Rarity of rocket-driven Penrose extraction in Kerr spacetime

An T. Le

arxiv: 2601.19616 · v3 · submitted 2026-01-27 · 🌌 astro-ph.HE · cs.SY· eess.SY· gr-qc· physics.comp-ph

Rarity of rocket-driven Penrose extraction in Kerr spacetime

An T. Le This is my paper

Pith reviewed 2026-05-16 10:59 UTC · model grok-4.3

classification 🌌 astro-ph.HE cs.SYeess.SYgr-qcphysics.comp-ph

keywords Penrose processKerr spacetimerocket propulsionenergy extractionergospheretest-particle trajectoriesblack-hole spinescape trajectories

0 comments

The pith

Rocket-driven Penrose extraction succeeds in at most 1 percent of trajectories and requires high spin plus precise tuning.

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

The paper simulates hundreds of thousands of rocket trajectories around rotating black holes to test whether a spacecraft can extract energy by ejecting exhaust with negative energy inside the ergosphere. It finds that successful extraction followed by escape to infinity is uncommon, occurring in no more than about one percent of cases across wide parameter ranges. Success requires the black hole to spin rapidly, the exhaust to be ejected at nearly the speed of light, and the initial orbit to be tuned carefully. When parameters are optimized the success rate climbs to seventy percent at the highest spin considered, yet a single thrust at closest approach uses less propellant than continuous steering. This indicates that rocket-based energy harvesting from black holes faces severe practical limits even in the simplest model.

Core claim

Across 320,000 simulated trajectories in the test-particle limit on a fixed Kerr background for equatorial prograde flybys, extraction with escape is rare in broad parameter scans (at most ∼1 percent) and requires high spin a/M ≳ 0.89, highly relativistic exhaust v_e ≳ 0.91c, and finely tuned initial conditions; under optimal tuning the success rate reaches ∼70 percent at a/M = 0.95, with a single periapsis impulse proving more propellant-efficient than the continuous-thrust controllers studied.

What carries the argument

Ejection of exhaust with negative Killing energy inside the ergosphere so that four-momentum conservation gives the remaining spacecraft positive energy, implemented through explicit steering prescriptions.

If this is right

Extraction with escape occurs in at most 1 percent of trajectories over broad scans of spin, exhaust speed, and orbit parameters.
Black-hole spin must satisfy a/M greater than or equal to 0.89.
Exhaust velocity must satisfy v_e greater than or equal to 0.91 times the speed of light.
Initial conditions must be finely tuned for success.
A single impulse at periapsis uses less propellant than continuous-thrust steering.

Where Pith is reading between the lines

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

Accounting for the spacecraft's own mass and the gradual loss of propellant could narrow the viable windows even further because inertia changes during the burn.
Non-equatorial trajectories might either enlarge the set of successful paths or introduce additional constraints from frame-dragging in three dimensions.
Practical engineering would need to target the narrow high-spin, high-velocity corner of parameter space rather than relying on generic flybys.

Load-bearing premise

The test-particle limit on a fixed Kerr background together with the chosen explicit steering prescriptions accurately represent the dynamics of a real spacecraft that must carry finite propellant mass and may experience back-reaction or non-equatorial motion.

What would settle it

A new suite of trajectories computed with finite spacecraft mass, gravitational back-reaction on the metric, or allowed non-equatorial motion would show whether the reported rarity, spin threshold, and efficiency ordering persist.

Figures

Figures reproduced from arXiv: 2601.19616 by An T. Le.

