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

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Summary

Introduction

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)

The Orbit of S2 in MOG
Data and Methodology
Results
Conclusions
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