| Issue |
A&A
Volume 595, November 2016
|
|
|---|---|---|
| Article Number | A38 | |
| Number of page(s) | 8 | |
| Section | Astrophysical processes | |
| DOI | https://doi.org/10.1051/0004-6361/201629075 | |
| Published online | 26 October 2016 | |
Approximate analytical calculations of photon geodesics in the Schwarzschild metric
1 Institut für theoretische Physik, Universität Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
e-mail: vittorio-df@issibern.ch
2 International Space Science Institute, Hallerstrasse 6, 3012 Bern, Switzerland
3 International Space Science Institute Beijing, No.1 Nanertiao, Zhongguancun, Haidian District, 100190 Beijing, PR China
4 INAF–Osservatorio Astronomico di Roma, Via Frascati, 33, Monteporzio Catone, 00078 Rome, Italy
Received: 8 June 2016
Accepted: 4 August 2016
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.
Key words: gravitation / stars: black holes / stars: neutron / X-rays: binaries / accretion, accretion disks
© ESO, 2016
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