Ultracompact Configurations

• Ultracompact configurations are systems exhibiting extreme spatial compactness, marked by light rings in astrophysical objects and subwavelength integration in photonic devices.
• In astrophysics, these configurations include horizonless stars, gravastars, and boson stars whose light ring dynamics and vanishing tidal Love numbers serve as probes of strong-field gravity.
• In photonics, ultracompact devices leverage advanced mode engineering and plasmonic effects to achieve dense integration and high performance in subwavelength footprints.

Ultracompact configurations are astrophysical or engineered systems exhibiting maximal spatial compactness subject to their physical constraints, typically characterized by the presence of trapping regions for electromagnetic or gravitational energy, critical compactness parameters, or deeply subwavelength confinement in photonic devices. In astrophysics, the ultracompact regime refers to self-gravitating objects whose external spacetime admits circular photon orbits (light rings) and is associated with black holes, horizonless stars, gravastars, and exotic alternatives. In photonics, ultracompact devices leverage advanced mode engineering, plasmonic effects, and tight waveguide separation to achieve dense integration well below canonical wavelength-limited footprints.

1. Astrophysical Definition and Classification

An ultracompact object (UCO) in general relativity is defined as a self-gravitating, horizonless configuration whose external spacetime admits a circular photon orbit, or light ring (Cardoso et al., 2014). For static, spherically symmetric metrics,

$ds^2=-f(r)dt^2+B(r)dr^2+r^2d\Omega^2,$

radial null geodesics are trapped at radius $r_{\rm LR}$ where $d/dr[f(r)/r^2]=0$. The stability of these orbits classifies them as unstable (Schwarzschild photon sphere) or stable (possible only with ultracompact matter distributions) (Cardoso et al., 2014, Fonseca et al., 24 Dec 2025).

Distinct classes include:

• Constant-density Schwarzschild stars extended beyond the Buchdahl bound.
• Gravastars with de Sitter interiors and thin shells (Cardoso et al., 2014).
• Boson stars and anisotropic stars with modified pressure profiles (Raposo et al., 2018, Marks et al., 24 Apr 2025).
• Particle-like solutions in Einstein-scalar-Gauss-Bonnet theories (Kleihaus et al., 2019).
• Ultracompact Schwarzschild stars with vanishing tidal Love numbers in the black-hole limit (Posada, 2021).

Ultracompactness is typically quantified by a critical compactness $C = M/R$, where for Schwarzschild black holes $C = 1/2$ and the Buchdahl limit for isotropic stars is $C = 4/9$.

2. Formation Conditions and Stability Criteria

The structural equations for equilibrium and stability vary depending on the exact framework:

• For isotropic and anisotropic stars, the equilibrium is governed by the Tolman–Oppenheimer–Volkoff (TOV) equation, modified to include tangential pressures or scalar/vector fields (Raposo et al., 2018, Tasinato, 2022).
• Ultracompact minihalos (UCMHs) form in cosmology via collapse of large primordial density fluctuations; self-similarity and isolation were once thought to guarantee an $r^{-9/4}$ density profile, yet $N$-body simulations reveal shallower inner profiles ($r^{-3/2}$ or $r^{-1}$) when initial conditions are Gaussian (Delos et al., 2017).

Stability analyses encompass:

• Linear radial-mode spectra via Sturm–Liouville eigenproblems, locating stability thresholds at maximal mass points (Raposo et al., 2018, Marks et al., 24 Apr 2025).
• Nonlinear time-evolution via 1+1 and 3+1 hydrodynamic and relativity simulations, testing stability against fragmentation, ergoregion instabilities, and gravitational-wave echo formation (Marks et al., 24 Apr 2025, Cardoso et al., 2014).

Configurations with anisotropic stress or non-standard equations of state can evade the Buchdahl bound and approach $C \to 1/2$ while maintaining stability under certain conditions (Raposo et al., 2018, Tasinato, 2022).

3. Geodesic Structure, Light Rings, and Echoes

The existence of light rings is a hallmark of ultracompactness. Geodesic analysis shows the formation of both unstable and stable circular photon orbits in sufficiently compact objects. For spherically symmetric spacetimes with dense matter shells (e.g., Hernquist, NFW, Jaffe profiles), increasing compactness $C$ leads to the emergence of double-well potentials for null rays, extra light rings, and even secondary horizons (Fonseca et al., 24 Dec 2025).

These trapping regions support long-lived modes, echo-like gravitational-wave signals, and can produce quasi-normal mode spectra modulated by multiple potential barriers (Rosato et al., 27 Jan 2025, Kleihaus et al., 2019). Time-domain studies highlight that echoes are governed not by low-frequency QNMs, but by high-frequency quasi-reflectionless scattering modes, with observable effects in ringdown signals and echo timings set by the round-trip travel time between potential barriers (Rosato et al., 27 Jan 2025, Cardoso et al., 2014).

