Periodic orbits and gravitational wave radiation in short hair black hole spacetimes for an extreme mass ratio system

Abstract For a short hair black hole(BH) that bypasses the “no-short-hair” theorem, its hair parameters have a significant impact near the event horizon and may thus carry the internal information of the BH. This paper studies the influence of the hair parameter $$Q_m$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Q</mml:mi> <mml:mi>m</mml:mi> </mml:msub> </mml:math> and the structural parameter $$k$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>k</mml:mi> </mml:math> of the short hair BH on the periodic orbits of particles and gravitational wave radiation in the extreme mass ratio(EMR) system. The research results show that $$Q_m$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Q</mml:mi> <mml:mi>m</mml:mi> </mml:msub> </mml:math> has a significant impact on the radius of the orbit, angular momentum, and the $$E-L$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>E</mml:mi> <mml:mo>-</mml:mo> <mml:mi>L</mml:mi> </mml:mrow> </mml:math> space. A larger value of $$k$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>k</mml:mi> </mml:math> weakens this effect and makes it degenerate with the Schwarzschild BH. In addition, an increase in $$Q_m$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Q</mml:mi> <mml:mi>m</mml:mi> </mml:msub> </mml:math> or a decrease in $$k$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>k</mml:mi> </mml:math> will lead to a reduction in the period of gravitational waves and a significant enhancement of the signal amplitude. These results provide new observational means for distinguishing short hair BH from classical BH and also offer new insights for verifying the no-hair theorem and understanding the physical behaviors near the event horizon.

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