Wyman几何中大质量粒子和光子运动轨道的定性和定量特征
Qualitative and quantitative features of orbits of massive particles and photons moving in Wyman geometry
摘要：
怀曼解取决于两个参数，质量$M$和标量电荷$σ$。如果将$M$固定为一个正值，比如说$M_0$，让$σ^2$沿实数线取值，它描述了三种不同类型的时空。对于$σ^2 >0$，时空是裸奇点;对于$σ^2 = 0$，时空是质量为$M_0$的史瓦西黑洞;最后，对于$-M_0^2 \leq σ^2 < 0$，时空是虫洞时空。本文主要研究在怀曼解的裸奇点和虫洞时空中运动的大质量粒子和光子的轨道的定性和定量特征。这些轨道是大质量粒子的类时测地线和光子的零测地线。结合四个测地线方程和一个由线元导出的附加方程，我们得到了一个大质量粒子的有效势和一个不同的光子的有效势。我们通过研究适当的有效势，研究了大质量粒子和光子的所有可能的轨道类型。我们注意到，对于$σ^2 >0$的某些值，存在一个无限大的势墙，阻止大质量粒子和光子到达裸奇点。我们还注意到，对于$-M_0^2 \leq σ^2 < 0$的某些值，势在任何地方都是有限的，这允许大质量粒子和光子从一个虫洞移动到另一个渐近平坦的区域。我们还计算了大质量粒子和光子分别在裸奇点和虫洞时空中运动的径向类时和零测地线。
英文摘要：
The Wyman's solution depends on two parameters, the mass $M$ and the scalar charge $σ$. If one fixes $M$ to a positive value, say $M_0$, and let $σ^2$ take values along the real line it describes three different types of spacetimes. For $σ^2 >0$ the spacetimes are naked singularities, for $σ^2 = 0$ one has the Schwarzschild black hole of mass $M_0$ and finally for $-M_0^2 \leq σ^2 < 0$ one has wormhole spacetimes. In the present work, we shall study qualitative and quantitative features of orbits of massive particles and photons moving in the naked singularity and wormhole spacetimes of the Wyman solution. These orbits are the timelike geodesics for massive particles and null geodesics for photons. Combining the four geodesic equations with an additional equation derived from the line element, we obtain an effective potential for the massive particles and a different effective potential for the photons. We investigate all possible types of orbits, for massive particles and photons, by studying the appropriate effective potential. We notice that for certain values of $σ^2 >0$, there is an infinity potential wall that prevents both massive particles and photons ever to reach the naked singularity. We notice, also, that for certain values of $-M_0^2 \leq σ^2 < 0$, the potential is finite everywhere, which allows massive particles and photons moving from one wormhole asymptotically flat region to the other. We also compute the radial timelike and null geodesics for massive particles and photons, respectively, moving in the naked singularities and wormholes spacetimes.
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