**Figure 2.** Figure 2: FIG. 2. Extraction-with-escape success rate versus black hole [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Thrust strategy comparison at [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Spin dependence of the extraction window. Panels show orbit classification in ( [PITH_FULL_IMAGE:figures/full_fig_p016_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Thrust parameter sensitivity for [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. Continuation of Fig. 5b into the extreme- [PITH_FULL_IMAGE:figures/full_fig_p018_6.png] view at source ↗

read the original abstract

We study rocket-driven Penrose extraction in the test-particle limit on a fixed Kerr background for equatorial prograde flybys under explicit steering prescriptions. A spacecraft ejects exhaust inside the ergosphere; when the exhaust attains negative Killing energy, the remaining spacecraft gains energy by 4-momentum conservation. Across 320{,}000 simulated trajectories spanning black-hole spin, exhaust velocity, and orbital parameters, extraction with escape is rare in broad parameter scans (at most ${\sim}1\%$) and requires high spin ($a/M\gtrsim 0.89$), highly relativistic exhaust ($v_e\gtrsim 0.91c$), and finely tuned initial conditions. Under optimal tuning the success rate reaches ${\sim}70\%$ at $a/M = 0.95$. For representative escape trajectories, a single periapsis impulse is more propellant-efficient than the continuous-thrust controllers studied here. All quoted thresholds are empirical and specific to the orbit family, prior, and steering protocol studied.

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.

Desk Editor's Note private letter to a colleague

Numerical survey finds rocket-driven Penrose extraction with escape succeeds in at most 1% of cases across broad scans but up to 70% with optimal tuning at high spins.

read the letter

The main result is that rocket-driven Penrose extraction followed by escape is rare in this setup. Across 320,000 trajectories in the test-particle limit on fixed Kerr, success stays below about 1% in broad scans and needs a/M above roughly 0.89, exhaust velocity above 0.91c, and tight initial conditions. With best-case tuning it reaches around 70% at a/M=0.95, and a single periapsis impulse beats the continuous-thrust controllers they tried for propellant use. All numbers are tied to equatorial prograde orbits and the specific steering rules used here. The paper does a solid job delivering the first large empirical map of these thresholds instead of stopping at analytic limits. The numerics are standard integration and the claims stay scoped to the model, which keeps the central statement internally consistent. The obvious limits are the test-particle approximation itself, which drops spacecraft mass and back-reaction, plus the lack of error bars on the reported percentages and no released code. Those are real but not fatal for a first quantitative survey. This is worth a look for people working on black-hole energy extraction or speculative high-energy propulsion. It deserves peer review because the sample size is large, the method is reproducible in principle, and the result adds concrete numbers to a known mechanism without overclaiming.

Referee Report

2 major / 1 minor

Summary. The manuscript numerically investigates rocket-driven Penrose extraction in the test-particle limit on a fixed Kerr background for equatorial prograde flybys under explicit steering prescriptions. Across 320,000 simulated trajectories spanning black-hole spin, exhaust velocity, and orbital parameters, extraction with escape is found to be rare (at most ~1%) in broad scans, requiring high spin (a/M ≳ 0.89), highly relativistic exhaust (v_e ≳ 0.91c), and finely tuned initial conditions; under optimal tuning the success rate reaches ~70% at a/M = 0.95. A single periapsis impulse is reported as more propellant-efficient than the continuous-thrust controllers studied.

Significance. If the numerical results hold within the stated scope, the work supplies quantitative empirical bounds showing that rocket-assisted Penrose extraction is rare and highly sensitive to parameters, which is useful for assessing the viability of energy-extraction mechanisms. The direct integration of 320,000 trajectories with explicit parameter scans provides a reproducible, falsifiable data set that strengthens the central empirical claim; the abstract's explicit qualification that all thresholds are specific to the orbit family, prior, and protocol avoids overgeneralization.

major comments (2)

[Results section (discussion of the 320,000-trajectory survey and reported percentages)] Results section (discussion of the 320,000-trajectory survey and reported percentages): the success rates (~1% in broad scans and ~70% under optimal tuning) are stated without error bars, confidence intervals, or binomial uncertainty estimates; given the finite sampling and the centrality of these figures to the rarity conclusion, this omission weakens the precision of the quantitative claims.
[Methods section (steering prescriptions and trajectory integration)] Methods section (steering prescriptions and trajectory integration): the rarity thresholds depend on the specific explicit steering laws chosen; although the abstract qualifies the results as protocol-specific, no quantitative sensitivity tests to modest variations in the controllers are provided, leaving open whether the ~1% upper bound is robust to reasonable changes in the steering implementation.

minor comments (1)

[Abstract and results] Abstract and results: the approximate symbol is rendered inconsistently as ∼ versus ~; uniform notation would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment and the recommendation for minor revision. We address each major comment below.

read point-by-point responses

Referee: Results section (discussion of the 320,000-trajectory survey and reported percentages): the success rates (~1% in broad scans and ~70% under optimal tuning) are stated without error bars, confidence intervals, or binomial uncertainty estimates; given the finite sampling and the centrality of these figures to the rarity conclusion, this omission weakens the precision of the quantitative claims.

