2025/03/04 by Igata, Takahisa
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Astrophysical Phenomena (astro-ph.HE) #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2503.02320
In static, spherically symmetric spacetimes, the deflection angle of photons in the strong deflection limit exhibits a logarithmic divergence. We introduce an analytical framework that clarifies the physical origin of this divergence by employing local, coordinate-invariant geometric quantities alongside the properties of the matter distribution. In contrast to conventional formulations -- where the divergence rate a is expressed via coordinate-dependent metric functions -- our approach relates a to the components of the Einstein tensor in an orthonormal basis adapted to the spacetime symmetry. By applying the Einstein equations, we derive the expression a=\frac1√1-8πRm2(ρm+Πm), where ρm and Πm denote the local energy density and tangential pressure evaluated at the photon sphere of areal radius Rm. This result reveals that a is intrinsically governed by the local matter distribution, with the universal value a=1 emerging when ρm+Πm=0. Notably, this finding resolves the long-standing puzzle of obtaining a=1 in a class of spacetimes supported by a massless scalar field. Furthermore, these local properties are reflected in the frequencies of quasinormal modes, suggesting a profound connection between strong gravitational lensing and the dynamical response of gravitational wave signals. Our framework, independent of any specific gravitational theory, offers a universal tool for testing gravitational theories and interpreting astrophysical observations.