Probing Kalb–Ramond field with extreme mass ratio inspirals

Abstract The extreme-mass-ratio inspirals (EMRIs) are emerging as precision laboratories for testing the gravity beyond general relativity. In this work, we investigate the Lorentz symmetry breaking (LSB) effect induced by the Kalb–Ramond (KR) field on the gravitational waveforms from the EMRI system. We observe that the LSB parameter $$ l $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>l</mml:mi> </mml:math> appears in the leading order for the corrections of energy and angular momentum fluxes, and as $$ |l| $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>|</mml:mo> <mml:mi>l</mml:mi> <mml:mo>|</mml:mo> </mml:mrow> </mml:math> increases, the differences in EMRI waveforms between the KR black hole and Schwarzschild black hole become more pronounced. We note that the LSB effect becomes detectable by LISA for values of $$|l|\sim 10^{-6}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mo>|</mml:mo> <mml:mi>l</mml:mi> <mml:mo>|</mml:mo> </mml:mrow> <mml:mo>∼</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>6</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> with a one-year observation period. Furthermore, we use the Fisher information matrix (FIM) approach for the parameter estimation and find the detection error for l can be constrained to $$\Delta l \sim 10^{-5}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>l</mml:mi> <mml:mo>∼</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> at $$\textrm{SNR} = 20$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtext>SNR</mml:mtext> <mml:mo>=</mml:mo> <mml:mn>20</mml:mn> </mml:mrow> </mml:math> , demonstrating the potential of space-based gravitational wave detectors to rigorously test the KR field.