Probing the gravity of a Schwarzschild black hole in the presence of a cloud of strings with EMRIs

TL;DR

Problem addressed: the imprint of a cloud of strings (CoS) on the spacetime around a Schwarzschild black hole and its observable signatures in EMRI gravitational waves. Approach: model the spacetime with the Letelier CoS metric $f(r)=1-\frac{2M}{r}-\alpha$, analyze equatorial timelike geodesics via the Lagrangian, derive the effective potential $V_{eff}$ and orbital frequencies, and compute adiabatic GW fluxes to evolve the orbit; compare resulting waveforms to the Schwarzschild case. Key contributions: characterization of MBO/ISCO shifts and the $p,e$ evolution under CoS, generation of GW waveforms showing cumulative dephasing, and a mismatch-based detectability assessment indicating LISA can distinguish CoS for $\alpha\gtrsim 2\times 10^{-6}$ after ~1 year. Significance: demonstrates a potential observational probe of stringy/topological defects near SMBHs using upcoming space-based GW detectors.

Abstract

Here, we explore the effect of the cloud of strings (CoS) on the gravitational waveforms of extreme mass ratio inspirals (EMRIs). The EMRI system consists of a supermassive black hole (BH) and a compact stellar mass object moving around it. We begin with studying the test particle motion around the Schwarzschild BH surrounded by a CoS by using the Lagrangian formalism. Moreover, we investigated the effect of the CoS parameter on the evolution of the semi-latus rectum and eccentricity. We then turn to the exploration of the impact of the CoS parameter on the gravitational waveforms of the EMRI system. The analysis performed shows that Laser Interferometer Space Antenna (LISA) could detect the CoS imprint in gravitational waveforms when the values of the string cloud parameter $α\gtrsim 2 \times 10^{-6}$.

Figures (6)

• Figure 1: The plot demonstrates the radial dependence of the effective potential of the massive particles for the different values of the CoS parameter (left panel) and orbital angular momentum (right panel). $\alpha=0.01$ is set for the right panel.
• Figure 2: Radial dependence of $\dot{r}^2$ for different values of the energy $E$. Here, $L$ equals to the $0.5(L_{ISCO}+L_{MBO})$.
• Figure 3: Evolution of the semi-latus rectum $p$ (left panel) and eccentricity $e$ (right panel) for different values of the CoS parameter $\alpha$. Here, the initial values of other parameters are $(M,m,p,e)=(10^6 M_{\odot},10 M_{\odot},10M,0.1)$.
• Figure 4: The plot demonstrates the complete quasi-circular orbits around the supermassive Schwarzschild BH surrounded by a CoS. Here, we set the CoS parameter as $\alpha=0.01$, and $(r_0,\phi_0)=(10M,\pi/2)$.
• Figure 5: The plot shows the gravitational waveforms of the EMRI system for the different values of the CoS parameter initially (left panels) and after a year (right panels).