Noble Gravitational Atoms

• Noble gravitational atoms are quantum gravitational bound states where gauge-neutral constituents interact exclusively via gravity, ensuring maximum stability.
• They display hydrogenic spectral properties with discrete energy levels derived from quantum Newtonian gravity and black hole–scalar field analogies.
• Their realizations, from dark-sector particles to black hole clouds and topological stars, offer testable insights into quantum gravity and modified theories.

A noble gravitational atom is a quantum gravitational bound state in which the constituent particles or fields possess maximal inertness—i.e., they carry no non-gravitational charges and interact solely through gravity. This concept generalizes the idea of "noble" atoms (with filled electronic shells and minimal external interactions) to gravitationally bound quantum systems, comprising both particle-particle and black hole–scalar field systems. Noble gravitational atoms arise in several settings: (1) two massive, gauge-neutral particles held by quantum Newtonian gravity; (2) bound states of quantum fields and massive astrophysical objects (black holes, neutron stars, topological solitons); and (3) gravitational bound states in modified or higher-dimensional gravity theories. Across these realizations, the defining feature is the predominance—or exclusivity—of gravitational binding, resulting in highly stable, discrete spectra with negligibly small decay rates or environmental broadening.

1. Theoretical Foundations and Definitions

The archetype of a noble gravitational atom is a two-body bound state where each particle is massive, gauge-neutral, and interacts through Newtonian gravity. The gravitational fine-structure constant is defined by

$$\alpha_G = \frac{G_N m_X^2}{\hbar c} = \left(\frac{m_X}{m_p}\right)^2$$

where $m_X$ is the constituent mass and $m_p$ the Planck mass. For two identical constituents, the Bohr radius is

$a_0 = \frac{2\hbar m_p^2}{m_X^3 c}$

and the energy spectrum is

$$E_n = -\frac{m_X c^2}{4 n^2} \left(\frac{m_X}{m_p}\right)^4$$

where $n$ is the principal quantum number. The "noble" qualifier signifies that no other fundamental force competes with gravity, ensuring maximal longevity and quantum purity (Nielsen et al., 2019).

In black hole and field contexts, a noble gravitational atom refers to a stationary, typically spherically symmetric, bound configuration of a massive, complex scalar (or other bosonic) field around an isolated or horizonless compact object, with mode structure and energy splitting analogous to atomic physics (Alcubierre et al., 27 Nov 2024, Alcubierre et al., 8 Dec 2025, Rocca et al., 17 Nov 2025).

2. Spectral Properties and Stability Mechanisms

The bound-state spectra are hydrogenic for small gravitational couplings. For a scalar field of mass $\mu$ bound to a central mass $M$, the spectrum is

$$\omega_{n\ell} \simeq \mu \left(1 - \frac{(\mu M)^2}{(\ell+n)^2}\right)$$

for $\mu M \ll 1$, with total angular momentum $\ell$. Lifetimes for the lowest states satisfy

$t_0 = 1/|\Im \omega| \gg t_{\text{Hubble}}$

except for high $\alpha_G$, where absorption into the black hole horizon can shorten the lifetime (Alcubierre et al., 27 Nov 2024). For extreme dilatonic black holes, the horizon forms an infinite barrier, yielding truly stationary modes ($\Im \omega = 0$); all probability flux is reflected, so cloud particles never penetrate the horizon, achieving perfect spectral sharpness and stability (Huang et al., 2022). In horizonless topological stars, perfectly reflecting boundary conditions also ensure strictly normal spectra ($\Im \omega = 0$), with level structures controlled by the Compton/deformation length of the field compared to the star size (Bah et al., 13 Nov 2025).

For multi-field configurations (e.g., $2\ell+1$ fields with definite $\ell$), assembling all angular modes yields spherically symmetric composite states—direct gravitational analogues to noble atoms with filled shells in atomic physics (Alcubierre et al., 8 Dec 2025, Tomaselli, 17 Dec 2024).

3. Astrophysical and Laboratory Realizations

Noble gravitational atoms are realized across energy hierarchy and scale:

• Super-Planckian dark matter: Massive, gauge-neutral dark-sector particles may form gravitational atoms after reheating, with cosmologically extended lifetimes, suppressed decay via gravitational wave emission, and unobservable GW frequency in minimal models ($\nu \gtrsim 10^{13}$ Hz) (Nielsen et al., 2019). Early matter-dominated cosmologies or nonminimal couplings can modestly lower observable frequencies to $\sim 10^7–10^{10}$ Hz.
• Compact objects and quantum field clouds: Scalar fields in quasi-bound states around Schwarzschild or Kerr black holes form extended, stable clouds ("wigs") with spectra matching the hydrogenic model (Alcubierre et al., 27 Nov 2024, Tomaselli, 17 Dec 2024, Alcubierre et al., 8 Dec 2025). These gravitational atoms persist for cosmological times if $\alpha_G = M \mu \lesssim 0.2$.
• Black holes with infinite horizon barriers: The GMGHS dilatonic black hole admits exact, perfectly stable exterior clouds, with quantized spectra and zero-entropy horizons, making it the strictest realization of the atomic analogy (Huang et al., 2022).
• Topological stars: Five-dimensional horizonless solitonic stars bound charged or neutral scalars in regular normal modes distinguishable from black-hole quasi-bound states, with precisely normal spectra free of dissipative broadening (Bah et al., 13 Nov 2025).
• Quantum states of neutral atoms above surfaces: Gravitational quantum states (GQS) of hydrogen, helium, and heavier atoms above mirror surfaces exploit the Airy function spectrum of a linear gravitational potential, with energy levels

$$E_n = \bigl( \hbar^2 g^2 m / 2 \bigr)^{1/3} \alpha_n$$

where $\alpha_n$ are zeros of the Airy function. Helium GQS on a cold neutron star surface, with transitions in the GHz range, represent a concrete laboratory for noble gravitational atom spectroscopy (Killian et al., 2023, Dalkarov et al., 2015).

