Tidal disruption of a neutron star near naked singularity

We investigate the tidal disruption of a neutron star (NS) near a black hole (BH), and for the first time, to the best of our knowledge, near a naked singularity (NaS). For a BH with a mass greater than about $10 M_{\odot}$, the tidal disruption of NS should occur within the event horizon, and hence neither can the stellar material escape nor a distant observer observe the disruption. Since NaS does not have an event horizon, a significant portion of the NS’s material can escape, and the tidal disruption can be observed by a distant observer. One could identify such an event from the observed emission from the disrupted NS’s material and the decay of the light curve of the disruption event. The escape of a significant fraction of the NS’s material may also have implications for the heavy elements in the universe. Moreover, observing such an event can be useful for confirming a NaS, probing its spacetime, and studying the motion of matter in such a geometry. This may help constrain the NS parameters and equation of state models. As a first step in this direction, we calculate here the tidal disruption radius and other parameters for a specific type (Joshi-Malafarina-Narayan type 1) of NaS and compare our results with observations.

💡 Research Summary

This paper investigates the tidal disruption of a neutron star (NS) by a compact object, comparing the standard Schwarzschild black hole (BH) with a specific naked singularity (NaS) model, the Joshi‑Malafarina‑Narayan type‑1 (JMN1) spacetime. The authors begin by reviewing the Cosmic Censorship Conjecture and the motivation for distinguishing horizon‑less singularities from black holes through observable phenomena such as tidal disruption events (TDEs). They note that for BHs with masses above roughly 10 M⊙, the tidal disruption radius of a typical 1.4 M⊙, 15 km NS lies inside the event horizon, making the disruption invisible to distant observers. By contrast, a naked singularity lacks an event horizon, allowing a substantial fraction of the disrupted material to escape and become observable.

The theoretical framework uses a static, spherically symmetric metric ds² = –f(r)dt² + g(r)dr² + r²(dθ²+sin²θ dφ²). Conserved energy e and angular momentum h are introduced, leading to an effective potential V_eff = f(r)(1 + h²/r²). For radial geodesics (h = 0) the motion reduces to a simple equation involving f(r) and g(r). The tidal forces are derived from the geodesic deviation equation D²η/Dτ² = R·η, employing an orthonormal tetrad tied to a freely‑falling observer. The authors obtain explicit expressions for the radial and transverse tidal accelerations (equations 12 and 13) in terms of f, g and their derivatives. The extremum of the radial tidal force yields the tidal disruption radius r_t.

In the Schwarzschild case, r_t follows the familiar scaling r_t ≈ R_NS (M/M_NS)^{1/3}. For BH masses M ≳ 10 M⊙, r_t falls within the Schwarzschild radius 2GM/c², so the disruption is hidden. The JMN1 naked singularity metric has f(r) ∝ r^{2M₀/(1–M₀)} and g(r) ∝ r^{–2/(1–M₀)} with a compactness parameter M₀ (0 < M₀ < 2/3). The authors show that for realistic values of M₀ the tidal radius lies outside the singularity, allowing debris to escape. Figure 1b illustrates how r_t depends sensitively on M₀, and the authors discuss three illustrative density thresholds (R_b1, R_b2, R_b3) corresponding to different values of the central pressure.

Observational implications are explored in two main aspects. First, the escaping material can produce electromagnetic signatures (optical, UV, X‑ray, γ‑ray) and undergo r‑process nucleosynthesis, potentially contributing to the galactic inventory of heavy elements such as gold and platinum. Because there is no horizon to trap radiation, the radiative efficiency could approach 100 % in principle, far exceeding the ∼5.7 % efficiency of a Schwarzschild BH accretion flow. Second, the fallback rate of bound debris is expected to follow the canonical t^{–5/3} law, but partial disruptions may yield alternative power‑law indices (e.g., t^{–9/4}), providing a diagnostic of the disruption geometry. Light‑curve decay and spectral evolution could thus be used to infer the presence of a naked singularity and to constrain the NS equation of state.

The paper acknowledges several limitations. The neutron star is treated as a point mass with a fixed radius, neglecting realistic internal structure, rotation, magnetic fields, and tidal deformation prior to disruption. Only the JMN1 model is examined; other naked‑singularity solutions (e.g., rotating or non‑self‑similar spacetimes) are not considered. Hydrodynamic effects such as shock formation, disk creation, and radiative transfer are omitted, so the predicted electromagnetic signatures are highly idealized. The compactness parameter M₀ is not linked to any astrophysical formation scenario, leaving the plausibility of a JMN1 naked singularity in nature uncertain. Finally, no numerical simulations or detailed spectral modeling are presented, limiting direct comparison with existing TDE observations.

Future work suggested includes (i) fully relativistic hydrodynamic simulations of NS tidal disruption in both BH and NaS spacetimes, (ii) incorporation of realistic NS equations of state, spin, and magnetic fields, (iii) exploration of a broader class of naked‑singularity metrics, (iv) quantitative modeling of light curves, spectra, and nucleosynthetic yields, and (v) coordinated multi‑messenger observations (optical/UV/X‑ray surveys such as ZTF, LSST, eROSITA together with gravitational‑wave detectors) to search for the distinctive signatures predicted for naked‑singularity TDEs. Such studies could provide empirical tests of the Cosmic Censorship Conjecture, improve our understanding of heavy‑element production, and open a new observational window onto horizon‑less compact objects.