The T3 Framework: Black Holes as Global Vortex Bound States T3 框架:黑洞作为全局涡旋束缚态
Abstract
Abstract This paper proposes a vortex bound state picture of black holes based on T3 ternary algebra (e²=1, i²=-1, ei=ie=0). Core updates in v1.4: Causal Structure Self-Consistency: V_c = c√2 is the Euclidean norm in velocity space; the axial projection is always ≤ c. The “superluminal” rotational component does not violate causality. Saturation Model: V_core(M) = V_c · [1 + V_sat·tanh((M/M₀)^(1/4))]. Small black holes are just critical, while large black holes approach a ceiling of V_max ∼ 2V_c. Pure Energy Language: Mass equals spin energy, with η(M) = 1 + V_sat·tanh(⋯). Black holes are “tightly locked” rather than “spinning fast”. Locked-State Phase Transition Temperature Picture (Core Correction in v1.4): Large-mass black holes reside in a ground-state lock: Vortex energy is completely locked, resulting in zero radiation (tested via Sgr A* observations). A phase transition occurs upon evaporation to a critical mass: Similar to electronic level transitions, a one-time non-thermal burst is released (the source of the hard tail of GRBs). T_φ is an intrinsic energy scale, decoupled from radiation. Its value is given by the solver (~16 K plateau, not 10¹⁶ K). T3 Gravitational Field Theory: The 12 components of the associator curvature are strictly explicit, and numerical solvers verify saturation convergence. κ=1/3 Heuristic Estimate: Derived from the associator structure, but the argument for equality in the strict inequality remains incomplete; this is annotated as an open problem. EHT Compatibility: Current V_sat=1 yields R_h ≈ 1.53 R_s, which is in tension with M87* shadow data. Reducing V_sat ∼ 0.1 achieves compatibility but requires readjusting the saturation narrative. 摘要 本文基于 T3 三维数代数(e²=1, i²=-1, ei=ie=0)提出黑洞的涡旋束缚态图像。v1.4 核心更新: 因果结构自洽:V_c = c√2 是速度空间的欧几里得模长,轴向投影始终 ≤ c,旋转分量的”超光速”不违反因果律。 饱和模型:V_core(M) = V_c · [1 + V_sat·tanh((M/M₀)^(1/4))],小黑洞刚好临界,大黑洞趋近天花板 V_max ∼ 2V_c。 纯能量语言:质量=自旋能量,η(M) = 1 + V_sat·tanh(⋯),黑洞”锁得紧”而非”转得快”。 锁死-相变温度图像(v1.4 核心修正): 大质量黑洞处于基态锁死:涡旋能量完全锁定,零辐射(通过 Sgr A* 观测检验) 蒸发到临界质量时发生相变:类似电子能级跃迁,一次性释放非热爆发(GRB 硬尾来源) T_φ 是内禀能量标度,与辐射解耦,数值由求解器给出(~16 K 平台,非 10¹⁶ K) T3 引力场论:结合子曲率 12 分量严格显式,数值求解器验证饱和收敛。 κ=1/3 启发式估计:从结合子结构给出,但严格不等式取等论证未完成,标注为开放问题。 EHT 兼容性:当前 V_sat=1 给出 R_h ≈ 1.53 R_s,与 M87* 阴影数据有张力。缩小 V_sat ∼ 0.1 可兼容,但需重新调整饱和叙事。
