An exact stationary axisymmetric vacuum solution within a metric-affine bumblebee gravity
A. A. Araújo Filho, J. R. Nascimento, A. Yu. Petrov, P. J. Porfírio
Abstract
Abstract Within the framework of the spontaneous Lorentz symmetry breaking (LSB), 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 μν . 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 LSB through the LV dimensionless parameter X = ξb 2 , with ξ is the nonminimal coupling constant, and b 2 = b μ b μ , with b μ is the vacuum expectation value of the bumblebee field; 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 of Mercury's perihelion.