论文标题
Lovelock重力的经典全息关系和替代边界条件
Classical Holographic Relations and Alternative Boundary Conditions for Lovelock Gravity
论文作者
论文摘要
我们获得了一般Lovelock重力的经典全息关系，并将完整的Lagrangian分解为批量项和表面项，以总导数$ \partial_μjj^μ$表示。通过经典的全息关系，我们的意思是$ J^μ$完全由批量项决定。我们发现，在这种独立的方法中，批量术语不是退化的，也不是一阶。然后，我们考虑Arnowitt-Deser-Misner（ADM）形式主义，其中叶面坐标$ w $被视为特殊。我们获得了经典的全息偏度关系，其一阶批量项不高于$ w $的一个导数。对于爱因斯坦重力，这两种方法导致了相同的批量项，但对于高阶洛夫洛克重力而言，这两项不同。在ADM方法中，经典的全息偏度配方使我们能够以不同的术语来考虑变异原理中的替代边界条件。我们在半经典近似中表明，在所有情况下，黑洞熵与在标准Dirichlet边界条件下获得的黑洞熵相同。我们还将形式主义推广到一般$ f（l _ {\ rm lovelock}^{（k）}）$ - 重力。
We obtain the classical holographic relation for the general Lovelock gravity and decompose the full Lagrangian into the bulk term and the surface term, expressed as a total derivative $\partial_μJ^μ$. By classical holographic relation, we mean that $J^μ$ is determined completely by the bulk term. We find that the bulk term is not degenerate, or first-order in this foliation-independent approach. We then consider the Arnowitt-Deser-Misner (ADM) formalism where the foliation coordinate $w$ is treated as special. We obtain the classical holographic-degenerate relation with the first-order bulk term that does not involve higher than one derivative of $w$. For Einstein gravity, the two approaches lead to the same bulk term, but different ones for higher-order Lovelock gravities. The classical holographic-degenerate formulation in the ADM approach allows us to consider alternative boundary conditions in the variation principle with different Myers terms. We show in the semiclassical approximation that the black hole entropy in all cases is the same as the one obtained under the standard Dirichlet boundary condition. We also generalize the formalism to general $f(L_{\rm Lovelock}^{(k)})$-gravity.
