标题： 静止标量测试电荷在外 Schwarzchild 黑洞外部的自力 显示英文标题

标题： The self-force on a static scalar test-charge outside a Schwarzschild black hole

摘要： 在施瓦茨希尔德黑洞外部的静态标量测试电荷上的自力的有限部分为零。 通过直接构造哈达玛基本解，我们得到了由固定在施瓦茨希尔德时空中的测试电荷产生的最小耦合标量场的闭合表达式。 使用闭合表达式，我们计算了保持电荷静止所需的必要外力。 尽管与标量场相关的能量贡献于粒子的重整化质量（从而影响其重量），但我们发现没有额外的自力作用在电荷上。 这个结果与类似的静电结果不同，在静电情况下，经过类似的质量重整化后，仍存在一个有限的排斥自力作用在施瓦茨希尔德黑洞外部的静态电测试电荷上。 我们使用卡特的黑洞质量变化定理来验证我们的力计算。 进行此计算的主要动机是发展计算作用在黑洞时空中的电荷和质量上的所有力——耗散力和非耗散力的技术和形式主义。 在附录中，我们回顾了闭合表达式的静电势的推导。 我们还展示了场的闭合表达式如何与无限级数解相关联。 显示英文摘要

摘要： The finite part of the self-force on a static scalar test-charge outside a Schwarzschild black hole is zero. By direct construction of Hadamard's elementary solution, we obtain a closed-form expression for the minimally coupled scalar field produced by a test-charge held fixed in Schwarzschild spacetime. Using the closed-form expression, we compute the necessary external force required to hold the charge stationary. Although the energy associated with the scalar field contributes to the renormalized mass of the particle (and thereby its weight), we find there is no additional self-force acting on the charge. This result is unlike the analogous electrostatic result, where, after a similar mass renormalization, there remains a finite repulsive self-force acting on a static electric test-charge outside a Schwarzschild black hole. We confirm our force calculation using Carter's mass-variation theorem for black holes. The primary motivation for this calculation is to develop techniques and formalism for computing all forces - dissipative and non-dissipative - acting on charges and masses moving in a black-hole spacetime. In the Appendix we recap the derivation of the closed-form electrostatic potential. We also show how the closed-form expressions for the fields are related to the infinite series solutions.