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An exact stationary axisymmetric vacuum solution within a metric--affine bumblebee gravity
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An exact stationary axisymmetric vacuum solution within a metric--affine bumblebee gravity
abstract
Within the framework of the spontaneous Lorentz symmetry breaking, we consider a metric--affine generalization of the gravitational sector of the Standard--Model Extension (SME), including the Lorentz--violating (LV) coefficients $u$ and $s^{\mu\nu}$. In this model, we derive the modified Einstein field equations in order to obtain a new axisymmetric vacuum spinning solution for a particular bumblebee's profile. Such a solution has the remarkable property of incorporating the effects of Lorentz symmetry breaking (LSB) through the LV dimensionless parameter $X=\xi b^2$, as the LSB is turned off, $X=0$, we recover the well--established result, the Kerr solution, as expected. Afterwards, we calculate the geodesics, the radial acceleration and thermodynamic quantities for this new metric. We also estimate an upper bound for $X$ by using astrophysical data of the advance Mercury's perihelion.
Forward citations
Cited by 9 Pith papers
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Full classification of static spherical vacuum solutions in bumblebee gravity with general VEVs reveals degeneracies at ξ=κ/2 and permits exact Schwarzschild solutions with non-zero matter.
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Exact Black Hole Solutions in Bumblebee Gravity with Lightlike or Spacelike VEVS
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Constraining Lorentz symmetry breaking in bumblebee gravity with extreme mass-ratio inspirals
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