黑洞拓扑与测地结构在对称Teleparallel f(Q)引力中的研究
Black Hole Topologies and Geodesic Structures in Symmetric Teleparallel f(Q) Gravity
AI总结：
本文研究了对称Teleparallel f(Q)引力中黑洞的拓扑与测地结构，推导出精确解并分析其热力学性质及奇点可达性。
摘要：
本文在对称Teleparallel引力框架下研究了黑洞解，采用$ f(Q) $模型，其中引力动力学由非度量性标量$ Q $控制。我们专注于$(2+1)$维中的静态、环对称时空，分析带电和不带电情况。通过采用幂律形式的$ f(Q) $，我们推导出精确的黑洞解，并探讨其热力学和几何性质。曲率和非度量性标量揭示出比广义相对论更严重的奇点。我们发现，视界半径随电荷参数增加而增加，而较高的非度量性系数$ c_{4} $或宇宙学常数$ Λ $值会合并或消除视界，减少总数量并改变时空原点附近的结构。我们基于欧拉特征数进行了详细的拓扑分析，并检验了时空的测地完整性。我们的发现表明，根据是否存在电荷，奇点可能或可能不被测地线到达。通过温度、熵和热容量计算确认热力学稳定性。本研究突显了$ f(Q) $引力在低维设置中的丰富结构，并为修改引力理论中奇点和黑洞拓扑性质提供了新的见解。
英文摘要：
Black hole solutions are studied here within the symmetric teleparallel formulation of gravity, employing the $f(Q)$ model in which the gravitational dynamics are governed by the non-metricity scalar $Q$. We focus on static, circularly symmetric spacetimes in $(2+1)$-dimensions, analyzing both charged and uncharged cases. By adopting a power-law form for $f(Q)$, we derive exact black hole solutions and explore their thermodynamic and geometric properties. Curvature and non-metricity scalars reveal central singularities stronger than those in general relativity. we find that the horizon radii increase with the charge parameter while higher values of the non-metricity coefficient, $c_{4}$, or the cosmological constant $Λ$ tend to merge or eliminate horizons, reducing their total number and altering the near-origin structure of the spacetime. We perform a detailed topological analysis based on the Euler characteristic and examine the geodesic completeness of the spacetime. Our findings show that, depending on the presence of electric charge, the singularity may or may not be reachable by geodesics. The thermodynamic stability is confirmed via temperature, entropy, and heat capacity calculations. This study highlights the rich structure of $f(Q)$ gravity in lower-dimensional settings and offers new insights into the nature of singularities and black hole topologies in modified gravity theories.
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