Testing Lorentz symmetry in strong gravitational fields provides a promising probe of extensions to general relativity. The supermassive black hole Sgr A* and the orbit of the S-stars offer a laboratory for such tests in a regime beyond weak field limit. We analyze the S2 star’s orbital data focusing on the Schwarzschild-like black hole within bumblebee gravity, where deviations from general relativity are encoded in a single Lorentz-violating parameter ℓ. Using a full 14-dimensional Markov Chain Monte Carlo analysis under uniform and Gaussian priors, we obtain <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\ell = -8.01 \times {10^{-5}}_{-2.09 \times 10^{-4}}^{+2.77 \times 10^{-4}}$</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mi>ℓ</mi> <mo>=</mo> <mo>−</mo> <mn>8.01</mn> <mo>×</mo> <msubsup> <mrow> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>5</mn> </mrow> </msup> </mrow> <mrow> <mo>−</mo> <mn>2.09</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msup> </mrow> <mrow> <mo>+</mo> <mn>2.77</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msup> </mrow> </msubsup> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\ell = 1.00 \times {10^{-5}}_{-2.91 \times 10^{-4}}^{+2.90 \times 10^{-4}}$</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mi>ℓ</mi> <mo>=</mo> <mn>1.00</mn> <mo>×</mo> <msubsup> <mrow> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>5</mn> </mrow> </msup> </mrow> <mrow> <mo>−</mo> <mn>2.91</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msup> </mrow> <mrow> <mo>+</mo> <mn>2.90</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msup> </mrow> </msubsup> </math></EquationSource> </InlineEquation> at 1σ confidence level, respectively. The results show that, with supermassive Sgr A* black hole as gravity source, the constraints on the Lorentz-violating parameter in the current model in our analysis can be tighter than those from Event Horizon Telescope imaging of Sgr A* as well as the pulsar-Sgr A* systems.

Probing a Lorentz-violating parameter from orbital precession of the S2 star around the galactic centre supermassive black hole

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发表日期：

2026年4月29日

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Qi Qi,
Yu Sang,
Xiao-Mei Kuang

摘要

Testing Lorentz symmetry in strong gravitational fields provides a promising probe of extensions to general relativity. The supermassive black hole Sgr A* and the orbit of the S-stars offer a laboratory for such tests in a regime beyond weak field limit. We analyze the S2 star’s orbital data focusing on the Schwarzschild-like black hole within bumblebee gravity, where deviations from general relativity are encoded in a single Lorentz-violating parameter ℓ. Using a full 14-dimensional Markov Chain Monte Carlo analysis under uniform and Gaussian priors, we obtain $\ell = -8.01 \times {10^{-5}}_{-2.09 \times 10^{-4}}^{+2.77 \times 10^{-4}}$ $ℓ = - 8.01 \times {10^{- 5}}_{- 2.09 \times 10^{- 4}}^{+ 2.77 \times 10^{- 4}}$ and $\ell = 1.00 \times {10^{-5}}_{-2.91 \times 10^{-4}}^{+2.90 \times 10^{-4}}$ $ℓ = 1.00 \times {10^{- 5}}_{- 2.91 \times 10^{- 4}}^{+ 2.90 \times 10^{- 4}}$ at 1σ confidence level, respectively. The results show that, with supermassive Sgr A* black hole as gravity source, the constraints on the Lorentz-violating parameter in the current model in our analysis can be tighter than those from Event Horizon Telescope imaging of Sgr A* as well as the pulsar-Sgr A* systems.