AI 中文总结
本文在3+1数值相对论中演化邦迪偶极子（正负质量双星），证实其自加速特性，测量加速度与间距、质量的标度关系，发现其无引力辐射，并演化出首个数值相对论中的负ADM质量幻影星。
AI 中文摘要
邦迪在1957年证明，具有相反主动引力质量的物体会自加速：负质量追逐其排斥的正质量，二者共同运动。我们在3+1数值相对论框架下演化这种“邦迪偶极子”：两个复标量遵循相同的克莱因-戈登动力学；仅幻影标量以负号项进入爱因斯坦方程——惯性质量与被动质量为正，主动质量为负。在包含34次演化的矩阵实验中（包括 runaway 对、对照组及参数扫描），质量匹配的静止释放对作为整体加速；到t=200时，中点移动了3.00±0.01，间距保持在1%以内，到t=400时达到0.056c的速度，加速度稳定在2%以内；总符号动量保持在0，偏差≤1%。力在两个轴上均为引力：在间距d=8到20范围内，加速度a∝d^(-2.03±0.01)；在质量2.5倍的范围内，a∝M^(0.97±0.06)；在等质量序列中，a d²/$\bar{M}$在2.4%以内等于1。交换场会使加速度反转至10^5分之2；规范、求解器深度和网格变化使漂移移动≤0.01%，盒子加倍则移动4%；同号对照组对即使在合并时，其质心也保持在≤8×10^(-4)以内。该 runaway 未携带可检测的引力辐射：符号偶极子无法辐射，四极矩的$\bar{Q}$恒定，测得的ℓ=2振幅随r^(-4.8)下降——属于近区而非通量。据我们所知，幻影星是数值相对论中首个演化的渐近平坦的负ADM质量天体；单独存在时，它能存活至t=1000，缓慢向外松弛。
英文摘要
Bondi showed in 1957 that bodies of opposite active gravitational mass self-accelerate: the negative chases the positive it repels, and the pair runs off together. We evolve this "Bondi dipole" in $3+1$ numerical relativity: two complex scalars share identical Klein-Gordon dynamics; only the phantom enters Einstein's equations with a minus sign -- inertial and passive masses positive, active mass negative. Across a matrix of thirty-four evolutions -- runaway pairs, controls, and parameter scans -- a mass-matched pair released at rest accelerates as a unit. The midpoint moves $3.00\pm0.01$ by $t=200$ with the separation held to 1%, and reaches a speed of $0.056c$ by $t=400$ with the acceleration steady to 2%; the total signed momentum holds at zero to $\lesssim 1$%. The force is gravity on both of its axes: $a\propto d^{-2.03\pm0.01}$ over $d=8$ to $20$, $a\propto M^{0.97\pm0.06}$ over a factor $2.5$ in mass, and $a\,d^2/\bar{M}=1$ within 2.4% on the equal-mass ladder. Swapping the sectors inverts the acceleration to two parts in $10^5$; gauge, solver-depth and mesh variations move the drift by $\lesssim 0.01$% and box doubling by 4%; same-sign control pairs hold their centroids to $\lesssim 8\times10^{-4}$ even while merging. The runaway carries no detectable gravitational radiation: the signed dipole cannot radiate, the quadrupole's $\ddot{Q}$ is constant, and the measured $\ell=2$ amplitude falls as $r^{-4.8}$ -- near zone, not flux. The phantom star is, to our knowledge, the first asymptotically flat body of negative ADM mass evolved in numerical relativity; alone it survives to $t=1000$, slowly relaxing outward.
Comments13 pages, 10 figures, 4 ancillary movies. Code, run matrix and packed campaign data: https://github.com/Nikchik-coder/GRTeclyn (tag v1.0-bondi-dipole)
