Shadows and thin accretion disk images of the $$\gamma $$-metric

Abstract The $$\gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>γ</mml:mi> </mml:math> -metric is a static, axially-symmetric singular solution of the vacuum Einstein’s equations without an event horizon. This is a two-parameter family of solutions, generic values of one of which (called $$\gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>γ</mml:mi> </mml:math> ) measure the deviation from spherical symmetry. We show that this can serve as a black hole mimicker, consistent with current observations. To this end, we first study the shadow cast by this geometry, in order to constrain the $$\gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>γ</mml:mi> </mml:math> -metric from observations. We find that for $$\gamma &lt; 1/2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>γ</mml:mi> <mml:mo>&lt;</mml:mo> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> , there are, in principle, no shadows cast. On the other hand, shadows cast for all values of $$\gamma \ge 1/2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>γ</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> are consistent with observations of M $$87^*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>87</mml:mn> <mml:mo>∗</mml:mo> </mml:msup> </mml:math> by the Event Horizon Telescope. We also study images of thin accretion disks in the $$\gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>γ</mml:mi> </mml:math> -metric background. In situations where the $$\gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>γ</mml:mi> </mml:math> -metric possesses light rings, these qualitatively mimic Schwarzschild black holes with the same ADM mass, while in the absence of such rings, they are drastically different from the black hole case.

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