Investigating the existence of gravitomagnetic monopole in M87*

We examine the possibility for the existence of gravitomagnetic monopole ($n_{\ast }$) in M87* by using the results obtained from its first Event Horizon Telescope image. By numerically deducing the shadow sizes in Kerr-Taub-NUT (KTN) spacetime, we show that the shadow size increases with increasing $\mathrm{\mid }{n}_{\ast }\mathrm{\mid }$ for a fixed Kerr parameter $\mathrm{\mid }{a}_{\ast }\mathrm{\mid }$ in case of the KTN black hole, whereas for a KTN naked singularity it increases with increasing $n_{\ast }$ for a fixed $a_{\ast }>0$ if $n_{\ast }>-\cot {17}^{\circ }$ . In general, the asymmetry of shadow shape increases if the central dark object in M87 is a KTN/Kerr naked singularity instead of a KTN/Kerr black hole. We find that a non-zero gravitomagnetic monopole is still compatible with the current EHT observations, in which case the upper limit of $n_{\ast }$ cannot be greater than $1.1$, i.e., $n_{\ast }\lesssim 1.1$ for the prograde rotation ($a_{\ast }>0$), and the lower limit of $n_{\ast }$ cannot be less than $-1.1$, i.e., $n_{\ast }\gtrsim -1.1$ for the retrograde rotation ($a_* < 0$). Moreover, if the circularity of the shadow can be measured on a precision of $\lesssim 1\mathrm{\%}$, the Kerr and KTN naked singularities can be falsified for M87*.