弯曲时空中粒子碰撞与加速、强引力透镜效应以及黑洞能量提取
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摘要
黑洞物理是广义相对论、量力力学、热力学和统计物理等诸多学科的的交叉领域,是物理学研究的前沿和热点领域,这是因为弄清多学科交叉领域中的一些基本问题的物理本质和规律,就能使这些学科乃至物理学得到更加全面、深入和协调地发展。本文对人们关注的弯曲时空中粒子加速与碰撞、强引力透镜效应以及黑洞能量提取机制进行了研究,得到了一些新结论：
第一、利用Banados. Silk(?)(?)West (BSW)提出的黑洞作为宇宙天体中粒子加速器的设想,即BSW机制,研究了两个不同静止质量粒子在Kerr-Taub-NUT寸空背景下碰撞及加速,得出了粒子碰撞后的质心能。结果表明：质心能不仅与Kerr-Taub-NUT寸空的旋转参数有关,而且与时空的NUT荷有关。尤其对于极端Kerr-Taub-NUT黑洞,无限制大的质心能约束了Kerr-Taub-NUT时空的旋转参数。和时空的NUT荷n的取值范围,约束条件为a的取值为范围[1,(?)2],而n在[0,1]区间取值。这是与Kerr和Kerr-Newman黑洞时空极为不同的新特性。
同时,研究了两个沿一般类时测地线运动的束缚或非束缚粒子在Kerr-Newman时空背景下粒子的BSW机制,得出了粒子碰撞体系的质心能。在直接碰撞和LSO碰撞过程中,无限制大的质心能对Kerr-Newman黑洞的旋转参数a和电荷q存在约束。粒子碰撞区域集中于赤道面的南北对称的纬度带,且黑洞的所带电荷阻碍了获得任意高质心能的碰撞区域纬度带的增大。
第二,研究了稳态的准Kerr致密天体的强引力透镜效应。假定银河系中心天体由旋转准Kerr度规所描述,计算了强引力透镜效应所产生的偏转角a(θ)及其系数b、a,同时给出相应天文可观测量并进行可行性分析。研究表明：四极矩修正参数ξ的存在显著的影响了相对论像的位置、偏转角以及相应的天文可观测量。当四极矩修正参数取正(负)值时,光球半径r(?)s、碰撞参数ups、偏转角系数b、相对论像的相对亮度rm及最内侧的像θ∞的视位置大于(小于)Kerr黑洞作为引透镜得到的相对应的结果。而偏转角系数a、偏转角α(θ)、相对论像的首像与其他像的角距s则小于(大于)Kerr黑洞作为引透镜得到的相对应的结果。因此可通过测定强引力透镜效应所产生的相对论像来探测天文黑洞所具有的四极矩信息以及偏离Kerr黑洞的程度。
第三、基于Penrose提出的黑洞能量提取机制,我们以Johannsen提出非Kerr旋转黑洞为对象,研究了非Kerr旋转黑洞的能层区域的性质。发现能层区域结构对形变参数的变化非常敏感,且能层的厚度随形变参数增大而增大,这是非Kerr旋转黑洞的一个重要特性。同时我们研究了Penrose过程的能量提取机制,分析了能层内形变参数(?)对负能量态的影响,得出正的形变参数能够扩大粒子的负能量态的取值范围。通过计算能量提取最大效率,发现形变参数能提高非Kerr旋转黑洞中能量提取最大效率。尤其值得注意得是：当α>M时,非Kerr度规所描述的旋转紧致天体Penrose过程的能量提取最大效率可超过60%,与极端Kerr黑洞能量提取最大效率为20.7%较相比,这是一个极大的提高。对非Kerr旋转黑洞的能量提取机制的研究结果可用来验证天文黑洞是否为广义相对论所给出Kerr旋转黑洞。
Black hole physics, as an intersectional field of general rela-tivity, quantum mechanics, particle physics, thermodynamics and statistics, is the frontier and hot research field of physics. Focus-ing on black hole physics can help us to understand the nature and laws of some basic issues of the physics, and can also make these disciplines gain a more comprehensive and coordinated de-velopment. This thesis is devoted to investigate three problems concerned by physicists, namely, particle collisions and acceler-ating, the strong gravitational lensing in the curved spacetime and energy extraction from black holes. The results are listed as follows:
Firstly, we introduce the hypothesis proposed by Banados, Silk and West (BSW) about the particle accelerators on the back-ground of black hole. Based on BSW mechanism, we study the collision of two particles with the different rest masses moving in the equatorial plane of a Kerr-Taub-NUT spacetime and get the center-of-mass (CM) energy for the particles. We find that the CM energy depends not only on the rotation parameter of the black hole, a, but also on the NUT charge of the Kerr-Taub-NUT spacetime, n. Especially, for the extremal Kerr-Taub-NUT space-time, an unlimited CM energy can be approached if the parameter a is in the range [1,(?)2] and the parameter n is in the range [0,1], which is different from that of the Kerr and Kerr-Newman black holes.
