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Hernquist dark matter halos around rotating black holes move the event horizon outward, lower Hawking temperature, and slow evaporation.

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2026-07-01 01:05 UTC pith:3FA4CAC7

load-bearing objection This paper uses the noncomplexification Newman-Janis algorithm on a static black hole in a Hernquist halo to generate a rotating metric and then runs the usual horizon, thermodynamic, and tunneling calculations. the 2 major comments →

arxiv 2606.30962 v1 pith:3FA4CAC7 submitted 2026-06-29 gr-qc hep-th

A rotating black hole in a Hernquist dark matter halo: horizon geometry, thermodynamics, and quantum emission

A. A. Ara\'ujo Filho , Arun Kumar , N. Heidari , C. F. S. Pereira , Amilcar R. Queiroz , V. B. Bezerra This is my paper
classification gr-qc hep-th
keywords rotating black holesHernquist halodark matterHawking radiationblack hole thermodynamicsNewman-Janis algorithmevent horizonsquantum tunneling
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper starts from a static black hole in a Hernquist dark matter distribution and builds its rotating version with the noncomplexification Newman-Janis algorithm. It then shows that the halo parameter shifts the outer horizon to larger radii, changes the ergoregion size, reduces surface gravity and temperature, raises entropy, and introduces a critical point in heat capacity. In the weak-halo slow-rotation limit the same distribution cuts the radiated luminosity and lengthens the evaporation time. A reader would care because these shifts alter how black holes lose mass and how their thermodynamic stability behaves when embedded in realistic galactic matter.

Core claim

The authors establish that the Hernquist halo displaces the outer event horizon toward larger radii, suppresses the Hawking temperature, increases the Bekenstein-Hawking entropy, changes local thermal stability through a Davies-type critical point, and in the weak halo and slow rotation regime reduces the luminosity and delays the evaporation process.

What carries the argument

The metric obtained from the noncomplexification Newman-Janis algorithm, whose radial function Δ(r) fixes the horizon locations and whose g_tt component fixes the stationary limit surfaces, both now carrying the halo density parameter ho together with the rotation parameter a.

Load-bearing premise

The noncomplexification Newman-Janis algorithm applied to the static black hole plus Hernquist halo produces a valid rotating spacetime whose metric functions correctly encode the combined effects of rotation and the halo parameter.

What would settle it

A direct check that the constructed metric fails to satisfy the Einstein equations sourced by the Hernquist stress-energy tensor plus vacuum, or an astrophysical measurement showing that a rotating black hole in a measured Hernquist halo has exactly the same horizon radius and temperature as the vacuum Kerr case.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The outer event horizon radius grows with the halo parameter ho while the horizon becomes oblate with increasing rotation parameter a.
  • Surface gravity and Hawking temperature fall as ho rises, so the black hole radiates less intensely.
  • Bekenstein-Hawking entropy rises with the halo contribution.
  • Heat capacity exhibits a Davies-type critical point that marks a change in local thermal stability.
  • In the weak-halo slow-rotation regime the Hawking luminosity drops and the total evaporation time lengthens.

Where Pith is reading between the lines

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

  • The same construction could be repeated for other common halo density profiles to compare how each profile alters evaporation timescales.
  • If the metric remains valid, the increased angular velocity of zero-angular-momentum observers would modify the innermost stable circular orbits around galactic-center black holes.
  • The delay in evaporation suggests that supermassive black holes surrounded by dense halos could retain more mass over cosmic time than isolated Kerr holes of the same initial mass.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 2 minor

Summary. The manuscript constructs a rotating black hole immersed in a Hernquist dark matter halo by applying the noncomplexification Newman-Janis algorithm to a static solution. It then examines the effects of the halo parameter ρ and rotation parameter a on horizon geometry (event horizons from Δ(r), ergoregions from g_tt=0), thermodynamics (surface gravity, Hawking temperature, Bekenstein-Hawking entropy, heat capacity with Davies-type critical point), and quantum emission (Hamilton-Jacobi tunneling rates, occupation numbers, luminosity and evaporation time via Stefan-Boltzmann), recovering Kerr and Schwarzschild limits in appropriate cases.