4. Spectroscopic Signatures and Observational Prospects

Gravitational atom transitions can produce monochromatic gravitational waves or electromagnetic lines corresponding to quantum-level spacings.

• Dark sector atoms: Decay of primordial gravitational atoms yields GW lines at ultra-high frequencies ($\nu \gtrsim 10^{13}\,\rm Hz$) or, in non-standard cosmologies, at lower accessible frequencies. Detection below the minimal frequency threshold ($\sim10^{13}$ Hz) would indicate a deviation from Einstein gravity or early matter domination (Nielsen et al., 2019).
• Black hole gravitational atoms: Superradiant clouds yield discrete graviton emission or, for a binary perturber, resonant transitions and "ionization" effects, with floating orbits and sharp GW signatures (Tomaselli, 17 Dec 2024). The analogy extends to selection rules, shell filling, and transition suppression for filled multiplets—configurations of maximal stability ("noble gravitational atoms") (Alcubierre et al., 8 Dec 2025, Tomaselli, 17 Dec 2024).
• Spectroscopy in laboratory or astrophysical systems: Transitions between GQS of helium on neutron stars produce magnetic-dipole lines in the GHz range; the narrowness of these lines is dictated by the lack of electric-dipole transitions in noble atoms (Dalkarov et al., 2015). In macroscopic black hole–field atoms, shifts in gravitational quasinormal mode frequencies are proportional to the compactness of the atom, $\delta \Upsilon_R \simeq a C$ (with $a\sim 5$), and are in principle detectable by current and next-generation GW detectors for compactness $C \gtrsim 10^{-3}$ (Rocca et al., 17 Nov 2025).

5. Effects of Extra Dimensions and Modified Gravity

Noble gravitational atoms are sensitive probes for physics beyond standard gravity. Compactified extra dimensions introduce Yukawa-type corrections to the Newtonian potential,

$$V(r) = -G_N \frac{M m}{r} \Bigl[1 + \alpha e^{-r/\lambda}\Bigr]$$

with $\alpha=2n$ and $\lambda = R_C$ (compactification radius). The energy spectrum experiences $\mathcal{O}(g^2)$ shifts, where $g = 2R_C/a_G$ (Floratos et al., 2010). Laboratory sensitivity to these spectral deviations is possible with neutron or atom interferometry and microfabricated test masses.

The infinite horizon barrier in extreme dilatonic black holes, as well as the zero Wald entropy, offer deep insight into how string-theoretic or modified-gravity objects realize genuine atomic stability in a gravitational context (Huang et al., 2022).

6. Classification, "Nobility," and Generalizations

The "nobility" of a gravitational atom is operationalized by spectral purity (quasi-normal vs normal modes), stability (lifetime vastly exceeding relevant external dynamical scales), and isolation from environmental/dissipative broadening. In the black hole–field context, spherically symmetric, multi-$m$ field configurations realize the maximal atomic analogy, with closed shells preventing lowest-order transitions and ensuring maximally suppressed decay (Alcubierre et al., 8 Dec 2025, Tomaselli, 17 Dec 2024). Table 1 displays key classes of noble gravitational atoms:

Realization	Key Features	Relevant References
Dark-sector two-body atom	Gauge-neutral particles, GW/CR signatures, Planckian physics probe	(Nielsen et al., 2019)
Black hole–scalar cloud	Hydrogenic/quasi-normal spectra, cosmological lifetimes	(Alcubierre et al., 27 Nov 2024, Alcubierre et al., 8 Dec 2025, Rocca et al., 17 Nov 2025)
Extreme GMGHS hole	Exact normal modes, perfect spectral purity, zero-entropy horizon	(Huang et al., 2022)
Topological star	Horizonless, normal spectra, Kaluza-Klein modes	(Bah et al., 13 Nov 2025)
Atom above surface/heavy star	Airy-spectrum, spectroscopically resolved gravitational quantum states	(Killian et al., 2023, Dalkarov et al., 2015)

The filling of complete angular momentum shells, the exclusive presence of gravitational binding, and the inability of environmental couplings to induce rapid decay collectively define the noble gravitational atom class.

7. Implications, Open Directions, and Experimental Opportunities

Noble gravitational atoms serve as high-fidelity laboratories for probing quantum aspects of gravity, Planck-scale physics, the nature of dark matter, and the structure of extra dimensions. The detection of narrow GW lines, or tiny frequency shifts in gravitational quasinormal modes following merger events, would provide direct evidence for quantum gravitational bound state structure (Rocca et al., 17 Nov 2025). Ongoing laboratory efforts (e.g., GRASIAN, neutron GQS, cold atom interferometry) are rapidly extending the quantum regime probed by atomic-scale noble gravitational atoms (Killian et al., 2023, Floratos et al., 2010). Astrophysical searches (e.g., for ultra-high-energy cosmic rays, anomalous GW lines, or dark matter–galaxy core profiles) constrain and inform the landscape of possible gravitational atom realizations.

The classification and analysis of noble gravitational atoms underscore a convergence of methods across quantum field theory, general relativity, atomic physics, and astrophysical observation, establishing this subject as a precise and richly structured probe of fundamental gravitational phenomena.