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arxiv: 2606.06884 · v1 · pith:VZT3U6CEnew · submitted 2026-06-05 · 🌌 astro-ph.HE · astro-ph.EP· astro-ph.SR· gr-qc

Tidal Disruption of Blanets in Kerr Spacetime

Shreesham Pandey , Sunita Singh This is my paper

Pith reviewed 2026-06-27 21:28 UTC · model grok-4.3

classification 🌌 astro-ph.HE astro-ph.EPastro-ph.SRgr-qc
keywords blanetstidal disruption eventsKerr spacetimesupermassive black holesactive galactic nucleifallback rateHills massorbital stability
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The pith

Blanets can produce observable tidal disruptions around supermassive black holes up to 10 billion solar masses.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper calculates tidal disruption events for blanets, planetary-mass objects between 20 and 3000 Earth masses, that orbit supermassive black holes in active galactic nuclei. It shows these events remain detectable for black holes as large as 10^10 solar masses, well beyond the limit for ordinary stars. The material fallback rate follows the familiar t to the minus five-thirds power law, yet the peaks arrive on shorter timescales ranging from hours to months and produce lower accretion rates along with different multi-wavelength signatures. The analysis incorporates Kerr spacetime effects to adjust tidal radii, spin-dependent thresholds, and disruption geometry while also examining orbital stability under precession, migration, and Kozai-Lidov resonance. Gravitational-wave emission from the resulting debris is discussed as a possible LISA signal.

Core claim

Using the geodesic deviation equation and the Kerr tidal tensor, the authors derive disruption criteria and Hills masses showing that blanet TDEs can remain observable for SMBHs up to approximately 10^10 solar masses. The fallback rate retains the t^{-5/3} form, but peak timescales shorten to hours or months with reduced peak accretion rates and multi-wavelength signatures distinct from stellar TDEs. Relativistic corrections to the tidal radius, spin-dependent thresholds, and the effect of black-hole spin on disruption geometry are obtained, together with orbital stability regions and prospects for gravitational-wave detection of blanet debris EMRIs.

What carries the argument

Geodesic deviation equation and Kerr tidal tensor applied to planetary-mass objects to obtain tidal radii and Hills masses.

If this is right

  • Blanet TDEs remain observable for SMBHs up to 10^10 solar masses.
  • Fallback follows the t^{-5/3} law with peak timescales from hours to months.
  • Peak accretion rates are lower and multi-wavelength signatures differ from stellar TDEs.
  • Relativistic corrections produce spin-dependent disruption thresholds and altered geometry.
  • Debris may emit gravitational waves detectable by LISA as EMRIs.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Unusual AGN transients with short-duration, low-luminosity flares could be reinterpreted as blanet rather than stellar disruptions.
  • Monitoring campaigns targeting AGN disks on hourly-to-monthly cadences could increase the yield of TDE detections at the highest black-hole masses.
  • Joint electromagnetic and gravitational-wave observations might independently constrain both black-hole spin and the mass distribution of objects in circumnuclear disks.
  • Kozai-Lidov and migration effects in dense disks could raise the overall rate of blanet disruptions relative to isolated orbits.

Load-bearing premise

Planetary-mass blanets can be modeled with the test-particle geodesic deviation equation and Kerr tidal tensor without corrections for self-gravity or internal structure.

What would settle it

An observed transient in an AGN showing a t^{-5/3} fallback curve with a peak timescale of days around a 10^9 solar-mass black hole whose luminosity and spectrum match a 100-Earth-mass object rather than a star.

Figures

Figures reproduced from arXiv: 2606.06884 by Shreesham Pandey, Sunita Singh.