Significance. If the metric construction holds, the work supplies an explicit model showing how a Hernquist halo displaces the outer horizon, suppresses temperature, increases entropy, alters thermal stability, and delays evaporation. Strengths include systematic recovery of standard limits and concrete expressions for modified thermodynamic and emission quantities; the approach is exploratory rather than data-driven.

major comments (2)
  1. [Metric construction (abstract and NJA section)] Abstract and metric-construction section: the rotating metric is obtained via the noncomplexification Newman-Janis algorithm applied to the static Hernquist-surrounded spacetime. This is a coordinate-transformation prescription rather than a solution-generating technique guaranteed to satisfy the Einstein equations with the original halo stress-energy tensor; any mismatch would invalidate the subsequent horizon locations, surface gravity, heat capacity, and tunneling rates derived from Δ(r) and the metric functions.
  2. [Thermodynamic quantities] Thermodynamics and stability section: the claim of a halo-induced Davies-type critical point in the heat capacity is load-bearing for the stability modification statement, yet its explicit location depends on the unverified rotating metric functions; without an independent check that the metric solves the field equations, the critical-point result cannot be taken as robust.
minor comments (2)
  1. Explicitly tabulate or plot the limiting cases a o0 and ho o0 for all derived quantities (horizons, temperature, luminosity) to confirm recovery of known results.
  2. Clarify the domain of validity of the weak-halo/slow-rotation approximations used for the luminosity and evaporation-time estimates.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and for highlighting important methodological points. We address each major comment below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [Metric construction (abstract and NJA section)] Abstract and metric-construction section: the rotating metric is obtained via the noncomplexification Newman-Janis algorithm applied to the static Hernquist-surrounded spacetime. This is a coordinate-transformation prescription rather than a solution-generating technique guaranteed to satisfy the Einstein equations with the original halo stress-energy tensor; any mismatch would invalidate the subsequent horizon locations, surface gravity, heat capacity, and tunneling rates derived from Δ(r) and the metric functions.

    Authors: We agree that the noncomplexification Newman-Janis algorithm is a coordinate transformation rather than a method that automatically preserves the original stress-energy tensor. This limitation is inherent to the technique and has been noted in the broader literature on its application to spacetimes with matter. In the revised manuscript we will add an explicit paragraph in the metric-construction section stating that the resulting metric is an effective description whose compatibility with the Einstein equations for the Hernquist halo must be verified separately, and we will qualify all subsequent results as holding within this effective model. We will also recover the Kerr and Schwarzschild limits explicitly to confirm consistency in the vacuum cases. revision: partial

  2. Referee: [Thermodynamic quantities] Thermodynamics and stability section: the claim of a halo-induced Davies-type critical point in the heat capacity is load-bearing for the stability modification statement, yet its explicit location depends on the unverified rotating metric functions; without an independent check that the metric solves the field equations, the critical-point result cannot be taken as robust.

    Authors: The Davies-type critical point is obtained directly from the heat-capacity expression constructed from the metric functions after the Newman-Janis procedure. Because the thermodynamic quantities are derived from the same metric used for the horizons and ergoregions, they remain internally consistent within the effective model. We will revise the thermodynamics section to state clearly that the location of the critical point is model-dependent and to reiterate the effective nature of the metric, thereby qualifying the stability claim without altering the explicit expressions. revision: partial

Circularity Check

0 steps flagged

No circularity: external parameters and derived quantities from metric

full rationale

The derivation begins with an externally specified static seed metric containing the Hernquist parameter ρ, applies the noncomplexification NJA to introduce the independent rotation parameter a, and then computes all subsequent quantities (Δ(r) roots for horizons, surface gravity for temperature, entropy, heat capacity, tunneling rates, luminosity) directly from the resulting metric components. No quantity is defined in terms of itself, no fitted parameter is relabeled as a prediction, and no load-bearing step reduces to a self-citation chain; standard limits recover Kerr/Schwarzschild cases, confirming the chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The construction rests on the validity of the Newman-Janis procedure for the given static metric and introduces the halo parameter ρ as a free input characterizing the dark matter distribution.