4. Tidal Love Numbers and Black-Hole Mimicry

The tidal deformability of ultracompact configurations is a sensitive diagnostic of their true nature. Tidal Love numbers $k_2$ for black holes vanish identically; for horizonless ultracompact Schwarzschild stars, $k_2$ decays exponentially with increasing compactness, approaching zero at $C\to1/2$, thereby mimicking black hole behavior with extreme fidelity (Posada, 2021, Raposo et al., 2018). Anisotropic models also exhibit rapidly vanishing $k_2$ in the black-hole limit, with scaling $k_2\propto (\Delta/M)^n$ as $\Delta\equiv R-2M\to0$ (Raposo et al., 2018). This exponential suppression renders tidal measurements ineffective in distinguishing ultracompact black-hole mimickers from genuine event horizons for $k_2\lesssim10^{-6}$ (Posada, 2021).

5. Photonic and Plasmonic Ultracompact Devices

Ultracompactness in photonic systems entails engineering components at or below the wavelength scale with minimal losses and maximal functional density. Recent advances include:

• Hybrid photonic-plasmonic light concentrators using nano-tapered metal structures on dielectric waveguides, achieving field concentration factors (FCF) of up to 13 in sub-micron devices (Luo et al., 2012).
• Branchless plasmonic interferometers leveraging parallel slot waveguides and compact antenna couplers, yielding $>$15% coupling efficiency within a footprint of $\sim \lambda_0\times$(sub-$\lambda_0$) (Thomaschewski et al., 2018).
• Photonic chips with closely spaced waveguides ($s\simeq \lambda_0/6$), using higher-order guided modes to suppress crosstalk and shrink circuit footprint by $2\times$–$5\times$ while sustaining low insertion losses and vanishing crosstalk (Yousry et al., 7 Aug 2025).
• Ultracompact optical circulators based on nonreciprocal magneto-photonic annular Bragg cavities, providing $20$-dB isolation within $(10\lambda)^2$ with strong robustness to fabrication imperfections (Śmigaj et al., 2011).
• Open-path high-$Q$ whispering gallery mode microresonators utilizing spatial mode multiplexing for photon recycling, achieving $Q=1.78\times10^5$ in a footprint $0.00137$ mm$^2$ ($6\times$ smaller than conventional microrings) (Xiong et al., 15 Oct 2025).

A concise comparative table appears below:

Device Type	Key Feature	Typical Footprint
Plasmonic light concentrator	FCF$\sim$13, $L<1\mathrm{\mu m}$	$<1\mathrm{\mu m}$
Branchless interferometer	$>$15% coupling, no bends	$<\lambda_0\times 8\mathrm{\mu m}$
Higher-order mode PICs	Crosstalk-free at $s\sim\lambda_0/6$	$2\times$–$5\times$ reduction
Magneto-photonic circulator	$20$-dB isolation, $130$GHz BW	$(10\lambda_0)^2$
Open-path WGMR	$Q\sim1.8\times10^5$, $FSR\sim1$nm	$0.0014$ mm$^2$

Photonic and plasmonic ultracompact configurations exploit symmetry, adiabatic field compression, spatial mode multiplexing, and advanced coupling architectures to achieve dense integration with robust performance.

6. Formation Mechanisms and Physical Implications

Formation of ultracompact configurations in astrophysics arises from extreme gravitational collapse, non-standard equations of state, high central densities, or strong anisotropic stresses. For UCMHs in cosmology, collapse of large primordial fluctuations was originally thought to produce extremely steep density cusps ($r^{-9/4}$), but simulations show that realistic Gaussian initial conditions cannot supply the required self-similar collapse (Delos et al., 2017). As a result, gamma-ray indirect detection bounds must be revised downward, although inclusion of later-forming halos can strengthen overall constraints on the primordial power spectrum.

In massive star formation, ultracompact HII regions result from rapid accretion and disk fragmentation, where secondary sinks intercept material and set the timescale for HII-region longevity to be the accretion duration, not the internal sound crossing time (Klessen et al., 2010).

The presence of light rings generically triggers potential nonlinear instabilities or fragmentation, undermining the long-term viability of horizonless ultracompact stars unless unrealistic dissipation occurs (Cardoso et al., 2014). In contrast, solitonic boson stars can retain long-term nonlinear stability on certain branches, confirming their status as black-hole mimickers (Marks et al., 24 Apr 2025).

7. Theoretical Frontiers and Observational Signatures

Ultracompact horizonless configurations are now recognized as critical laboratories for probing the limits of general relativity, quantum gravity, and exotic matter. Theories including vector-tensor gravity and higher-curvature couplings (e.g., Einstein-scalar-Gauss-Bonnet) admit globally regular, ultracompact particle-like solutions with nontrivial multipole responses and echo signals (Kleihaus et al., 2019, Tasinato, 2022). Gravitational-wave echoes, exponentially suppressed tidal Love numbers, reflectionless scattering modes, and echo-driven spectral modulations are promising observational signatures for distinguishing ultracompact objects from true black holes (Rosato et al., 27 Jan 2025, Posada, 2021).

Photonic systems continue to push ultracompactness to practical limits via advanced mode engineering and tolerance-robust device architectures, foundational for next-generation integration in information processing, sensing, and quantum technologies (Luo et al., 2012, Xiong et al., 15 Oct 2025, Yousry et al., 7 Aug 2025).

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In summary, ultracompact configurations embody the intersection of extreme physical confinement, nontrivial geodesic and wave properties, advanced mode engineering, and stability analysis across both relativistic astrophysics and photonic technologies. Their classification, formation, and observable signatures underpin ongoing efforts in strong-field tests, dark-matter constraints, compact-object astrophysics, and nanophotonic device science.