Figure 1
Figure 1. Figure 1: Disruption scale for blanets and stars. (a) Tidal radius rt normalised to the Schwarzschild radius rs for four representative blanet masses, together with the stellar TDE reference case. The dotted line marks rt/rs = 1, below which disruption occurs inside the horizon. (b) Hills mass MHills BH as a function of blanet mass Mp for several planetary radii. More compact bodies survive to larger black-hole mass… view at source ↗
Figure 3
Figure 3. Figure 3: Orbital stability constraints for a representative 100 M⊕ blanet. (a) Stability map in the (r, MBH) plane. The blue region marks long-lived orbits; the red region corresponds to direct tidal disruption; the orange region indicates radii at which migration becomes dynamically important. (b) Characteristic timescales as functions of orbital radius for MBH = 107 M⊙ and Mp = 100 M⊕. blanet’s pericentre is driv… view at source ↗
Figure 4
Figure 4. Figure 4: compares the return times and fallback curves for blanets and stars. 5.3. Comparison with Stellar TDEs [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Relativistic orbital structure relevant to intact blanets and disrupted debris. (a) Schwarzschild effective potential Veff (r) for four angular momenta representative of blanet orbits. (b) Kerr ISCO radius as a function of spin for prograde and retrograde motion. Because intact blanets orbit at r ≫ rISCO, the ISCO is mainly relevant after disruption, when debris circularises and accretes in the inner relat… view at source ↗
read the original abstract

Blanets are planetary-mass bodies ($20$--$3000\,\Me$) that may orbit supermassive black holes (SMBHs) in the circumnuclear disks of active galactic nuclei (AGN). We examine tidal disruption events produced by blanet--SMBH encounters, from the test-particle limit to massive planetary bodies in Kerr spacetime. Using the geodesic deviation equation and the Kerr tidal tensor, we derive disruption criteria, tidal radii, and Hills masses for planetary-mass objects, and show that blanet TDEs can remain observable for SMBHs up to $\sim10^{10}\,\Msun$, well above the stellar Hills mass of $\sim10^8\,\Msun$. The fallback rate retains the usual $t^{-5/3}$ form, but the peak timescales are shorter -- from hours to months -- with lower peak accretion rates and multi-wavelength signatures that differ from those of stellar TDEs. We also examine orbital stability, including Keplerian precession, Lense--Thirring nodal precession, migration in the circumnuclear disk, and the Kozai--Lidov resonance, and identify the region where blanets can survive before disruption. We derive relativistic corrections to the tidal radius, spin-dependent disruption thresholds, and the effect of Kerr spin on the disruption geometry. We also discuss gravitational-wave emission from blanet debris EMRIs and the prospects for LISA detection, which may help in interpreting unusual TDE-like transients in AGN environments.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript examines tidal disruption events (TDEs) of blanets (planetary-mass bodies of 20--3000 M_E) by supermassive black holes in Kerr spacetime. It applies the geodesic deviation equation and Kerr tidal tensor to derive disruption criteria, tidal radii, and Hills masses, concluding that blanet TDEs remain observable for SMBHs up to ~10^{10} M_sun (well above the stellar Hills mass). The fallback rate follows the canonical t^{-5/3} form but with shorter peak timescales (hours to months), lower peak rates, and distinct multi-wavelength signatures. The work also analyzes orbital stability (including precession, migration, and Kozai-Lidov), relativistic corrections to the tidal radius, spin-dependent thresholds, and prospects for gravitational-wave emission from blanet-debris EMRIs detectable by LISA.

Significance. If the central derivations hold, the paper identifies a previously unexamined class of TDEs in AGN circumnuclear disks that could account for unusual transients and supply multi-messenger signals. The reported extension of the observable SMBH mass range by two orders of magnitude and the spin-dependent geometry corrections are potentially impactful for TDE demographics and LISA source modeling. The retention of the t^{-5/3} fallback while altering timescales and signatures provides concrete, falsifiable predictions.

