Light paths of normal and phantom Einstein-Maxwell-dilaton black holes

TL;DR

This paper analytically derives null geodesics for normal and phantom Einstein-Maxwell-dilaton black holes using elliptic functions, enabling matter type identification through deflection angles and time delays.

Contribution

It provides explicit formulas for light paths in these black holes, incorporating parameters that distinguish normal from phantom types, and discusses observational implications.

Findings

Deflection angles depend on black hole parameters and matter type.

Time delay formulas can identify matter nature.

Phantom black holes lack certain null geodesics.

Abstract

Null geodesics of normal and phantom Einstein-Maxwell-dilaton black holes are determined analytically by the Weierstrass elliptic functions. The black hole parameters other than the mass enter, with the appropriate signs, the formula for the angle of deflection to the second order in the inverse of the impact parameter allowing for the identification of the nature of matter (phantom or normal). Such identification is also possible via the time delay formula and observation of relativistic images. Scattering experiencesmay favor black holes of Einstein-anti-Maxwell-dilatonic theory for their high relative discrepancy with respect to the Schwarzschild value. For the cases we restrict ourselves to, phantom black holes are characterized by the absence of many-world and two-world null geodesics.