a Cartesian plane, the basis vectors are constant and do not change as you move around the space. In general relativity, the basis vectors can vary depending on the curvature of the space and the position of the observer.
Basis vectors are essential in general relativity because they allow us to define and describe the geometry of a curved space. They also enable us to express physical quantities, such as velocity and acceleration, in a meaningful way within this space.
Basis vectors are used in calculations within general relativity to transform between different coordinate systems and to express physical quantities in a covariant form. They are also used to define the metric tensor, which is a fundamental concept in general relativity.
Yes, basis vectors can be visualized in a curved space. In a two-dimensional space, the basis vectors can be represented by two arrows that are tangent to the surface at a given point. In a three-dimensional space, three arrows are needed to represent the basis vectors, one for each dimension.