渐近平坦Symmergent黑洞周围的自旋粒子动力学与观测红移
Spinning Particle Dynamics and Observational Redshift around an Asymptotically Flat Symmergent Black Hole
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中文总结 AI 辅助
本研究针对渐近平坦symmergent引力的微扰可变标量曲率分支，推导了不同类型粒子的动力学方程与相关物理量，分析了参数对时空形变的影响，为探测可变曲率区段提供了观测依据。
中文摘要 AI 辅助
我们研究了渐近平坦symmergent引力的微扰可变标量曲率分支中的类时粒子动力学、碰撞能量学以及光子频移。其低能真空作用量包含一项$R^{2}$修正，修正项的系数由底层量子场论的玻色子-费米子不平衡决定。在线性阶数下，外部几何通过满足线性方程的径向模式与史瓦西时空共形。我们保留了一个独立的、依赖于边界条件的振幅，并将分析限制在微扰区域内。symmergent参数$γ$的两种符号会产生不同的分布：$γ>0$时会产生汤川抑制的形变，而$γ<0$时会产生振荡的逆半径形变。我们推导了中性、带电以及自旋有质量粒子的径向方程、有效势、圆轨道条件和临界稳定性条件。带电粒子在试验场近似下处理，而自旋粒子满足带有图尔齐耶夫（Tulczyjew）条件的马西森-帕帕佩特鲁-狄克逊（Mathisson–Papapetrou–Dixon）方程。我们还计算了中性粒子碰撞的质心能量，以及由圆测地线源切向发射、被无穷远处静态观测者探测到的光子的频移。红移和蓝移因子满足$(1+z_{+})(1+z_{-})=1/A(r_e)$，直接将它们的乘积与发射处的时移函数联系起来。$γ>0$分支会产生与史瓦西动力学相比的平滑短程偏差，而$γ<0$分支可以产生振荡径向带，其中存在圆轨道解，其稳定性必须单独检验。这些可观测量为可变曲率区段提供了互补的探测手段，不过它们的定量解释也取决于形变振幅，对于振荡分支而言还取决于其相位。
英文摘要
We investigate timelike particle dynamics, collision energetics, and photon frequency shifts in the perturbative variable-scalar curvature branch of asymptotically flat symmergent gravity. The low-energy vacuum action contains an $R^{2}$ correction whose coefficient is set by the boson--fermion imbalance of the underlying quantum field theory. At linear order, the exterior geometry is conformal to Schwarzschild spacetime through a radial mode satisfying a linear equation. We retain an independent boundary-condition-dependent amplitude and restrict the analysis to the perturbative domain. The two signs of the symmergent parameter $γ$ yield distinct profiles: $γ>0$ gives a Yukawa-suppressed deformation, whereas $γ<0$ produces an oscillatory inverse-radius deformation. We derive radial equations, effective potentials, circular-orbit and marginal-stability conditions for neutral, electrically charged, and spinning massive particles. Charged particles are treated in the test-field approximation, while spinning particles obey the Mathisson--Papapetrou--Dixon equations with the Tulczyjew condition. We also compute the center-of-mass energy of neutral-particle collisions and the frequency shifts of photons emitted tangentially by circular geodesic sources and detected by a static observer at infinity. The redshift and blueshift factors satisfy $(1+z_{+})(1+z_{-})=1/A(r_e)$, directly linking their product to the lapse function at emission. The $γ>0$ branch yields smooth, short-range deviations from Schwarzschild dynamics, whereas the $γ<0$ branch can generate oscillatory radial bands admitting circular-orbit solutions whose stability must be tested independently. These observables provide complementary probes of the variable-curvature sector, although their quantitative interpretation also depends on the deformation amplitude and, for the oscillatory branch, its phase.
