Approximate analytical calculations of photon geodesics in the Schwarzschild metric

Abstract

We develop a method for deriving approximate analytical formulae to integrate photon geodesics in a Schwarzschild spacetime. Based on this, we derive the approximate equations for light bending and propagation delay that have been introduced empirically. We then derive for the first time an approximate analytical equation for the solid angle. We discuss the accuracy and range of applicability of the new equations and present a few simple applications of them to known astrophysical problems.

arXiv comment8 pages, 10 Figures; Received: 08 June 2016 / Accepted: 04 August 2016and accepted from A&A

References in corpus (9)

• Measuring the neutron star equation of state using X-ray timing
• Gravitational Bending of Light Near Compact Objects
• Pulse profiles of millisecond pulsars and their Fourier amplitudes
• The Reflection Component from Cygnus X-1 in the Soft State Measured by NuSTAR and Suzaku
• Iron Line Profiles in Strong Gravity
• Determining Neutron Star Properties by Fitting Oblate-Star Waveforms To X-ray Burst Oscillations
• Bounds on Compactness for LMXB Neutron Stars from X-ray Burst Oscillations
• Constraints on the Mass and Radius of the Neutron Star XTE J1807-294
• Effects of Spot Size on Neutron-Star Radius Measurements from Pulse Profiles

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