Dynamics of neutral and charged objects in gravitational fields coupled to nonlinear electrodynamics

考虑非线性电动力学有几个原因：(i)它遵循基于弦理论的量子引力场景，（ii）它遵循量子电动力学（海森堡-欧拉）的有效理论，（iii）它被提出是为了摆脱标准电动力学（Born-Infeld）中出现的无穷大，（iv）在爱因斯坦场方程的背景下，非线性电动力学模型导致规则的黑洞解。虽然所有的实验结果都符合标准量子电动力学，但弦理论的结果和重力理论背景下产生的特殊特征使得进一步研究这类理论，以及在实验室（例如强激光脉冲）和天体物理学（例如中子星、磁星和伽马射线暴）中进行新的实验测试是值得的。在这个德国和墨西哥的联合项目中，我们希望在非线性电动力学的框架内，以系统的方式研究光和中性粒子和带电粒子在时空中的传播。由于非线性，光不会沿着零测地线传播，从而导致诸如形状动力学、透镜效应或法拉第效应等特殊效应。非线性通常会导致双折射，也会导致倍频等效应。我们还想考虑带电粒子的非线性诱导反反应，它可能在极端情况下起作用。此外，还将考虑具有自旋、磁矩、电偶极子和高阶电荷多极子的扩展粒子。这些结果可能对理解中子星、磁星、吸积盘、伽马射线暴等附近的物理现象很重要，也将用于分析或提出强电磁场（如强激光脉冲）中的新实验。在这种情况下，我们也想找到具有非线性电动力学的爱因斯坦方程的新解，特别是试图找到扩展标准理论中的克尔-纽曼解的旋转解。

There are several reasons why to consider nonlinear electrodynamics: (i) it follows from quantum gravity scenarios based on string theory, (ii) it follows as effective theory from quantum electrodynamics (Heisenberg-Euler), (iii) it has been proposed in order to get rid of the infinities appearing in standard electrodynamics (Born-Infeld), and (iv) in the context of the Einstein field equations nonlinear electrodynamics models lead to regular black hole solutions. Though all experimental results are in accordance with standard quantum electrodynamics, the results from string theory and the particular features arising in the context of gravity theories make it worth to further investigate this class of theories, also towards new experimental tests in the laboratory (e.g. strong laser pulses) and in astrophysics (e.g. neutron stars, magnetars and gamma ray bursts). In this joint German-Mexican project we would like to investigate in a sytematic manner the propagation of light and of neutral and charged particles in space-times given within the framework of nonlinear electrodynamics. Due to the nonlinearity light does not propagate along null geodesics leading to particular effects for, e.g., shape dynamics, lensing, or the Faraday effect. The nonlinearity in general leads to birefringence and also should lead to effects like frequency doubling. We also want to take into acount the nonlinearity-induced backreaction for charged particles which may play a role in extreme situations. Furthermore, also extended particles with spin, magnetic moments, electric dipoles and higher-order charge multipoles will be considered. These results may be important for understanding the physics in the vicinity of neutron stars, magnetars, accretion discs, gamma ray bursts, etc., and also will be used to analyse or propose new experiments in strong electromagnetic fields like in strong laser pulses. In this context we also would like to find new solutions of the Einstein equations with nonlinear electrodynamics, in particular try to find rotating solutions extending the Kerr-Newman solution in the standard theory.