Gravitational Bending of Light Near Compact Objects

By A. Beloborodov. 2002

249 citations recorded by the source corpus.

A photon emitted near a compact object at an angle α with respect to the radial direction escapes to infinity at a different angle ψ > α. This bending of light is caused by a strong gravitational field. We show that, in a Schwarzschild metric, the effect is described by 1 - cos α = (1 - cos ψ)(1 - rg/R), where R/rg is the emission radius in Schwarzschild units. The formula is approximate, and it applies at R ≥ 2rg only; however, at these radii it has amazing accuracy, fully sufficient in many applications. As one application, we develop a new formulation for the light-bending effects in pulsars. It reveals the simple character of these effects and gives their quantitative description with practically no loss of accuracy (for the typical radius of a neutron star R = 3rg the error is 1%). The visible fraction of a star surface is shown to be Sv/4πR2 = [2(1 - rg/R)]-1, which is for R = 3rg. The instantaneous flux of a pulsar comes from one or two antipodal polar caps that rotate in the visible zone. The pulse produced by one blackbody cap is found to be sinusoidal (light bending impacts the pulse amplitude but not its shape). When both caps are visible, the pulse shows a plateau: the variable parts of the antipodal emissions precisely cancel each other. The pulsed fraction of blackbody emission with antipodal symmetry has an upper limit Amax = (R - 2rg)/(R + 2rg). Pulsars with A > Amax must be asymmetric.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/838f05c09492dbf72aa8e4d40b23331ec51b8474

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In Astronomy and Astrophysics

Citations in the corpus

Observing the Inner Shadow of a Black Hole: A Direct View of the Event Horizon (2021, background): “31ah, 0 2 o* Note that the Schwarzschild approximation ( ) =+g r M2 20 follows from an analytic approximation for Schwarzschild geodesics given by Beloborodov (2002).”
A Deep Chandra Survey of the Globular Cluster 47 Tucanae: Catalog of Point Sources (2005, unknown): “SinceMSPs are highly compact, X-rays from surface hot spots will be bent by gravity to allow observers to see 75% of the neutron star surface (Pechenick et al. 1983; Beloborodov 2002; S. Bogdanov et al. 2005, in preparation).”
Physics of strongly magnetized neutron stars (2006, methodology): “This can be accomplished using the standard, well-developed procedure (Pechenick et al 1983, Beloborodov 2002).”
Frequency-dependent effects of gravitational lensing within plasma (2015, methodology): “With the convenient classification scheme of Beloborodov (2002) we show separate examples of each pulse class for antipodal configurations.”
On the Nature of the X-ray Emission of Accreting Millisecond Pulsar SAX J1808.4-3658 (2002, methodology): “Using the formalism developed by Beloborodov (2002) we derive here simple analytical formulae for the light curves and theoscillation amplitudes that could be useful for understanding the main physical effects.”