Deflection angle and shadow behaviors of quintessential black holes in arbitrary dimensions
Abstract
Abstract Motivated by M-theory/superstring inspired models, we investigate certain behaviors of the deflection angle and the shadow geometrical shapes of higher dimensional quintessential black holes associated with two values of the dark energy (DE) state parameter, being <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>ω</mml:mi> <mml:mo>=</mml:mo> <mml:mo>−</mml:mo> <mml:mfrac> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:mfrac> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>ω</mml:mi> <mml:mo>=</mml:mo> <mml:mo>−</mml:mo> <mml:mfrac> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:mfrac> </mml:math> . Concretely, we derive the geodesic equation of photons on such backgrounds. Thanks to the Gauss–Bonnet theorem corresponding to the optical metric, we compute the leading terms of the deflection angle in the so-called weak-limit approximation. After that, we inspect the effect of DE and the space–time dimension d on the calculated optical quantities. Introducing DE via the field intensity c and the state parameter ω , we find that the shadow size and the deflection angle increase by increasing values of the field intensity c . However, we observe that the high dimensions decrease such quantities for ω -models exhibiting similar behaviors. Then, we consider the effect of the black hole charge, on these optical quantities, by discussing the associated behaviors. The present investigation recovers certain known results appearing in ordinary four dimensional models.