Help with Notation: (Λ-1)μν=Λνμ ≡ ημρΛρσησν

  • Thread starter Thread starter grzz
  • Start date Start date
  • Tags Tags
    Notation
grzz
Messages
1,030
Reaction score
26
During my reading I met with,

(Λ-1)μν = Λνμ ≡ ημρΛρσησν.

Is it correct to say that η raises and lowers the indices of Λ giving Λμν, which, in turn, will give (Λ-1)μν = Λμν?

Thanks for any help.
 
Physics news on Phys.org
The indices are not balanced. Check again the exact positioning.
 
Thanks Dextercioby for your help.
Does that mean that there is a misprint in what I read and the μ and the ν of the η must be exchanged?
 
Thread 'Dirac's integral for the energy-momentum of the gravitational field'

Thread 'Dirac's integral for the energy-momentum of the gravitational field'

See Dirac's brief treatment of the energy-momentum pseudo-tensor in the attached picture. Dirac is presumably integrating eq. (31.2) over the 4D "hypercylinder" defined by ##T_1 \le x^0 \le T_2## and ##\mathbf{|x|} \le R##, where ##R## is sufficiently large to include all the matter-energy fields in the system. Then \begin{align} 0 &= \int_V \left[ ({t_\mu}^\nu + T_\mu^\nu)\sqrt{-g}\, \right]_{,\nu} d^4 x = \int_{\partial V} ({t_\mu}^\nu + T_\mu^\nu)\sqrt{-g} \, dS_\nu \nonumber\\ &= \left(...
View full post »

Thread 'A sufficient condition for integrability of equation ##\nabla g=0##'

In Philippe G. Ciarlet's book 'An introduction to differential geometry', He gives the integrability conditions of the differential equations like this: $$ \partial_{i} F_{lj}=L^p_{ij} F_{lp},\,\,\,F_{ij}(x_0)=F^0_{ij}. $$ The integrability conditions for the existence of a global solution ##F_{lj}## is: $$ R^i_{jkl}\equiv\partial_k L^i_{jl}-\partial_l L^i_{jk}+L^h_{jl} L^i_{hk}-L^h_{jk} L^i_{hl}=0 $$ Then from the equation: $$\nabla_b e_a= \Gamma^c_{ab} e_c$$ Using cartesian basis ## e_I...
View full post »

Thread 'Describing the Big Bang'

I started reading a National Geographic article related to the Big Bang. It starts these statements: Gazing up at the stars at night, it’s easy to imagine that space goes on forever. But cosmologists know that the universe actually has limits. First, their best models indicate that space and time had a beginning, a subatomic point called a singularity. This point of intense heat and density rapidly ballooned outward. My first reaction was that this is a layman's approximation to...
View full post »

Similar threads

I Index Notation for Lorentz Transformation
Replies
11
Views
9K
I Issues with the variation of Christoffel symbols
Replies
10
Views
3K
Questions about Properties of the Godel Metric
Replies
6
Views
2K
Transformation to locally flat coordinates
Replies
20
Views
5K
I Symbol for matrix representative of a tensor
Replies
5
Views
3K
A Help with Weinberg p. 72 -- time dt for a photon to travel a distance d⃗x
Replies
36
Views
4K
Christoffel symbols derivation
Replies
5
Views
5K
Deriving Geodetic Line by Einstein: Clarifying Difficulties
Replies
2
Views
1K
Help with Lorentz Transformation Notation & Matrix Entries
Replies
5
Views
1K
I Purpose of Tensors, Indices in Tensor Calculus Explained
Replies
10
Views
3K

Hot Threads

Recent Insights

Back
Top