论文标题
2+1尺寸的爱因斯坦重力，带有广告$ _3 $和Minkowski背景
Non-singular vortices with positive mass in 2+1 dimensional Einstein gravity with AdS$_3$ and Minkowski background
论文作者
论文摘要
在以前的工作中，在爱因斯坦重力中带有ADS $ _3 $的Black Hole Vortex解决方案，标量物质配置文件在Origin $ r = 0 $处具有奇异性。在本文中，我们发现数值静态涡流解决方案，标量和量规场在ADS $ _3 $背景中的Einstein Gravity下具有非单个轮廓。获得了不同的绕组数量$ n $，VEV $ V $和宇宙常数$λ$的涡流。这些涡旋具有正质量，并且不是BTZ黑洞，因为它们没有事件范围。质量是通过两种方式确定的：通过减去两个单独的渐近指标的数值和纯粹在物质字段上的积分。随着宇宙常数变得更加负面，涡流的质量增加，这与涡流的核心相吻合（压缩）。然后，我们将重力的涡旋在渐近平坦的时空中，用于$α= 1/（16πg）$的不同值。在起源时，时空的曲率最高，没有奇异性。它过渡到渐近锥形时空，角度不足，随着$α$的减少，它显着增加。为了进行比较，我们还考虑了平时无重力的涡流。对于这种情况，一个人无法通过第一种方法获得质量（减去两个指标），但是通过限制过程，可以获得一个积分质量公式。在没有量规场的情况下，涡流的能量存在众所周知的对数差异。通过重力，我们以新的眼光提出这种分歧。我们表明，该度量获得了一个对数项，这是$ 2+1 $的尺寸实现牛顿重力潜力时，当一般相对论补充了标量场时。这打开了我们在结论中讨论的新颖可能性。
In previous work, black hole vortex solutions in Einstein gravity with AdS$_3$ background were found where the scalar matter profile had a singularity at the origin $r=0$. In this paper, we find numerically static vortex solutions where the scalar and gauge fields have a non-singular profile under Einstein gravity in an AdS$_3$ background. Vortices with different winding numbers $n$, VEV $v$ and cosmological constant $Λ$ are obtained. These vortices have positive mass and are not BTZ black holes as they have no event horizon. The mass is determined in two ways: by subtracting the numerical values of two separate asymptotic metrics and via an integral that is purely over the matter fields. The mass of the vortex increases as the cosmological constant becomes more negative and this coincides with the core of the vortex becoming smaller (compressed). We then consider the vortex with gravity in asymptotically flat spacetime for different values of the coupling $α=1/(16 πG)$. At the origin, the spacetime has its highest curvature and there is no singularity. It transitions to an asymptotic conical spacetime with angular deficit that increases significantly as $α$ decreases. For comparison, we also consider the vortex without gravity in flat spacetime. For this case, one cannot obtain the mass by the first method (subtracting two metrics) but remarkably, via a limiting procedure, one can obtain an integral mass formula. In the absence of gauge fields, there is a well-known logarithmic divergence in the energy of the vortex. With gravity, we present this divergence in a new light. We show that the metric acquires a logarithmic term which is the $2+1$ dimensional realization of the Newtonian gravitational potential when General Relativity is supplemented with a scalar field. This opens up novel possibilities which we discuss in the conclusion.
