Gravitational-Wave Signature of an Inspiral into a Supermassive Horizonless Object

TL;DR

The paper investigates whether gravitational waves from extreme-mass-ratio inspirals can reveal event horizons by contrasting a Schwarzschild black hole with a horizonless supermassive boson star (SMBS) whose exterior spacetime matches Schwarzschild but interior differs. It models the central object as a spherically symmetric soliton formed from a complex scalar field and simulates the inspiral of a stellar-mass compact object in the extreme mass ratio limit, using a hybrid quadrupole approach to compute gravitational radiation. A two-stage evolution scheme evolves orbital elements and then reconstructs the real-space trajectory to generate waveforms, with interior geometry supporting stable geodesics and a two-step plunge that imprints distinctive interior-driven features on the waveform. The results indicate that post-plunge gravitational radiation persists for horizonless interiors, including abrupt eccentricity growth and interior-driven modulations, offering a potential observable discriminant for LISA, though the waveforms are presently approximate and call for refinement via higher multipoles and full perturbative treatments.

Abstract

Event horizons are among the most intriguing of general relativity's predictions. Although on firm theoretical footing, direct indications of their existence have yet to be observed. With this motivation in mind, we explore here the possibility of finding a signature for event horizons in the gravitational waves (GWs) produced during the inspiral of stellar-mass compact objects (COs) into the supermassive ($\sim 10^6 M_\odot$) objects that lie at the center of most galaxies. Such inspirals will be a major source for LISA, the future space-based GW observatory. We contrast supermassive black holes with models in which the central object is a supermassive boson star (SMBS). Provided the COs interact only gravitationally with the SMBS, stable orbits exist not just outside the Schwarzschild radius but also inside the surface of the SMBS as well. The absence of an event horizon allows GWs from these orbits to be observed. Here we solve for the metric in the interior of a fairly generic class of SMBS and evolve the trajectory of an inspiraling CO from the Schwarzschild exterior through the plunge into the exotic SMBS interior. We calculate the approximate waveforms for GWs emitted during this inspiral. Geodesics within the SMBS surface will exhibit extreme pericenter precession and other features making the emitted GWs readily distinguishable from those emitted during an inspiral into a black hole.

Figures (9)

• Figure 1: The metric functions $e^{2u(r)}$ and $e^{2\bar{v}(r)}$ as functions of radius. The solid curves correspond to a boson star with $R = 2.869 M$ while the the dashed curves are for a black hole of the same mass. Outside the boson-star surface the two curves are identical, while for $r < R$ the solid curves are a numerical solution to Eq. (\ref{['E:metODE']}) and the dashed curves are the Schwarzschild metric functions $e^{2u(r)} = (1 - 2GM/r)$, $e^{2\bar{v}(r)} = (1 - 2GM/r)^{-1}$.
• Figure 2: The effective potential $V(r)$ of the boson star for three different values of the angular momentum. The solid, short-dashed, and long-dashed curves have $L^2 = 24 M^2$, $18 M^2$, and $12 M^2$ respectively. The large black dots on each curve show the location of the outer minimum. For $L^2 = 12 M^2$, the lowest angular momentum for which there are two minima, the black dot is located at the innermost stable circular orbit $r = 6M$.
• Figure 3: The phase-space trajectories $\{ p(t), e(t) \}$ for three different EMRIs into a supermassive boson star. The solid, dashed, and dotted curves begin with eccentricities $e_0 = 0.8$, 0.4, and 0.0 respectively. The top panel shows the complete EMRI from $p_0/M = 10.0$, while the lower panel is a close-up of the post-plunge phase of the EMRI that appears in the upper-left corner of the top panel. In both panels time increases from right to left as $p/M$ decreases monotonically.
• Figure 4: The phase-space trajectories $\{ L(t), E(t) \}$ for the three EMRIs depicted in Fig. \ref{['F:pe']}. As before, the solid, dashed, and dotted curves begin with eccentricities $e_0 = 0.8$, 0.4, and 0.0 respectively. The large black dots correspond to the points at which the COs plunge into the boson star. Note that the curves cross each other, implying that two different geodesics can be characterized by the same energy and angular momentum. This feature, unique to the boson-star case, follows from the existence of bound geodesics both interior and exterior to the local maximum of the effective potential for certain energy and angular momenta. No such crossing appear in Fig. \ref{['F:pe']} as $p$ and $e$ do uniquely specify a given geodesic.
• Figure 5: The real-space trajectory $\{ x(t), y(t) \}$ for an initially circular EMRI. For purposes of clarity, only a period of approximately 150,000 s in the vicinity of the plunge is depicted.