- #1
pleasehelpmeno
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Am i right in thinking:
[itex] g^{\mu\nu}g_{\mu\nu}=4 \mbox{ and } g^{\mu\nu}T_{\mu\nu}=T [/itex] ?
[itex] g^{\mu\nu}g_{\mu\nu}=4 \mbox{ and } g^{\mu\nu}T_{\mu\nu}=T [/itex] ?
The left-hand side is a scalar. The right-hand side is not.pleasehelpmeno said:[itex]g^{\mu\nu}T_{\mu\nu}=T [/itex] ?
Components of the stress-energy tensor have two indices, not four. You could however define T by ##T=T^\mu{}_\mu##. The right-hand side is defined by ##T^\mu{}_\mu =T^{\mu\nu}g_{\mu\nu}##.pleasehelpmeno said:sorry shouldn't it be [itex] T^{\mu \nu}_{\mu \nu} = T [/itex]?
A tensor is a mathematical object used to represent quantities that have multiple components, such as vectors and matrices. It is often used in physics and engineering to describe physical quantities and their transformations.
Contracting a tensor involves summing over repeated indices in a tensor expression. This results in a new tensor with fewer indices than the original.
This expression represents the contraction of two tensors, g^{\mu\nu} and g_{\mu\nu}, resulting in the scalar quantity of 4. It is known as the trace of the tensor g^{\mu\nu}.
The 4 in the equation represents the dimensionality of the space in which the tensor is defined. In four-dimensional spacetime, the trace of the tensor g^{\mu\nu} will always be 4.
This equation is used in general relativity to describe the curvature of spacetime. It is also used in other fields of physics, such as quantum field theory, to represent symmetries and conservation laws.