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Area deficits and the Bel-Robinson tensor | | Ted Jacobson
; José M. M. Senovilla
; Antony J. Speranza
; | | Date: |
20 Oct 2017 | | Abstract: | The first law of causal diamonds relates the area deficit of a small ball
relative to flat space to the matter energy density it contains. At second
order in the Riemann normal coordinate expansion, this energy density should
receive contributions from the gravitational field itself. In this work, we
study the second-order area deficit of the ball in the absence of matter and
analyze its relation to possible notions of gravitational energy. In the small
ball limit, any proposed gravitational energy functional should evaluate to the
Bel-Robinson energy density $W$ in vacuum spacetimes. A direct calculation of
the area deficit reveals a result that is not simply proportional to $W$. We
discuss how the deviation from $W$ is related to ambiguities in defining the
shape of the ball in curved space, and provide several proposals for fixing
these shape ambiguities. | | Source: | arXiv, 1710.7379 | | Services: | Forum | Review | PDF | Favorites | |
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