Times of arrival (TOA) of signals in the Kerr-MOG black hole

Abstract

Modified gravity (MOG) theories are alternatives to general relativity (GR) that arose primarily from the need to explain the observed galactic flat rotation curves without invoking the elusive dark matter hypothesized by GR. A well known MOG is the Scalar–Tensor–Vector–Gravity developed by Moffat, who has also found a spinning solution called the Kerr-MOG black hole (BH) characterized by the spin a and MOG parameter $$\alpha $$, the latter determining the strength of the gravitational vector forces. We consider the static-MOG metric ($$a=0$$) to first understand how the nature of geometry drastically changes depending on different sectors of $$\alpha $$. Then we study the influence of $$\alpha $$ in each sector on a new astrophysical diagnostic caused by frame dragging, viz., the difference $$\varDelta t$$ in the times of arrival at the observer of signals emanating from a variable pulsar (PSR) passing behind a Kerr-MOG lens in a PSR-BH binary system. The study generalizes the zeroth order Laguna–Wolszczan formula up to third PPN order in $$\left( 1/r\right) $$ using thin-lens approximation, which reveals how $$\varDelta t$$ is influenced both by a and $$\alpha $$. The magnitude and sign of $$\alpha $$ indicate deviations from GR ($$\alpha =0$$) and future measurements may constrain $$\alpha $$ provided a suitable binary is identified.