Speaker
Description
We examine the geometrical difference between non-extremal black hole(NXBH), extremal black hole(XBH) and naked singularity(NS) via Lense-Thirring(LT) effect in spinning modified-gravity(MOG). For NXBH, we find that the LT frequency ($\Omega_{LT}$) is proportional to the angular-momentum($J=a\,{\cal M}$) parameter or spin parameter($a$) i.e. $\Omega_{LT}\propto J $ or $\Omega_{LT}\propto a $[where ${\cal M}=M(1+\alpha)$ is ADM mass, $\alpha$ is MOG parameter and $M$ is Komar mass] and is inversely proportional to the cubic value of radial parameter i.e. $\Omega_{LT}\propto \frac{1}{r^3}$.
For XBH ($a^2=\frac{G_{N}^2{\cal M}^2}{1+\alpha}$), we find LT frequency is proportional to the angular-momentum parameter i.e. $\Omega_{LT}\propto \frac{1}{\sqrt{1+\alpha}}$ and is inversely proportional to the cubic value of radial parameter i.e. $\Omega_{LT}\propto \frac{1}{r^3}$. While for NS, we find $\Omega_{LT}\propto \frac{{\cal M}^3}{J^3}$ and $\Omega_{LT}\propto \frac{\left[r-\left(\frac{\alpha}{1+\alpha}\right)\frac{G_{N}{\cal M}}{2} \right]}
{\sqrt{1+\left(\frac{\alpha}{1+\alpha}\right)\frac{G_{N}^2{\cal M}^2}{a^2}}}$ in the limit $\theta=0$ and $a=\frac{J}{{\cal M}}>>r$. It depends both on the angular momentum parameter and MOG parameter~$\alpha$.