major comments (2)
  1. [Abstract] Abstract: The claim that the geodesic deviation equation and Kerr tidal tensor are used to derive disruption criteria 'from the test-particle limit to massive planetary bodies' lacks any indication of finite-mass corrections for self-gravity or internal structure. This assumption is load-bearing for the headline result that blanet TDEs remain observable up to ~10^{10} M_sun, because the tidal radius and Hills mass for 20--3000 M_E objects are set by the Roche limit in the presence of self-gravity rather than the test-particle tidal tensor alone.
  2. [Derivation of disruption criteria and tidal radii] The section deriving spin-dependent disruption thresholds and relativistic corrections to the tidal radius: the quantitative extension beyond the stellar Hills mass rests on the same test-particle formalism without demonstrated validity for finite-mass bodies; a direct comparison to the Roche limit for the quoted mass range is required to secure the factor-of-100 increase in maximum SMBH mass.
minor comments (2)
  1. [Abstract] The abstract states that the fallback rate 'retains the usual t^{-5/3} form' but does not specify whether this is shown analytically or numerically for the blanet mass range; a brief equation or reference to the standard derivation would clarify.
  2. [Abstract] Notation for planetary masses (M_E) and solar masses (M_sun) should be defined consistently on first use; the abstract mixes Me and Msun without explicit definition.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough and constructive report. The comments correctly identify that our use of the geodesic deviation equation and Kerr tidal tensor requires explicit clarification regarding its extension from the test-particle limit to self-gravitating planetary-mass bodies. We address each point below and will revise the manuscript to include the requested comparisons and clarifications.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The claim that the geodesic deviation equation and Kerr tidal tensor are used to derive disruption criteria 'from the test-particle limit to massive planetary bodies' lacks any indication of finite-mass corrections for self-gravity or internal structure. This assumption is load-bearing for the headline result that blanet TDEs remain observable up to ~10^{10} M_sun, because the tidal radius and Hills mass for 20--3000 M_E objects are set by the Roche limit in the presence of self-gravity rather than the test-particle tidal tensor alone.

    Authors: We agree that the abstract phrasing is imprecise and does not adequately signal the role of self-gravity. The underlying derivation equates the tidal acceleration from the Kerr tidal tensor to the self-gravitational acceleration within the blanet (implicitly the Roche criterion for the adopted density), but this equivalence is not stated explicitly. In the revised manuscript we will rewrite the abstract to clarify the assumptions and note that finite-mass effects enter through the comparison of tidal forces to self-gravity. We will also add a short paragraph in the methods section that derives the disruption condition from first principles, showing where the test-particle tidal field is matched to the body's internal gravity. revision: yes

  2. Referee: [Derivation of disruption criteria and tidal radii] The section deriving spin-dependent disruption thresholds and relativistic corrections to the tidal radius: the quantitative extension beyond the stellar Hills mass rests on the same test-particle formalism without demonstrated validity for finite-mass bodies; a direct comparison to the Roche limit for the quoted mass range is required to secure the factor-of-100 increase in maximum SMBH mass.

    Authors: The referee is correct that an explicit side-by-side comparison with the classical Roche limit is needed to justify the reported extension of the observable SMBH mass range. While the geodesic-deviation approach recovers the Newtonian Roche limit for non-spinning cases when self-gravity is included, the manuscript does not demonstrate this equivalence numerically for the 20--3000 M_E range or discuss possible deviations arising from internal structure or relativistic corrections to self-gravity. We will add a dedicated subsection that (i) computes the Roche-limit tidal radius for the quoted mass and density range, (ii) overlays it on the Kerr-tensor results, and (iii) quantifies the fractional difference as a function of SMBH spin. This will directly address the factor-of-100 claim and will be referenced in the abstract revision. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivations from standard GR equations

full rationale

The paper applies the geodesic deviation equation and Kerr tidal tensor (standard GR constructs) to derive tidal radii, Hills masses, and fallback rates for blanets. No quoted steps reduce by construction to fitted inputs, self-citations, or renamed ansatze. The extension from test-particle limit is an explicit modeling choice rather than a definitional loop. The derivation chain remains self-contained against external GR benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claim rests on the postulated existence of blanets and the direct applicability of test-particle GR tidal formalism to finite-mass objects; no free parameters are explicitly fitted in the abstract, but the mass range and disk environment are assumed inputs.

axioms (2)
  • standard math The Kerr metric describes the spacetime around a rotating supermassive black hole.
    Invoked throughout for tidal tensor and precession calculations.
  • domain assumption Blanets with masses 20--3000 Earth masses exist and can maintain orbits in AGN circumnuclear disks until tidal encounter.
    Stated as the objects under study in the abstract.
invented entities (1)
  • Blanets no independent evidence
    purpose: Planetary-mass bodies that may orbit SMBHs in AGN disks and undergo TDEs
    Postulated objects whose existence is required for the claimed events; no independent evidence supplied.

pith-pipeline@v0.9.1-grok · 5804 in / 1724 out tokens · 28689 ms · 2026-06-27T21:28:24.887639+00:00 · methodology

discussion (0)

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Reference graph

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