free parameters (2)
  • ρ
    Halo density parameter that sets the strength of the Hernquist dark matter distribution.
  • a
    Rotation parameter of the black hole, standard in Kerr-like metrics.
axioms (1)
  • domain assumption The noncomplexification Newman-Janis algorithm applies to the static black hole metric with Hernquist halo.
    This is the explicit starting assumption used to construct the rotating solution from the static one.

pith-pipeline@v0.9.1-grok · 5852 in / 1407 out tokens · 39897 ms · 2026-07-01T01:05:49.113282+00:00 · methodology

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read the original abstract

We investigate the geometrical, thermodynamic, and quantum emission properties of a rotating black hole immersed in a Hernquist dark matter halo. Starting from a static black hole spacetime surrounded by a Hernquist distribution, we construct its rotating counterpart through the noncomplexification formulation of the Newman-Janis algorithm and analyze the modifications induced by the halo parameter $\rho$ and the rotation parameter $a$. The horizon structure is determined from the roots of the radial function $\Delta(r)$, while the stationary limit surfaces and the corresponding ergoregions are obtained from the condition $g_{tt}=0$. We show that the Hernquist contribution displaces the outer event horizon toward larger radii and modifies the size of the ergoregion, whereas rotation controls the oblateness of the horizon and the strength of frame dragging. The angular velocity of zero angular momentum observers is also increased by the surrounding matter distribution. We further derive the surface gravity, Hawking temperature, Bekenstein-Hawking entropy, and heat capacity, showing that the dark matter halo suppresses the temperature, increases the entropy, and changes the local thermal stability through a Davies-type critical point. The quantum tunneling rate is obtained from the Hamilton-Jacobi method, leading to the corresponding occupation number and particle creation density. Finally, we estimate the Hawking luminosity (radiation), evaporation time, and spectral emission rates within a Stefan-Boltzmann approximation. In the weak halo and slow rotation regime, the Hernquist distribution reduces the luminosity and delays the evaporation process. All standard Kerr and Schwarzschild results are recovered in the appropriate limiting cases.

Figures

Figures reproduced from arXiv: 2606.30962 by A. A. Ara\'ujo Filho, Amilcar R. Queiroz, Arun Kumar, C. F. S. Pereira, N. Heidari, V. B. Bezerra.

