CAJ | 학술논문

在 Reissner-Nordstr?m时空下,给出分离变量后的 Dirac 方程的径向方程和角向方程。按照Chandrasekhar的方法,通过定义乌龟坐标变换,将径向耦合方程退耦成独立的一维波动方程,并给出方程中势的表达式。考虑到极端 Reissner-Nordstr?m 黑洞内外视界是重合的,这将导致黑洞的质量和电荷量相同。在准极端 Reissner-Nordstr?m 背景时空下,讨论了当粒子的能量大于势垒高度时,Dirac粒子被黑洞的散射情况。首先,将势函数用一组阶梯函数代替；之后,利用量子力学的方法给出透射反射系数以及波函数的数值变化曲线；最后,比较分析不同质量的粒子被散射的情况。从结果来看,不同质量 Dirac 粒子的散射是明显不同的,质量越大的粒子散射越强。从这个角度来讲,黑洞也可以看做是一个质量摄谱仪。
재 Reissner-Nordstr?m시공하,급출분리변량후적 Dirac 방정적경향방정화각향방정。안조Chandrasekhar적방법,통과정의오구좌표변환,장경향우합방정퇴우성독립적일유파동방정,병급출방정중세적표체식。고필도겁단 Reissner-Nordstr?m 흑동내외시계시중합적,저장도치흑동적질량화전하량상동。재준겁단 Reissner-Nordstr?m 배경시공하,토론료당입자적능량대우세루고도시,Dirac입자피흑동적산사정황。수선,장세함수용일조계제함수대체；지후,이용양자역학적방법급출투사반사계수이급파함수적수치변화곡선；최후,비교분석불동질량적입자피산사적정황。종결과래간,불동질량 Dirac 입자적산사시명현불동적,질량월대적입자산사월강。종저개각도래강,흑동야가이간주시일개질량섭보의。
Dirac equations are separated into radial and angular equations in Reissner-Nordstr?m (RN)geometry.By tortoise coordinate transformation,the radial parts of Dirac equations are decoupled into independent one-dimensional wave equations according to Chandrasekhar’s method.The form of the potential in the wave equations is also given.For extreme RN black holes,the two black hole horizons are coincidence,which leads to the equal mass and the electric charge of the black hole.In quasi-extreme Reissner-Nordstr?m geometry,the case that the energies of the waves are greater than the height of the potential barrier is considered.First,the potential is replaced by a collection of step functions.Second, the reflection and transmission coefficients and the wave functions are computed by quantum mechanics method.Last,the solutions to Dirac equations with different masses are compared.The results show that Dirac particles with different mass are scattered obviously different,the greater the mass is,the stronger the scattering is.Therefore,the black hole can act as a mass spectrograph.