Authors: We agree that including uncertainty estimates would improve the precision of the reported success rates. In the revised manuscript we will add binomial confidence intervals (using the Wilson score interval) to the percentages quoted in the Results section, computed from the number of successful trajectories in each parameter bin or scan. With a total of 320,000 trajectories the statistical uncertainties are modest, but reporting them explicitly will strengthen the quantitative claims. revision: yes
Referee: Methods section (steering prescriptions and trajectory integration): the rarity thresholds depend on the specific explicit steering laws chosen; although the abstract qualifies the results as protocol-specific, no quantitative sensitivity tests to modest variations in the controllers are provided, leaving open whether the ~1% upper bound is robust to reasonable changes in the steering implementation.

Authors: We agree that the ~1% upper bound is tied to the particular explicit steering prescriptions. Although the abstract already qualifies all thresholds as protocol-specific, we will revise the Methods section to include an expanded discussion that more prominently cautions readers against generalizing the rarity result beyond the controllers implemented here. A full quantitative sensitivity study would require substantial additional simulations and is therefore left for future work; the revision will frame this explicitly as a limitation of the present study. revision: partial

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper's central results are empirical counts of successful extraction trajectories obtained by direct numerical integration of the Kerr geodesic equations under explicit steering laws. No parameters are fitted to a data subset and then relabeled as predictions; success rates (e.g., ~1% in broad scans, ~70% under optimal tuning) are simple tallies from 320,000 independent simulations. The test-particle limit and equatorial prograde family are modeling choices stated up front, not derived from the output statistics. No self-citations, uniqueness theorems, or ansatze are used to justify the reported rarity thresholds. The derivation chain reduces to standard conserved quantities (Killing energy, angular momentum) plus 4-momentum conservation at exhaust ejection, all independent of the final success-rate numbers.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The study rests on the standard Kerr metric and geodesic motion with added thrust; no new entities are postulated and the scanned parameters are treated as inputs rather than fitted constants.

free parameters (2)

black-hole spin a/M
Input parameter scanned over a range; not fitted to any target result.
exhaust velocity v_e
Input parameter scanned over a range; not fitted to any target result.

axioms (2)

standard math Spacetime is described by the Kerr metric
Standard assumption for rotating black holes in general relativity.
domain assumption Test-particle limit applies
Spacecraft mass is negligible compared with the black hole; stated in the abstract.

pith-pipeline@v0.9.0 · 5476 in / 1485 out tokens · 33055 ms · 2026-05-16T10:59:08.377814+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Across 320,000 simulated trajectories spanning black-hole spin, exhaust velocity, and orbital parameters, extraction with escape is rare in broad parameter scans (at most ∼1%) and requires high spin (a/M≳0.89), highly relativistic exhaust (v_e≳0.91c), and finely tuned initial conditions.
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The cumulative efficiency over the maneuver is: η_cum = (E_f − E_0)/(m_0 − m_f) = ΔE/Δm.

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

26 extracted references · 26 canonical work pages

[1]

The decay occurs inside the ergosphere:r + < r < rerg

work page
[2]

The captured particle has negative Killing energy: E2 <0

work page
[3]

Positive total energyE 1 >0 alone is insuf- ficient, since positive-energy bound orbits exist in Kerr

The escaping fragment follows a geodesic that reaches spatial infinity; for a massive particle, this requires specific energyE 1/m1 >1 (unbound) to- gether with an allowed radial turning-point struc- ture. Positive total energyE 1 >0 alone is insuf- ficient, since positive-energy bound orbits exist in Kerr. A necessary condition forE 2 <0 is that the frag...

work page
[4]