At the same time, we study the collision of two general geodesic particles around the Kerr-Newman black hole and get the CM energy of the non-marginally and marginally bound crit-ical particles in the direct collision and LSO collision scenarios. We also find the constraint conditions that arbitrarily high CM energy can be obtained for the near-horizon collision of two gen-eral geodesic particles in the extremal Kerr-Newman black hole. Note that the charge decreases the value of the latitude in which arbitrarily high CM energy can occur, and collision area is located in the north and south of the equator symmetrical latitudes.
Secondly, we investigate the strong gravitational lensing on the background of the quasi-Kerr compacted objects. Assuming that the massive compact object at the center of our galaxy can be described by quasi-Kerr spacetime, we obtain the photon radius, the coefficients and observable quantities of the strong gravita-tional lensing. At the same time, we estimate the astronomical observation of the relativistic image and analyse the feasibility of observation. Moreover, as the quadrupolar correction parame-ter ξ becomes negative the radius of the photon sphere becomes smaller, which implies that the photons are more easily captured by the quasi-Kerr compact object with the negative quadrupo-lar correction parameter ξ than that of the Kerr black hole. It is interesting to note that, when the quadrupolar correction pa-rameter ξ takes the positive (negative) value, the photon-sphere radius rps, the minimum impact parameter ups, the coefficient b, the relative magnitudes rm and the angular position of the rela-tivistic images θ∞are larger (smaller) than the results obtained in the Kerr black hole, but the coefficient a, the deflection an-gle α(θ) and the angular separation s are smaller (larger) than that of the Kerr black hole. Based on the above results, we come to the conclusion that there are some significant effects of the quadrupolar correction parameter ξ on the coefficients and ob-servable parameters of the strong gravitational lensing. These results, in principle, may provide a possibility to test how astro-nomical black holes with arbitrary quadrupole moments deviate from the Kerr black hole in the future astronomical observations.
Finally, based on Penrose process, the properties of the er-gosphere and the energy extraction by Penrose process in a ro-tating non-Kerr black hole are investigated. It is shown that the ergosphere is sensitive to the deformation parameter and the relative shape of the ergosphere becomes thick with increase of the parameter∈. It is of interest to note that, comparing with the Kerr black hole, the deformation parameter∈enhances the maximum efficiency of the energy extraction process greatly. Es-pecially, for the case of a> M, the non-Kerr metric describes a superspining compact object and the maximum efficiency can exceed60%, while it is only20.7%for the extremal Kerr black hole. This results may provide a possibility to test whether an astronomical black hole is described by Kerr black holes in the general relativity.
第一、利用Banados. Silk(?)(?)West (BSW)提出的黑洞作为宇宙天体中粒子加速器的设想,即BSW机制,研究了两个不同静止质量粒子在Kerr-Taub-NUT寸空背景下碰撞及加速,得出了粒子碰撞后的质心能。结果表明：质心能不仅与Kerr-Taub-NUT寸空的旋转参数有关,而且与时空的NUT荷有关。尤其对于极端Kerr-Taub-NUT黑洞,无限制大的质心能约束了Kerr-Taub-NUT时空的旋转参数。和时空的NUT荷n的取值范围,约束条件为a的取值为范围[1,(?)2],而n在[0,1]区间取值。这是与Kerr和Kerr-Newman黑洞时空极为不同的新特性。
同时,研究了两个沿一般类时测地线运动的束缚或非束缚粒子在Kerr-Newman时空背景下粒子的BSW机制,得出了粒子碰撞体系的质心能。在直接碰撞和LSO碰撞过程中,无限制大的质心能对Kerr-Newman黑洞的旋转参数a和电荷q存在约束。粒子碰撞区域集中于赤道面的南北对称的纬度带,且黑洞的所带电荷阻碍了获得任意高质心能的碰撞区域纬度带的增大。
第二,研究了稳态的准Kerr致密天体的强引力透镜效应。假定银河系中心天体由旋转准Kerr度规所描述,计算了强引力透镜效应所产生的偏转角a(θ)及其系数b、a,同时给出相应天文可观测量并进行可行性分析。研究表明：四极矩修正参数ξ的存在显著的影响了相对论像的位置、偏转角以及相应的天文可观测量。当四极矩修正参数取正(负)值时,光球半径r(?)s、碰撞参数ups、偏转角系数b、相对论像的相对亮度rm及最内侧的像θ∞的视位置大于(小于)Kerr黑洞作为引透镜得到的相对应的结果。而偏转角系数a、偏转角α(θ)、相对论像的首像与其他像的角距s则小于(大于)Kerr黑洞作为引透镜得到的相对应的结果。因此可通过测定强引力透镜效应所产生的相对论像来探测天文黑洞所具有的四极矩信息以及偏离Kerr黑洞的程度。
第三、基于Penrose提出的黑洞能量提取机制,我们以Johannsen提出非Kerr旋转黑洞为对象,研究了非Kerr旋转黑洞的能层区域的性质。发现能层区域结构对形变参数的变化非常敏感,且能层的厚度随形变参数增大而增大,这是非Kerr旋转黑洞的一个重要特性。同时我们研究了Penrose过程的能量提取机制,分析了能层内形变参数(?)对负能量态的影响,得出正的形变参数能够扩大粒子的负能量态的取值范围。通过计算能量提取最大效率,发现形变参数能提高非Kerr旋转黑洞中能量提取最大效率。尤其值得注意得是：当α>M时,非Kerr度规所描述的旋转紧致天体Penrose过程的能量提取最大效率可超过60%,与极端Kerr黑洞能量提取最大效率为20.7%较相比,这是一个极大的提高。对非Kerr旋转黑洞的能量提取机制的研究结果可用来验证天文黑洞是否为广义相对论所给出Kerr旋转黑洞。
