[论文解读] Nonlinear electrodynamics and the gravitational redshift of pulsars

Herman J. Mosquera Cuesta, J. M. Salim|arXiv (Cornell University)|Mar 2, 2004

Pulsars and Gravitational Waves Research被引用 3

一句话总结

本文研究了Born-Infeld非线性电动力学（NLED）如何通过改变真空电磁行为，影响高度磁化的脉冲星（尤其是磁星）周围的时空几何结构。研究结果表明，该效应会在光谱线中引发显著的引力红移偏移，这一现象可作为超越Euler-Heisenberg近似的NLED的潜在观测特征。

ABSTRACT

The idea that the nonlinear electromagnetic interaction, i. e., light propagation in vacuum, can be geometrized was developed by Novello et al. (2000) and Novello & Salim (2001). Since then a number of physical consequences for the dynamics of a variety of systems have been explored. In a recent paper Mosquera Cuesta & Salim (2003) presented the first astrophysical study where such nonlinear electrodynamics (NLEDs) effects were accounted for in the case of a highly magnetized neutron star or pulsar. In that paper the NLEDs was invoked {\\it a l\\`a} Euler-Heisenberg, which is an infinite series expansion of which only the first term was used for the analisys. The immediate consequence of that study was an overall modification of the space-time geometry around the pulsar, which is ``perceived'', in principle, only by light propagating out of the star. This translates into an significant change in the surface redshift, as inferred from absorption (emission) lines observed from a super magnetized pulsar. The result proves to be even more dramatic for the so-called magnetars, pulsars endowed with magnetic ($B$) fields higher then the Schafroth quantum electrodynamics critical $B$-field. Here we demonstrate that the same effect still appears if one calls for the NLEDs in the form of the one rigorously derived by Born & Infeld (1934) based on the special relativistic limit for the velocity of approaching of an elementary particle to a pointlike electron [From the mathematical point of view, the Born & Infeld (1934) NLEDs is described by an exact Lagrangean, whose dynamics has been successfully studied in a wide set of physical systems.].

研究动机与目标

• 研究Born-Infeld非线性电动力学（NLED）对高度磁化中子星附近时空几何的影响。
• 评估此前基于Euler-Heisenberg近似研究的NLED效应，在更严格的Born-Infeld拉格朗日量框架下是否依然成立。
• 确定此类由NLED引起的几何修正是否会导致脉冲星星体光谱线引力红移的可观测变化。
• 评估NLED对磁星的影响，其中磁场强度超过 Schwinger 临界场强。

提出的方法

• 采用精确的Born-Infeld拉格朗日量作为非线性电动力学的基础，避免微扰展开。
• 将Born-Infeld NLED框架应用于建模脉冲星典型强磁场下的真空极化效应。
• 推导由于NLED引起的修正电磁应力-能量张量导致的脉冲星周围时空度规的修正。
• 利用修正后的度规分析光谱线的引力红移，与标准广义相对论预测进行比较。
• 聚焦于磁星区域，其磁场强度接近或超过 Schwinger 临界场强（~4.4×10^13 G）。

实验结果

研究问题

• RQ1 Born-Infeld形式的非线性电动力学是否会在脉冲星中产生可测量的引力红移修正？
• RQ2 与Euler-Heisenberg近似相比，采用精确的Born-Infeld拉格朗日量如何影响时空几何结构？
• RQ3 磁星中的NLED效应是否会导致观测到的发射线或吸收线红移发生可探测的偏移？
• RQ4 NLED引起的几何修正是否仅通过光在真空中的传播被观测到，如理论所预测？

主要发现

• Born-Infeld NLED框架显著改变了高度磁化脉冲星周围的时空几何结构。
• 这种几何变化导致从光谱线推断出的引力红移出现可测量的偏移，即使磁场超过Schwinger临界场强亦然。
• 即使使用精确的Born-Infeld拉格朗日量，该效应依然存在，证实该结果并非微扰Euler-Heisenberg近似下的人为产物。
• 该修正仅被通过真空传播的光线所感知，与NLED改变真空光学性质的观点一致。
• 本研究证实，由于极端磁场的存在，NLED效应在磁星中更为显著，使其成为检验非线性电动力学的理想候选天体。