Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2010-06-16
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
6 pages; added a new argument in section 3, results unchanged
Scientific paper
The Bel-Robinson tensor $T_{\alpha\beta\mu\nu}$ was proposed in 1958. The main application of this tensor is for describing gravitational energy. It is known that $T_{\alpha\beta\mu\nu}$ has many nice properties such as being completely symmetric. It is easy to prove this property using spinors as shown in Penrose's book. The present paper provides an alternative way, using the tensorial method to prove that $T_{\alpha\beta\mu\nu}$ is indeed totally symmetric. Moreover, we also found that the well known identity in vacuum, $R_{\alpha\lambda\sigma\tau}R_{\beta}{}^{\lambda\sigma\tau} \equiv 1/4g_{\alpha\beta}R_{\rho\lambda\sigma\tau} R^{\rho\lambda\sigma\tau}$, which can be proven by the same tensorial method.
No associations
LandOfFree
A simple tensorial proof for the completely symmetric property of the Bel-Robinson tensor does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A simple tensorial proof for the completely symmetric property of the Bel-Robinson tensor, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A simple tensorial proof for the completely symmetric property of the Bel-Robinson tensor will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-100285