Gravitational wave radiation from periodic orbits in regular black holes

Abstract

Gravitational wave radiation from periodic orbits in some standard regular black hole spacetimes is studied, primarily using known methods (numerical and analytic). We demonstrate specific differences with the singular Schwarzschild geometry by analysing orbit characteristics, gravitational wave strain profiles, and the corresponding power spectrum density, for different values of the regularising parameter `$g$'. Further, we assess our results vis-a-vis the LISA sensitivity curves and show how our results may be useful while developing templates for detecting regular black holes as viable alternatives to the singular ones. The appendices to our article contain details on errors in our estimates and provide for the first time, some exact analytical expressions on gravitational wave radiation from different types of periodic orbits in Schwarzschild spacetime.

Figures (25)

• Figure 1: Plot of the effective potentials of the Bardeen and Hayward spacetimes for different values of $g$ with $L=3.6M$.
• Figure 2: Plot of the allowed values of $E$ and $L/M$ for bound orbits for the Bardeen and Hayward black hole for different values of $g$.
• Figure 3: The trajectory of a typical $(1,2,0)$ orbit after $\phi$ has evolved by $2\pi$, $4\pi$, and $6\pi$, respectively. The starting point is marked with a red arrow.
• Figure 4: Variation of $q$ with $E$ for different values of $\epsilon$ (left) and $g$ (right) for the Bardeen regular black hole.
• Figure 5: Variation of $q$ with $L/M$ for different values of $g$ (left) and $E$ (right) for the Bardeen regular black hole.