Black hole physics, as an intersectional field of general rela-tivity, quantum mechanics, particle physics, thermodynamics and statistics, is the frontier and hot research field of physics. Focus-ing on black hole physics can help us to understand the nature and laws of some basic issues of the physics, and can also make these disciplines gain a more comprehensive and coordinated de-velopment. This thesis is devoted to investigate three problems concerned by physicists, namely, particle collisions and acceler-ating, the strong gravitational lensing in the curved spacetime and energy extraction from black holes. The results are listed as follows:
Firstly, we introduce the hypothesis proposed by Banados, Silk and West (BSW) about the particle accelerators on the back-ground of black hole. Based on BSW mechanism, we study the collision of two particles with the different rest masses moving in the equatorial plane of a Kerr-Taub-NUT spacetime and get the center-of-mass (CM) energy for the particles. We find that the CM energy depends not only on the rotation parameter of the black hole, a, but also on the NUT charge of the Kerr-Taub-NUT spacetime, n. Especially, for the extremal Kerr-Taub-NUT space-time, an unlimited CM energy can be approached if the parameter a is in the range [1,(?)2] and the parameter n is in the range [0,1], which is different from that of the Kerr and Kerr-Newman black holes.
At the same time, we study the collision of two general geodesic particles around the Kerr-Newman black hole and get the CM energy of the non-marginally and marginally bound crit-ical particles in the direct collision and LSO collision scenarios. We also find the constraint conditions that arbitrarily high CM energy can be obtained for the near-horizon collision of two gen-eral geodesic particles in the extremal Kerr-Newman black hole. Note that the charge decreases the value of the latitude in which arbitrarily high CM energy can occur, and collision area is located in the north and south of the equator symmetrical latitudes.
Secondly, we investigate the strong gravitational lensing on the background of the quasi-Kerr compacted objects. Assuming that the massive compact object at the center of our galaxy can be described by quasi-Kerr spacetime, we obtain the photon radius, the coefficients and observable quantities of the strong gravita-tional lensing. At the same time, we estimate the astronomical observation of the relativistic image and analyse the feasibility of observation. Moreover, as the quadrupolar correction parame-ter ξ becomes negative the radius of the photon sphere becomes smaller, which implies that the photons are more easily captured by the quasi-Kerr compact object with the negative quadrupo-lar correction parameter ξ than that of the Kerr black hole. It is interesting to note that, when the quadrupolar correction pa-rameter ξ takes the positive (negative) value, the photon-sphere radius rps, the minimum impact parameter ups, the coefficient b, the relative magnitudes rm and the angular position of the rela-tivistic images θ∞are larger (smaller) than the results obtained in the Kerr black hole, but the coefficient a, the deflection an-gle α(θ) and the angular separation s are smaller (larger) than that of the Kerr black hole. Based on the above results, we come to the conclusion that there are some significant effects of the quadrupolar correction parameter ξ on the coefficients and ob-servable parameters of the strong gravitational lensing. These results, in principle, may provide a possibility to test how astro-nomical black holes with arbitrary quadrupole moments deviate from the Kerr black hole in the future astronomical observations.
Finally, based on Penrose process, the properties of the er-gosphere and the energy extraction by Penrose process in a ro-tating non-Kerr black hole are investigated. It is shown that the ergosphere is sensitive to the deformation parameter and the relative shape of the ergosphere becomes thick with increase of the parameter∈. It is of interest to note that, comparing with the Kerr black hole, the deformation parameter∈enhances the maximum efficiency of the energy extraction process greatly. Es-pecially, for the case of a> M, the non-Kerr metric describes a superspining compact object and the maximum efficiency can exceed60%, while it is only20.7%for the extremal Kerr black hole. This results may provide a possibility to test whether an astronomical black hole is described by Kerr black holes in the general relativity.
引文
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