Gravitational wave from extreme mass-ratio inspirals as a probe of extra dimensions

Abstract

The field of gravitational waves is rapidly progressing due to the noticeable advancements in the sensitivity of gravitational-wave detectors that has enabled the detection prospects of binary black hole mergers. Extreme mass ratio inspiral (EMRI) is one of the most compelling and captivating binary systems in this direction, with the detection possibility by the future space-based gravitational wave detector. In this article, we consider an EMRI system where the primary or the central object is a spherically symmetric static braneworld black hole that carries a \textit{tidal charge} $Q$. We estimate the effect of the tidal charge on total gravitational wave flux and orbital phase due to a non-spinning secondary inspiralling the primary. We further highlight the observational implications of the tidal charge in EMRI waveforms. We show that LISA (Laser Interferometer Space Antenna) observations can put a much stronger constraint on this parameter than black hole shadow and ground-based gravitational wave observations, which can potentially probe the existence of extra dimensions.

Figures (5)

• Figure 1: Plots of total energy flux ($\mathcal{F}$) as a function of orbital radius ($\hat{r}$) for distinct values of $Q$.
• Figure 2: Plots for the change of inspiralling phase of the secondary over time for different values of $Q$.
• Figure 3: Change in GW phase ($\Delta\Phi^{\text{end}}_{\text{GW}}$) at the ISCO for different values of the tidal charge $Q$.
• Figure 4: Gravitational wave signal from the inspiral of a $30~M_\odot$ compact object into a supermassive black hole of mass $10^6~M_\odot$ for $Q=10^{-2}$ (top panel) and $Q=10^{-4}$ (botom panel). We consider the inspiral starts at $2r^{\textrm{ISCO}}$ and ends when the compact object reaches $r^{\textrm{ISCO}}$ (beyond this point, adiabatic approximation breaks down). In each panel, the leftmost plot depicts the waveform $(D/\mu)h_+$ over the whole inspiral period, where $D$ is the luminosity distance from the source to the detector, and $\mu$ is the mass of the compact object. The plots in the middle represent the waveform for the first 15 days since the start of the inspiral, whereas the rightmost plots depict the same for the last 15 days of the inspiral.
• Figure 5: The mismatch between the gravitational waveform originating from an EMRI system with primary object described by $M=10^{6}M_{\odot}$ and secondary with $\mu=30 M_{\odot}$.