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Extending the sensitivity of terrestrial gravitational-wave detectors below 20 Hz is a long-standing challenge, limited by ground motion and inertial sensing noise. In this Letter, we demonstrate ultra-high-vacuum compatible inertial isolation and position sensing technologies that achieve active platform stabilization down to 10 mHz. Our laser position sensors reach a <inline-formula><mml:math><mml:mrow><mml:mi>sub</mml:mi><mml:mtext>-</mml:mtext><mml:mi>pm</mml:mi><mml:mo>/</mml:mo><mml:msqrt><mml:mrow><mml:mi>Hz</mml:mi></mml:mrow></mml:msqrt></mml:mrow></mml:math></inline-formula> sensitivity above 10 mHz, independent of the input light polarization, representing a 100-fold improvement over the current LIGO position sensors. In addition, our inertial sensors provide at least a factor of 5 improvement in low-frequency sensitivity compared to state-of-the-art commercial seismometers. We integrate these technologies into a LIGO-like interferometer model and predict a low-frequency sensitivity improvement of up to an order of magnitude at 10 Hz, with enhanced linearity and calibration stability. This extension increases the detection horizon for intermediate-mass black hole binaries of mass <inline-formula><mml:math><mml:mrow><mml:msup><mml:mrow><mml:mn>10</mml:mn></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup><mml:msub><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mo>⊙</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> by a factor of 3 and increases the SNR for all lower mass binaries. Our results provide the first experimental demonstration of a practical pathway to sub-10 Hz operation of terrestrial gravitational-wave detectors and establish key technologies for next-generation observatories such as Cosmic Explorer and Einstein Telescope.

Finding intermediate-mass black holes (IMBHs) and measuring their masses and spins are key to understanding massive black hole formation. White dwarf (WD)-IMBH binaries provide a unique probe because they emit both electromagnetic radiation and gravitational waves (GWs), thereby conveying richer information. However, such multimessenger sources often enter the regime of strong gravity, where existing models often fail to capture their relativistic dynamics. Here, we develop a fully relativistic model for the tidal response of a WD close to an IMBH, and use it to study the secular orbital evolution as well as the GW signal. We find that for IMBHs more massive than <inline-formula><mml:math><mml:msup><mml:mn>10</mml:mn><mml:mn>5</mml:mn></mml:msup><mml:msub><mml:mi>M</mml:mi><mml:mo>⊙</mml:mo></mml:msub></mml:math></inline-formula>, tidal interaction becomes relativistic and sensitive to IMBH spin. The interaction generally dissipates binary orbital energy and angular momentum, but due to relativistic frame rotation, which reduces phase coherence across pericenter passages, the orbit-averaged tidal dissipation rate can be suppressed by up to <inline-formula><mml:math><mml:mo>∼</mml:mo><mml:mn>50</mml:mn><mml:mo>%</mml:mo></mml:math></inline-formula> relative to Newtonian predictions. Including tidal dissipation leads to more rapid damping of the orbital eccentricity, to the extent that the pericenter distance may even increase over time, potentially explaining quasiperiodic eruptions and secular orbital period growth. Such tidal effect accumulates into measurable phase and amplitude deviations in the GW signal. For typical space-based observations, the GW waveform mismatch can reach <inline-formula><mml:math><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mn>0.1</mml:mn><mml:mo>)</mml:mo></mml:math></inline-formula> within six months. Our results indicate that relativistic tidal dissipation is both dynamically important and observationally essential for reliably predicting the multimessenger signals of WD-IMBH systems.

The gravitational wave <inline-formula><mml:math><mml:mi>ω</mml:mi></mml:math></inline-formula> mode spectrum presents a unique window into the dense interior of neutron stars, probing physics inaccessible to electromagnetic observations. This work investigates the <inline-formula><mml:math><mml:mi>ω</mml:mi></mml:math></inline-formula> modes of compact stars composed of quarkyonic matter. The quarkyonic model, which describes a crossover transition between nucleonic and quark matter treated as quasiparticles, is formulated within the relativistic mean-field (RMF) theory using the G3 and IOPB-I parametrizations. This core is surrounded by a mantle of hadronic matter, creating a multicomponent stellar interior. The overall equation of state (EOS) is governed by two key parameters: the transition density (<inline-formula><mml:math><mml:msub><mml:mi>n</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:math></inline-formula>), and the QCD confinement scale (<inline-formula><mml:math><mml:msub><mml:mi>Λ</mml:mi><mml:mrow><mml:mi>cs</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>), which are varied to construct models consistent with current astrophysical constraints on mass and radius. We compute the complex eigenfrequencies (damped oscillations) of the fundamental and first excited <inline-formula><mml:math><mml:mi>ω</mml:mi></mml:math></inline-formula> modes using the phase-amplitude method within a full general relativistic framework. Our simulations reveal that the admixed quarkyonic structure produces a unique <inline-formula><mml:math><mml:mi>ω</mml:mi></mml:math></inline-formula> mode signature, distinctly different from pure hadronic or hybrid stars. The spectrum exhibits a strong, degenerate dependence on the EOS, where the stiffening effect of the quarkyonic matter influences oscillation frequencies and damping times in a characteristic manner. We also demonstrate that <inline-formula><mml:math><mml:mi>ω</mml:mi></mml:math></inline-formula> mode frequencies for quarkyonic stars follow approximate universal relations, largely independent of the EOS.