Ejects mass at exhaust velocityv e (in the space- craft’s rest frame)

work page
[5]

Chooses a thrust orientation such that the exhaust carries retrograde angular momentum (L z,ex <0)

work page
[6]

extraction-with-escape success,

Inside the ergosphere, the exhaust can then have Eex <0, transferring energy to the remaining spacecraft. Conceptually, each infinitesimal exhaust element plays the role of the captured negative-energy fragment in the classical single-decay, while the remaining spacecraft plays the role of the escaping fragment; the rocket engine provides control over the...

work page
[7]

and retrograde (L z <0) conditions to map the fail- ure boundaries around the mission-relevant prograde un- 11 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 Specific energy E0 2.0 2.5 3.0 3.5 4.0 4.5 5.0Angular momentum Lz/M r+ = 1.71M rerg = 2.00M E = 1 (a) a/M = 0.7 rp=1.8 rp=1.9 rp=2.0 rp=2.1 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 Specific energy E0 2.0 2.5...

work page 1934
[8]

Broad Parameter Study We performed systematic parameter sweeps across a broad (E 0, Lz) domain for five spin values:E 0 ∈ [0.95,2.0],L z ∈[−3.0,6.0], using an 80×80 grid (6,400 samples per spin). We choose this domain to encompass all orbits from marginally bound (E 0 ≈1) to moderately relativistic (E 0 = 2), and from strongly retrograde to strongly progr...

work page
[9]

,0.88 plusa/M∈ {0.89,0.90,0.92,0.95,0.99}, with 10,000 LHS sam- ples per spin in the focused region

Spin Threshold Analysis To precisely characterize the spin depen- dence, we performed a sweep over 14 spin val- ues:a/M= 0.80,0.81, . . . ,0.88 plusa/M∈ {0.89,0.90,0.92,0.95,0.99}, with 10,000 LHS sam- ples per spin in the focused region. Table II shows the results. Across this spin threshold sweep (140,000 additional LHS trajectories, separate from the m...

work page
[10]

sweet spot

Focused Sweet-Spot Study We define the “sweet spot” as the region of (E 0, Lz) space corresponding to deep-ergosphere flybys with escape-capable angular momentum, identified from the orbit classification in Fig. 1. Physically, this is the inter- section of two constraints: (i) periapsis deep enough in- side the ergosphere forE ex <0 to be robustly achieva...

work page
[11]

Penrose and R

R. Penrose and R. M. Floyd, Extraction of rotational energy from a black hole, Nature Physical Science229, 177 (1971)

work page 1971
[12]

Christodoulou, Reversible and irreversible transfor- mations in black-hole physics, Physical Review Letters 25, 1596 (1970)

D. Christodoulou, Reversible and irreversible transfor- mations in black-hole physics, Physical Review Letters 25, 1596 (1970)

work page 1970
[13]

J. M. Bardeen, W. H. Press, and S. A. Teukolsky, Ro- tating black holes: locally nonrotating frames, energy extraction, and scalar synchrotron radiation, The Astro- physical Journal178, 347 (1972)

work page 1972
[14]

R. M. Wald, Energy limits on the penrose process, The Astrophysical Journal191, 231 (1974)

work page 1974
[15]

Piran, J

T. Piran, J. Shaham, and J. Katz, High efficiency of the penrose mechanism for particle collisions, The Astrophys- ical Journal Letters196, L107 (1975)

work page 1975
[16]

Ba˜ nados, J

M. Ba˜ nados, J. Silk, and S. M. West, Kerr black holes as particle accelerators to arbitrarily high energy, Physical review letters103, 111102 (2009)

work page 2009
[17]

Bejger, T

M. Bejger, T. Piran, M. Abramowicz, and F. H˚ akanson, Collisional penrose process near the horizon of extreme kerr black holes, Physical review letters109, 121101 (2012)

work page 2012
[18]

Berti, R

E. Berti, R. Brito, and V. Cardoso, Ultrahigh-energy de- bris from the collisional penrose process, Physical Review Letters114, 251103 (2015)

work page 2015
[19]

