arXiv 0809.38672008-09-23gr-qc

Gravitational energy in a small region for the modified Einstein and Landau-Lifshitz pseudotensors

Lau Loi So

备注：: 7
发表信息：: Class.Quant.Grav.26:185004,2009
DOI：: 10.1088/0264-9381/26/18/185004

英文摘要：

The purpose of the classical Einstein and Landau-Lifshitz pseudotensors is for determining the gravitational energy. Neither of them can guarantee a positive energy in holonomic frames. In the small sphere approximation, it has been required that the quasilocal expression for the gravitational energy-momentum density should be proportional to the Bel-Robinson tensor $B_{αβμν}$. However, we propose a new tensor $V_{αβμν}$ which is the sum of certain tensors $S_{αβμν}$ and $K_{αβμν}$, it has certain properties so that it gives the same gravitational "energy-momentum" content as $B_{αβμν}$ does. Moreover, we show that a modified Einstein pseudotensor turns out to be one of the Chen-Nester quasilocal expressions, while the modified Landau-Lifshitz pseudotensor becomes the Papapetrou pseudotensor; these two modified pseudotensors have positive gravitational energy in a small region.

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