[Paper Review] Constraint on parameters of a rotating black hole in Einstein-bumblebee theory by quasi-periodic oscillations

Zejun Wang, Songbai Chen+1 more|arXiv (Cornell University)|Dec 6, 2021

Astrophysical Phenomena and Observations51 references4 citations

TL;DR

This study constrains the Lorentz symmetry breaking parameter $ l $ in Einstein-bumblebee gravity using quasi-periodic oscillations (QPOs) from three black hole binaries—GRO J1655-40, XTE J1550-564, and GRS 1915+105—via the relativistic precession model. It finds that QPO data from GRO J1655-40 yield the tightest constraint, with a best-fit $ l = -0.1048 $, implying higher Hawking temperature and weaker Penrose energy extraction compared to Kerr black holes, while general relativity ($ l = 0 $) remains consistent within $ 1\sigma $ uncertainty.

ABSTRACT

We have studied quasi-periodic oscillations frequencies in a rotating black hole with Lorentz symmetry breaking parameter in Einstein-bumblebee gravity by relativistic precession model. We find that in the rotating case with non-zero spin parameter both of the periastron and nodal precession frequencies increase with the Lorentz symmetry breaking parameter, but the azimuthal frequency decreases. In the non-rotating black hole case, the nodal precession frequency disappears for arbitrary Lorentz symmetry breaking parameter. With the observation data of GRO J1655-40, XTE J1550-564, and GRS 1915+105, we find that the constraint on the Lorentz symmetry breaking parameter is more precise with data of GRO J1655-40 in which the best-fit value of the Lorentz symmetry breaking parameter is negative. This could lead to that the rotating black hole in Einstein-bumblebee gravity owns the higher Hawking temperature and the stronger Hawking radiation, but the lower possibility of exacting energy by Penrose process. However, in the range of $1 σ$, we also find that general relativity remains to be consistent with the observation data of GRO J1655-40, XTE J1550-564 and GRS 1915+105.

Motivation & Objective

• To constrain the Lorentz symmetry breaking parameter $ l $ in Einstein-bumblebee gravity using observed quasi-periodic oscillations (QPOs) from stellar-mass black hole binaries.
• To investigate how Lorentz violation affects fundamental frequencies—azimuthal, periastron, and nodal precession—around rotating black holes in this modified gravity theory.
• To assess the consistency of Einstein-bumblebee gravity with observational data, particularly whether general relativity ($ l = 0 $) remains viable within uncertainty.
• To evaluate the astrophysical implications of a negative $ l $, including changes in Hawking radiation and Penrose process efficiency.

Proposed method

• Adopts the relativistic precession model to relate observed QPO frequencies (azimuthal, periastron, nodal) to orbital frequencies of test particles in the equatorial plane of a rotating black hole in Einstein-bumblebee gravity.
• Uses the exact rotating black hole solution in Einstein-bumblebee gravity, parameterized by mass $ M $, spin $ a $, and Lorentz violation parameter $ l $, with the metric derived from a bumblebee vector field with spontaneous Lorentz symmetry breaking.
• Derives the effective potential and circular orbit conditions to compute the three fundamental frequencies: $ \nu_\phi $, $ \nu_{\text{per}} $, and $ \nu_{\text{nod}} $, as functions of $ M $, $ a $, and $ l $.
• Performs a Bayesian parameter estimation using QPO frequency data from GRO J1655-40, XTE J1550-564, and GRS 1915+105 to constrain $ M $, $ a $, and $ l $.
• Compares the resulting $ 1\sigma $ confidence regions for $ l $ across the three sources to assess the precision of constraints.

Experimental results

Research questions

• RQ1 How does the Lorentz symmetry breaking parameter $ l $ in Einstein-bumblebee gravity affect the fundamental precession frequencies of test particles around a rotating black hole?
• RQ2 Which black hole binary system provides the tightest observational constraint on $ l $, and why?
• RQ3 What are the astrophysical consequences of a negative $ l $, particularly regarding Hawking radiation and energy extraction via the Penrose process?
• RQ4 Is general relativity ($ l = 0 $) consistent with the observed QPO frequencies from GRO J1655-40, XTE J1550-564, and GRS 1915+105 within $ 1\sigma $ uncertainty?

Key findings

• The Lorentz symmetry breaking parameter $ l $ is constrained most precisely using data from GRO J1655-40, yielding a best-fit value of $ l = -0.1048 $.
• For $ a \neq 0 $, both periastron and nodal precession frequencies increase with $ l $, while the azimuthal frequency decreases.
• In the non-rotating case, the nodal precession frequency vanishes regardless of $ l $, as $ \nu_\theta = \nu_\phi $.
• A negative $ l $ implies that the black hole in Einstein-bumblebee gravity has a larger outer ergosurface and horizon radius, but a reduced ergoregion width, decreasing the efficiency of energy extraction via the Penrose process.
• A negative $ l $ leads to a higher Hawking temperature and stronger Hawking radiation compared to the Kerr black hole.
• General relativity ($ l = 0 $) remains within the $ 1\sigma $ confidence region for all three sources, indicating consistency with current QPO observations.