J. D. Schnittman, Revised upper limit to energy extrac- tion from a kerr black hole, Physical Review Letters113, 261102 (2014)

work page 2014
[20]

Leiderschneider and T

E. Leiderschneider and T. Piran, Maximal efficiency of the collisional penrose process, Physical Review D93, 20 043015 (2016)

work page 2016
[21]

R. D. Blandford and R. L. Znajek, Electromagnetic ex- traction of energy from kerr black holes, Monthly Notices of the Royal Astronomical Society179, 433 (1977)

work page 1977
[22]

Tchekhovskoy, R

A. Tchekhovskoy, R. Narayan, and J. C. McKinney, Effi- cient generation of jets from magnetically arrested accre- tion on a rapidly spinning black hole, Monthly Notices of the Royal Astronomical Society: Letters418, L79 (2011)

work page 2011
[23]

Comisso and F

L. Comisso and F. A. Asenjo, Magnetic reconnection as a mechanism for energy extraction from rotating black holes, Physical Review D103, 023014 (2021)

work page 2021
[24]

Koide and K

S. Koide and K. Arai, Energy extraction from a rotating black hole by magnetic reconnection in the ergosphere, The Astrophysical Journal682, 1124 (2008)

work page 2008
[25]

Chandrasekhar,The Mathematical Theory of Black Holes(Clarendon Press, 1983)

S. Chandrasekhar,The Mathematical Theory of Black Holes(Clarendon Press, 1983)

work page 1983
[26]

M. Bhat, S. Dhurandhar, and N. Dadhich, Energetics of the kerr-newman black hole by the penrose process, Journal of Astrophysics and Astronomy6, 85 (1985)

work page 1985

[1] [1]

The decay occurs inside the ergosphere:r + < r < rerg

work page

[2] [2]

The captured particle has negative Killing energy: E2 <0

work page

[3] [3]

Positive total energyE 1 >0 alone is insuf- ficient, since positive-energy bound orbits exist in Kerr

The escaping fragment follows a geodesic that reaches spatial infinity; for a massive particle, this requires specific energyE 1/m1 >1 (unbound) to- gether with an allowed radial turning-point struc- ture. Positive total energyE 1 >0 alone is insuf- ficient, since positive-energy bound orbits exist in Kerr. A necessary condition forE 2 <0 is that the frag...

work page

[4] [4]

Ejects mass at exhaust velocityv e (in the space- craft’s rest frame)

work page

[5] [5]

Chooses a thrust orientation such that the exhaust carries retrograde angular momentum (L z,ex <0)

work page

[6] [6]

extraction-with-escape success,

Inside the ergosphere, the exhaust can then have Eex <0, transferring energy to the remaining spacecraft. Conceptually, each infinitesimal exhaust element plays the role of the captured negative-energy fragment in the classical single-decay, while the remaining spacecraft plays the role of the escaping fragment; the rocket engine provides control over the...

work page

[7] [7]

and retrograde (L z <0) conditions to map the fail- ure boundaries around the mission-relevant prograde un- 11 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 Specific energy E0 2.0 2.5 3.0 3.5 4.0 4.5 5.0Angular momentum Lz/M r+ = 1.71M rerg = 2.00M E = 1 (a) a/M = 0.7 rp=1.8 rp=1.9 rp=2.0 rp=2.1 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 Specific energy E0 2.0 2.5...

work page 1934

[8] [8]

Broad Parameter Study We performed systematic parameter sweeps across a broad (E 0, Lz) domain for five spin values:E 0 ∈ [0.95,2.0],L z ∈[−3.0,6.0], using an 80×80 grid (6,400 samples per spin). We choose this domain to encompass all orbits from marginally bound (E 0 ≈1) to moderately relativistic (E 0 = 2), and from strongly retrograde to strongly progr...

work page

[9] [9]

,0.88 plusa/M∈ {0.89,0.90,0.92,0.95,0.99}, with 10,000 LHS sam- ples per spin in the focused region

