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The problem of quasilocal energy has been extensively studied mainly in fourdimensions. Here we report results regarding the quasilocal energy in spacetimedimension $n\geq 4$. After generalising three distinct quasilocal energydefinitions to higher dimensions under appropriate assumptions, we evaluatetheir small sphere limits along lightcone cuts shrinking towards the lightconevertex. The results in vacuum are conveniently represented in terms of theelectromagnetic decompositions of the Weyl tensor. We find that the limits atpresence of matter yield the stress tensor as expected, but the vacuum limitsare in general not proportional to the Bel-Robinson superenergy $Q$ indimensions $n>4$. The result defies the role of the Bel-Robinson superenergy ascharacterising the gravitational energy in higher dimensions, albeit the factthat it uniquely generalises. Surprisingly, the Hawking energy and theBrown-York energy exactly agree upon the small sphere limits across alldimensions. The new vacuum limit $\mathcal{Q}$, however, cannot be interpretedas a gravitational energy because of its non-positivity. Furthermore, we alsogive the small sphere limits of the Kijowski-Epp-Liu-Yau type energy in higherdimensions, and again we see $\mathcal{Q}$ in place of $Q$. Our work extendsearlier investigations of the small sphere limits [1, 2, 3, 4], and alsocomplements [5].

The small sphere limit of quasilocal energy in higher dimensions along lightcone cuts