Figure 1
Figure 1. Figure 1: Radial behavior of ∆(r) for different values of the model parameters. In the left panel, we fix a = 0.1 and M = 1 and vary the Hernquist parameter ρ, whereas, in the right panel, we set ρ = 0.1 and M = 1 and vary the rotation parameter a. Increasing ρ shifts ∆(r) downward, while increasing a shifts it upward. its first-order correction becomes singular in this limit. The extremal configuration must instead… view at source ↗
Figure 2
Figure 2. Figure 2: Behavior of the outer event horizon radius rh for different values of the Hernquist parameter ρ in the left panel and of the rotation parameter a in the right panel. The remaining parameters are fixed at the values indicated in the respective panels [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Three-dimensional representation of the outer event horizon radius rh in the (a, ρ) parameter space for a fixed value of the black hole mass. Since Σ(r, θ) is nonvanishing outside the curvature singularity, the stationary limit surfaces follow from ∆(r) − a 2 sin2 θ = 0, or, equivalently, r 2 f(r) + a 2 cos2 θ = 0. After multiplying by (r + 2M), the corresponding cubic equation becomes E(r, ρ, θ) ≡ [PITH_… view at source ↗
Figure 4
Figure 4. Figure 4: Two-dimensional representations of the outer event horizon for selected values of the Hernquist and rotation parameters. The parameter choices are indicated in the respective panels. The resulting first-order correction is r ± e,1 (θ) = 16πM3 [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Ergosphere profiles for different configurations of the system. In the left panel, we fix ρ = 0.001 and M = 1 and vary the rotation parameter a, whereas, in the right panel, we set a = 0.5 and M = 1 and consider different values of ρ. In [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Three-dimensional representations of the event horizon and ergosphere for ρ = 0.001 and different values of the rotation parameter a: a = 0.6 (top left), a = 0.7 (top right), a = 0.8 (bottom left), and a = 0.9 (bottom right). For the rotating black hole surrounded by the Hernquist dark matter distribution, Eq. (48) gives [111, 112] ω(r, θ; ρ, a) = a [r 2 + a 2 − ∆(r)] (r 2 + a 2 ) 2 − a 2∆(r) sin2 θ . (49)… view at source ↗
Figure 7
Figure 7. Figure 7: Three–dimensional representations of the event horizon and ergosphere for a = 0.9 and different values of the dark matter parameter ρ: ρ = 10−4 (top left), ρ = 5 × 10−4 (top right), ρ = 10 × 10−4 (bottom left), and ρ = 20 × 10−4 (bottom right). The Kerr result is recovered by removing the dark matter contribution, namely, by taking ρ → 0. In this limit, Eq. (49) reduces to ωKerr(r, θ) = 2aMr (r 2 + a 2 ) 2… view at source ↗
Figure 8
Figure 8. Figure 8: The angular velocity ω(r, ρ, a) as a function of the radial coordinate r for different values of ρ (left panel) and the rotation parameter a (right panel). The influence of the Hernquist parameter can also be established directly from Eq. (49). For positive a, M, and r, one obtains ∂ω ∂ρ = 32πaM3 r 2 (r 2 + a 2 ) (r 2 + a 2 cos2 θ) (r + 2M) [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Hawking temperature T(ρ, a, M) as a function of the black hole mass M for different values of the Hernquist dark matter parameter ρ, with the rotation parameter fixed at a = 0.1. The curves were obtained from the complete temperature and horizon equations. Increasing ρ suppresses the Hawking temperature and shifts the zero-temperature extremal configuration, whose perturbative position is given by Mext ≃ a… view at source ↗
Figure 10
Figure 10. Figure 10: Entropy S(ρ, a, M) as a function of the black hole mass M for different values of the Hernquist dark matter parameter ρ, with the rotation parameter fixed at a = 0.9. The entropy increases with both M and ρ, reflecting the enlargement of the event horizon area induced by the surrounding dark matter distribution. among the curves becomes increasingly pronounced for larger values of M, which indicates that … view at source ↗
Figure 11
Figure 11. Figure 11: Heat capacity CV (ρ, a, M) as a function of the black hole mass M for different values of the Hernquist dark matter parameter ρ, with the rotation parameter fixed at a = 0.4. The divergence separates locally stable configurations with CV > 0 from unstable configurations with CV < 0 and marks a Davies-type critical point. To remove the coordinate singularity at ∆(rh) = 0, we introduce the advanced coordina… view at source ↗
Figure 12
Figure 12. Figure 12: Particle occupation number ⟨NωJ ⟩ in the low–frequency regime for small values of J. The top panel shows the effect of varying the Hernquist parameter ρ at fixed a, whereas the bottom panel shows the effect of varying the rotation parameter a at fixed ρ. In both panels, the particle occupation number decreases as the corresponding parameter increases. Equation (100) should be understood as a thermal estim… view at source ↗
Figure 13
Figure 13. Figure 13: Particle creation density dn/dω as a function of the frequency ω. The top panel shows the effect of varying the Hernquist parameter ρ at fixed a, whereas the bottom panel shows the effect of varying the rotation parameter a at fixed ρ. Therefore, the tunnelling method determines the thermal factor, while the greybody factor controls the fraction of particles that can propagate through the exterior effecti… view at source ↗
Figure 14
Figure 14. Figure 14: Particle number density n as a function of the Hernquist parameter ρ for different values of the rotation parameter a. T can produce a more pronounced modification in the number of particles created. In [PITH_FULL_IMAGE:figures/full_fig_p029_14.png] view at source ↗

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