论文标题
重力耦合到量规场的准本地能量的方面
Aspects of Quasi-local energy for gravity coupled to gauge fields
论文作者
论文摘要
我们研究了与$ 2- $ surface $σ$相关的准本地能量的各个方面，这些$σ$界定了一个类似空间的域$ 3+1+1 $尺寸时空的重力，在重力状态下耦合到仪表字段。 Wang-yau准局部能量以及由于重力与量规场的耦合而产生的额外术语构成了膜$σ= \partialΩ$中包含的总能量（$ \ MATHCAL {QLE} $）。我们专注于Kerr-Newman的空间家族，其中包含一个u（1）量规场与重力和外界结合。通过明确的计算，我们表明总能量满足了Bekenstein类型不等式的较弱版本$ \ MATHCAL {QLE}> \ frac {q^{2}} {2r} {2R} $对于大球形膜而言，$ Q $是收费的，$ r $是膜的半径。关闭角动量（ReissnerNordström）产生$ \ MATHCAL {QLE}> \ frac {q^{2}} {2R} {2R} $，用于所有持续的半径膜，其中包含地平线，在这种情况下，在这种情况下，充电因子完全平等，与Bekenstein的右侧相等。此外，我们表明，单调的总准本地能量从$ 2M_ {IRR}+v_ {q} $（$ m_ {inr {inr} $是不可弥补的质量，$ v_ {q} $是$ m $ $ m $ shomp shobs shobs nebromply Inflotial nebromply Inflotial nevermute shone n o n Bromp a a nebromply Inflote的质量。
We study the aspects of quasi-local energy associated with a $2-$surface $Σ$ bounding a space-like domain $Ω$ of a physical $3+1$ dimensional spacetime in the regime of gravity coupled to a gauge field. The Wang-Yau quasi-local energy together with an additional term arising due to the coupling of gravity to a gauge field constitutes the total energy ($\mathcal{QLE}$) contained within the membrane $Σ=\partialΩ$. We specialize in the Kerr-Newman family of spacetimes which contains a U(1) gauge field coupled to gravity and an outer horizon. Through explicit calculations, we show that the total energy satisfies a weaker version of a Bekenstein type inequality $\mathcal{QLE}> \frac{Q^{2}}{2R}$ for large spherical membranes, $Q$ is the charge and $R$ is the radius of the membrane. Turning off the angular momentum (Reissner Nordström) yields $\mathcal{QLE}> \frac{Q^{2}}{2R}$ for all constant radii membranes containing the horizon and in such case the charge factor appearing in the right-hand side exactly equals to that of Bekenstein's inequality. Moreover, we show that the total quasi-local energy monotonically decays from $2M_{irr}+V_{Q}$ ($M_{irr}$ is the irreducible mass, $V_{Q}$ is the electric potential energy) at the outer horizon to $M$ ($M$ is the ADM mass) at the space-like infinity under the assumption of a small angular momentum of the black hole.
