Bilocal geodesic operators in static spherically-symmetric spacetimes

Abstract

We present a method to compute exact expressions for optical observables for static spherically symmetric spacetimes in the framework of the bilocal geodesic operator formalism. The expressions are obtained by solving the linear geodesic deviation equations for null geodesics, using the spacetime symmetries and the associated conserved quantities. We solve the equations in two different ways: by varying the geodesics with respect to their initial data and by directly integrating the equation for the geodesic deviation. The results are very general and can be applied to a variety of spacetime models and configurations of the emitter and the observer. We illustrate some of the aspects with an example of Schwarzschild spacetime, focusing on the behaviour of the angular diameter distance, the parallax distance, and the distance slip between the observer and the emitter outside the photon sphere.

arXiv comment30 pages, 3 figures

References in corpus (12)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• Black holes, hidden symmetries, and complete integrability
• Particle motion near high-spin black holes
• Geometric optics in general relativity using bilocal operators
• Optical drift effects in general relativity
• Direction of light propagation to order G^2 in static, spherically symmetric spacetimes: a new derivation
• Reduced phase space optics for general relativity: Symplectic ray bundle transfer
• Time transfer functions in Schwarzschild-like metrics in the weak-field limit: A unified description of Shapiro and lensing effects
• The Angular-Diameter-Distance-Maximum and Its Redshift as Constraints on $\Lambda \ne 0$ FLRW Models
• Geometric optics in relativistic cosmology: new formulation and a new observable
• Weighing the spacetime along the line of sight using times of arrival of electromagnetic signals
• Testing the null energy condition with precise distance measurements

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