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.

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

References in corpus (1)

• Pulse profiles of millisecond pulsars and their Fourier amplitudes

Cited by in corpus (13)

• Testing wormhole solutions in extended gravity through the Poynting-Robertson effect
• General relativistic Poynting-Robertson effect to diagnose wormholes existence: static and spherically symmetric case
• Disk origin of broad optical emission lines of the TDE candidate PTF09djl
• Study of null and time-like geodesics in the exterior of a Schwarzschild black hole with quintessence and cloud of strings
• Analytical study of light ray trajectories in Kerr spacetime in the presence of an inhomogeneous anisotropic plasma
• Analytical expressions for pulse profile of neutron stars in plasma environments
• Exploring departures from Schwarzschild black hole in $f(R)$ gravity
• Propagation of light in the presence of gravity generated by static and spherically symmetric curved space-times using Maxwell equations
• Sensitivity of pulsar light curves to spacetime geometry and efficacy of analytic approximations
• Relativistic time delay analysis of pulsar signals near ultra-compact objects
• Accurate analytical modeling of light rays in spherically symmetric spacetimes: Applications in the study of black hole accretion disks and polarimetry
• Light propagation around a Kerr-like black hole immersed in an inhomogeneous anisotropic plasma in Rastall gravity: Analytical solutions to the equations of motion
• The role of elliptic integrals in calculating the gravitational lensing of a charged Weyl black hole surrounded by plasma