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arXiv 1807.03068gr-qc
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$f(T)$扩展引力理论中的致密星

Compact stars in $f(T)$ extended theory of gravity

Sasa Ilijic, Marko Sossich

备注：
LaTeX, 12 pages, 3 figures, v2: references added
发表信息：
Phys. Rev. D 98, 064047 (2018)
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摘要：

我们认为静态球对称的自引力配置的完美流体的框架内的扭转为基础的扩展理论的重力。特别地，我们使用的协变配方的$f(T)$重力与$f(T) = T + \fracα{2} T^2$，并为流体，我们假设多方状态方程的绝热指数$Γ= 2$。构造的解有一个明确定义的半径[如在广义相对论（GR）]，可以被认为是非旋转致密星的模型。粒子数-恒星半径曲线显示，$α$的（负）值可以支持更小（更多）数量的粒子对抗重力，然后在GR中。为了解释恒星内的能量密度和压力，我们采用GR图片，其中由于$f(T)$的非线性效应被视为$f(T)$流体，其与多变流体一起贡献有效能量动量。我们发现，足够大的正$α$引起的能量密度和主压力的$f(T)$流体，发生在内部的恒星的突然符号变化（相变）。相应的径向分布的有效能量密度是近似恒定的中心区域的恒星，模仿一个不可压缩的核心。这种有趣的现象在具有负$α$的构型中没有发现。

英文摘要：

We consider static spherically symmetric self-gravitating configurations of the perfect fluid within the framework of the torsion-based extended theory of gravity. In particular, we use the covariant formulation of $f(T)$ gravity with $f(T) = T + \fracα{2} T^2$, and for the fluid we assume the polytropic equation of state with the adiabatic exponent $Γ= 2$. The constructed solutions have a sharply defined radius [as in General Relativity (GR)] and can be considered as models of nonrotating compact stars. The particle number--to--stellar radius curves reveal that with positive (negative) values of $α$ smaller (greater) number of particles can be supported against gravity then in GR. For the interpretation of the energy density and the pressure within the star we adopt the GR picture where the effects due to nonlinearity of $f(T)$ are seen as a $f(T)$ fluid, which together with the polytropic fluid contributes to the effective energy momentum. We find that sufficiently large positive $α$ gives rise to an abrupt sign change (phase transition) in the energy density and in the principal pressures of the $f(T)$ fluid, taking place within the interior of the star. The corresponding radial profile of the effective energy density is approximately constant over the central region of the star, mimicking an incompressible core. This interesting phenomenon is not found in configurations with negative $α$.

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