# Relativity: Gravity pseudotensor, Gibbons-Hawking-York term

1. Mar 1, 2015

### Bartolius

In our course on General Relativity the professor explained the linearized version of Einstein's Equation and the emission of gavitational waves, then made a little digression on the conservation of energy in a gravitational system. He showed that the search for a conserved object (Momentum tensor of matter is covriantly conserved, so it doesn't fit our search) leads to the contruction of a pseudotensor from the sum of the Momentum Tensor of matter and the non-linear part of Einstein's Tensor. Then he constructed conserved quantities from the integral over all our volume and showed that all the information on conserved quantities lives on the boundary (a holographic property).
My questions are:
1 did I understand the logical process or did i mess up something? I ask this because I borrowed some notes from a friend and he seems to have done a little mess with covariant and classical derivatives of tensors.

2 How the covariant conservation of Einstein's tensor implies the conservation of it's linear part? on my friends notes is written that it can be shown by series, I assume that the covariant conservation equation for Einstein's tensor must hold at every order, and the linear term only receives contribution from the divergence (non covariant for the Christoffels are first order) of the linear part of Einsteins tensor.

3 this is about another topic: I studied Hilbert-Einstein's action and the necessity of a correction in the form of the Gibbons-Hawking-York term, but I lack any example in which that term plays a relevant role: I read around the internet that it is important for the entropy of horizons, and that it reproduces the famous A/4 proportionality relation for the entropy of a Schwarzschild Black-hole, but nothing more. Where can I find more informations on the importance of this term?

Thanks

2. Mar 6, 2015