论文标题
黑洞和模拟重力之间的一致性 - $（2+1）$ - 尺寸重力
Consistency between black hole and mimetic gravity -- Case of $(2+1)$-dimensional gravity
论文作者
论文摘要
我们表明，具有约束$ g^{ρσ} \ partial_ρϕ \partial_σdary的模拟理论= 1 $无法意识到地平线的黑洞几何形状。为了克服此类问题，我们可能会将模拟约束更改为$ω（ϕ）g^{ρσ} \ partial_ρϕ \ partial_σϕ = -1，其中$ω（ϕ）$是标量字段$ ϕ $的函数。例如，我们考虑使用这种修改的约束来考虑$（2+1）$ - 尺寸模拟重力，并具有模拟电势并构建黑洞（BH）溶液。我们研究了三个不同的类别：在第一类中，我们假设Lagrange乘数和模拟潜力正在消失，并获得了BH解决方案，该溶液完全与GR的BH完全匹配，尽管模仿场的非平地度可确保在{\ IT JCAP 01（2019）058}中介绍的研究。在第二类中，我们获得了具有恒定模拟势和Lagrange乘数的非平凡形式的BH。在第三类中，我们获得了一种新的BH解决方案，该解具有模拟场，Lagrange乘数和模拟电势的非变化值。在任何情况下，解决方案都与时空相对应，但我们表明，约束的形式主义有效。
We show that the mimetic theory with the constraint $g^{ρσ}\partial_ρϕ\partial_σϕ=1$ cannot realize the black hole geometry with the horizon(s). To overcome such issue, we may change the mimetic constraint a little bit by $ω(ϕ) g^{ρσ}\partial_ρϕ\partial_σϕ=-1,$ where $ω(ϕ)$ is a function of the scalar field $ϕ$. As an example, we consider $(2+1)$-dimensional mimetic gravity with the mimetic potential and construct black hole (BH) solutions by using this modified constraint. We study three different classes: In the first class, we assume the Lagrange multiplier and mimetic potential are vanishing and obtain a BH solution that fully matches the BH of GR despite the non-triviality of the mimetic field which ensures the study presented in {\it JCAP 01 (2019) 058}. In the second class, we obtain a BH having constant mimetic potential and a non-trivial form of the Lagrange multiplier. In the third class, we obtain a new BH solution with non-vanishing values of the mimetic field, the Lagrange multiplier, and the mimetic potential. In any case, the solutions correspond to the space-time with only one horizon but we show that the formalism for the constraint works.
