What are the units of the Ricci tensor?
On the LHS of the equation, the metric tensor gµν is dimensionless so the Ricci tensor Rµν, Ricci scalar R, and the cosmological constant Λ all have natural units of GeV2, or mass squared since energy and mass are equivalent.
Does a tensor have a unit?
It has no units. A metric tensor in any coordinate can have no units, just look at how the components of a diagonal metric tensor fits into the distance formula, if it had units the units on the left would not match the units on teh right.
What is the order of Ricci tensor?
The Ricci tensor is a second order tensor about curvature while the stress- energy tensor is a second order tensor about the source of gravity (energy density).
Who invented the Ricci tensor?
G. Ricci
Tensor calculus has been invented by G. Ricci. He called the new branch of mathematics an absolute differential calculus and developed it during the ten years of 1887—1896.
Is Ricci tensor symmetric?
Thus, the Ricci tensor is symmetric with respect to its two indices, that is, (12.49) Using the Ricci tensor (12.44), we can define the Ricci scalar as follows: (12.50)
What are the components of a tensor?
The components of a tensor T are the coefficients of the tensor with respect to the basis obtained from a basis {ei} for V and its dual basis {εj}, i.e. Using the properties of the tensor product, it can be shown that these components satisfy the transformation law for a type (p, q) tensor.
What is tensor and its types?
A tensor is a vector or matrix of n-dimensions that represents all types of data. All values in a tensor hold identical data type with a known (or partially known) shape. The shape of the data is the dimensionality of the matrix or array. A tensor can be originated from the input data or the result of a computation.
Who is the father of tensor?
Gregorio Ricci-Curbastro
0. Born on 12 January 1853 in Lugo in what is now Italy, Gregorio Ricci-Curbastro was a mathematician best known as the inventor of tensor calculus.
What rank is Ricci tensor?
The rank of a tensor can be thought of as the number of distinct indices that the tensor has. Thus is a fourth-rank tensor, while the Ricci tensor is a second-rank tensor. On the other hand, the Ricci scalar is a scalar quantity and hence a zero-rank tensor.