Abstract
We have used publicly available kinematic data for the S2 star to constrain the parameter space of MOdified Gravity. Integrating geodesics and using a Markov Chain Monte Carlo algorithm, we have provided the first constraint on the scales of the Galactic Centre for the parameter α of the theory, which represents the fractional increment of the gravitational constant G with respect to its Newtonian value. Namely, α≲0.662 at 99.7% confidence level (where α=0 reduces the theory to General Relativity).
Highlights
Scalar-Tensor-Vector Gravity (STVG), referred to in the literature as MOdifiedGravity (MOG), is a theory of gravity firstly proposed in [1] as an alternative to Einstein’s theory of General Relativity (GR)
In order to fit our orbital model to such data we employ the Markov Chain Monte Carlo (MCMC) sampler in emcee [23], and we evaluate the integrated autocorrelation time of the chains to check the convergence of the algorithm
While both analyses are compatible with GR, the additional information carried by the single orbital precession data point at pericentre results in a more peaked distribution for α in case B, whose upper limit decrease by 55.6% with respect to analysis A
Summary
Scalar-Tensor-Vector Gravity (STVG), referred to in the literature as MOdified. Gravity (MOG), is a theory of gravity firstly proposed in [1] as an alternative to Einstein’s theory of General Relativity (GR). Under these assumptions (and by setting the speed of light in vacuum to c = 1), one obtains [13] the following line element: ds2 This Schwarzschild-like metric is the most general spherically symmetric static solution in MOG, and it provides an exact description of the gravitational√field around a pointlike nonrotating source of mass M (and a fifth-force charge Q = αGN M). It differs from the classical one in GR (to which it reduces when α = 0) by a different definition of the ∆ function:. As shown in [9], particles around a MOG BH experience an increased orbital precession, whose first-order expression explicitly depends on the parameter α and is given in Equation (1)
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