Spin Threshold Analysis To precisely characterize the spin depen- dence, we performed a sweep over 14 spin val- ues:a/M= 0.80,0.81, . . . ,0.88 plusa/M∈ {0.89,0.90,0.92,0.95,0.99}, with 10,000 LHS sam- ples per spin in the focused region. Table II shows the results. Across this spin threshold sweep (140,000 additional LHS trajectories, separate from the m...

work page

[10] [10]

sweet spot

Focused Sweet-Spot Study We define the “sweet spot” as the region of (E 0, Lz) space corresponding to deep-ergosphere flybys with escape-capable angular momentum, identified from the orbit classification in Fig. 1. Physically, this is the inter- section of two constraints: (i) periapsis deep enough in- side the ergosphere forE ex <0 to be robustly achieva...

work page

[11] [11]

Penrose and R

R. Penrose and R. M. Floyd, Extraction of rotational energy from a black hole, Nature Physical Science229, 177 (1971)

work page 1971

[12] [12]

Christodoulou, Reversible and irreversible transfor- mations in black-hole physics, Physical Review Letters 25, 1596 (1970)

D. Christodoulou, Reversible and irreversible transfor- mations in black-hole physics, Physical Review Letters 25, 1596 (1970)

work page 1970

[13] [13]

J. M. Bardeen, W. H. Press, and S. A. Teukolsky, Ro- tating black holes: locally nonrotating frames, energy extraction, and scalar synchrotron radiation, The Astro- physical Journal178, 347 (1972)

work page 1972

[14] [14]

R. M. Wald, Energy limits on the penrose process, The Astrophysical Journal191, 231 (1974)

work page 1974

[15] [15]

Piran, J

T. Piran, J. Shaham, and J. Katz, High efficiency of the penrose mechanism for particle collisions, The Astrophys- ical Journal Letters196, L107 (1975)

work page 1975

[16] [16]

Ba˜ nados, J

M. Ba˜ nados, J. Silk, and S. M. West, Kerr black holes as particle accelerators to arbitrarily high energy, Physical review letters103, 111102 (2009)

work page 2009

[17] [17]

Bejger, T

M. Bejger, T. Piran, M. Abramowicz, and F. H˚ akanson, Collisional penrose process near the horizon of extreme kerr black holes, Physical review letters109, 121101 (2012)

work page 2012

[18] [18]

Berti, R

E. Berti, R. Brito, and V. Cardoso, Ultrahigh-energy de- bris from the collisional penrose process, Physical Review Letters114, 251103 (2015)

work page 2015

[19] [19]

J. D. Schnittman, Revised upper limit to energy extrac- tion from a kerr black hole, Physical Review Letters113, 261102 (2014)

work page 2014

[20] [20]

Leiderschneider and T

E. Leiderschneider and T. Piran, Maximal efficiency of the collisional penrose process, Physical Review D93, 20 043015 (2016)

work page 2016

[21] [21]

R. D. Blandford and R. L. Znajek, Electromagnetic ex- traction of energy from kerr black holes, Monthly Notices of the Royal Astronomical Society179, 433 (1977)

work page 1977

[22] [22]

Tchekhovskoy, R

A. Tchekhovskoy, R. Narayan, and J. C. McKinney, Effi- cient generation of jets from magnetically arrested accre- tion on a rapidly spinning black hole, Monthly Notices of the Royal Astronomical Society: Letters418, L79 (2011)

work page 2011

[23] [23]

Comisso and F

L. Comisso and F. A. Asenjo, Magnetic reconnection as a mechanism for energy extraction from rotating black holes, Physical Review D103, 023014 (2021)

work page 2021

[24] [24]

Koide and K

S. Koide and K. Arai, Energy extraction from a rotating black hole by magnetic reconnection in the ergosphere, The Astrophysical Journal682, 1124 (2008)

work page 2008

[25] [25]

Chandrasekhar,The Mathematical Theory of Black Holes(Clarendon Press, 1983)

S. Chandrasekhar,The Mathematical Theory of Black Holes(Clarendon Press, 1983)

work page 1983

[26] [26]

M. Bhat, S. Dhurandhar, and N. Dadhich, Energetics of the kerr-newman black hole by the penrose process, Journal of Astrophysics and Astronomy6, 85 (1985)

work page 1985