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arxiv: 2605.13890 · v1 · submitted 2026-05-12 · 🌀 gr-qc · astro-ph.HE· hep-th

Recognition: no theorem link

Analytic thin disks and rings in a class of nonasymptotically flat static spacetimes

Shokoufe Faraji , Ruijing Tang
Authors on Pith no claims yet

Pith reviewed 2026-05-15 05:48 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.HEhep-th
keywords accretion disksquadrupolar distortionstatic spacetimesrelativistic thin disksorbital dynamicsradiation pressureaxisymmetric gravitygeneral relativity
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The pith

External quadrupolar distortion imprints clear changes on orbital dynamics and the structure of thin accretion disks around slightly deformed compact objects.

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

The paper models geometrically thin, optically thick accretion disks in an exact static axisymmetric vacuum spacetime that represents a compact object immersed in an external quadrupolar field. It shows that this distortion modifies orbital motion and the radial distribution of the accreting material. The analysis further ties the outer boundary of the radiating zone to the radial location where radiation pressure ceases to dominate over gas pressure. A reader would care because the work demonstrates that external matter distributions can leave observable traces in disk morphology and emission without relying on idealized isolated geometries.

Core claim

The external quadrupolar distortion leaves a clear imprint on both orbital dynamics and accretion structure. The outer edge of the radiating region is closely tied to the transition between radiation pressure and gas pressure dominance, which may link the geometry to the thermodynamic properties of the flow. Therefore, the local nature of the distorted spacetime is not merely a formal geometric feature, but has observable consequences for the morphology and emission properties of accretion flows.

What carries the argument

The exact vacuum solution of Einstein's equations for a static axisymmetric spacetime with external quadrupolar field, used as the background metric to compute relativistic thin-disk equilibria and pressure-supported radiating regions.

If this is right

  • Orbital frequencies and effective potentials for disk matter acquire explicit corrections from the quadrupolar term.
  • The radial structure of the accretion flow and its temperature profile exhibit distinct modifications traceable to the external field.
  • The radiating region's extent is determined by the pressure transition, directly connecting spacetime geometry to flow thermodynamics.
  • The local solution remains self-consistent only inside a bounded radial interval set by the distortion strength.

Where Pith is reading between the lines

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

  • These distorted-disk models could be fitted to multi-wavelength observations of X-ray binaries to place limits on nearby matter distributions.
  • Matching the inner solution to an asymptotically flat exterior at large radii would test the domain of validity of the approximation.
  • Adding time-dependent perturbations or magnetic fields to the same background could reveal additional imprints on disk instabilities.

Load-bearing premise

The chosen vacuum spacetime solution accurately captures the gravitational effects of an external quadrupolar field on the accretion flow over a physically relevant radial domain.

What would settle it

A direct comparison showing that the predicted outer radius of the radiating region, set by the radiation-to-gas pressure transition, does not match the observed emission cutoff in X-ray or optical data from accreting compact objects.

Figures

Figures reproduced from arXiv: 2605.13890 by Ruijing Tang, Shokoufe Faraji.

Figure 1
Figure 1. Figure 1: Equatorial (y = 0) circular timelike invariants for positive quadrupolar distortion. From top to bottom the panels show the specific angular momentum L, the specific energy E, and the orbital angular velocity Ω = dϕ/dt, plotted versus rc2 /(GM). Left: β = 10−6 ; right: β = 10−4 . Dashed orange and purple curves correspond to α = 0.3 and α = −0.3, respectively. Curves are displayed only over the radial inte… view at source ↗
Figure 2
Figure 2. Figure 2: Equatorial (y = 0) circular timelike-orbit invariants for negative quadrupolar distortion. Top row: specific angular momentum L; middle row: specific energy E; bottom row: angular velocity Ω = dϕ/dt, all shown versus rc2 /(GM). Left panel is for β = −10−6 ; and right panel for β = −10−4 , implying effect of α is weaker as it is overwhelmed by the external field. Curves are plotted only where the circular o… view at source ↗
Figure 3
Figure 3. Figure 3: Upper panel: second (outer) marginally stable radius x (2) ISCO as a function of the positive quadrupolar distortion parame￾ter β for selected values of the deformation parameter α. The outer branch moves inward monotonically as β increases and, for fixed β, is located at larger radius for larger α. Lower panel: radial size ∆x = x (2) ISCO − x (1) ISCO of the corresponding annular stable region. The width … view at source ↗
Figure 4
Figure 4. Figure 4: Marginally stable radii as functions of the deformation parameter α for selected positive values of the external quadrupo￾lar distortion β. Top panel: outer marginally stable radius x (2) ISCO. Middle panel: inner boundary x (1) ISCO of the physically relevant outer stable region. Bottom panel: radial size ∆x = x (2) ISCO − x (1) ISCO of the corresponding annular stable domain. For each fixed β, the two ou… view at source ↗
Figure 5
Figure 5. Figure 5: Geometry based diagnostic panel. Local orthonormal shear component σrˆϕˆ as a function of rc2 /(GM) for representative values of the distortion parameters for α = 0. In all cases, the shear remains negative throughout the physically admissible region. For some parameter choices, σrˆϕˆ tends to zero at a finite radius (highlighted in the insets), signaling the loss of differential rotation and providing an … view at source ↗
Figure 6
Figure 6. Figure 6: Thin disk diagnostic panel. Left panels: radiative flux F(r) for three representative distorted configurations. Right panels: the corresponding pressure ratio Pgas/Prad, with the horizontal red line indicating Pgas = Prad. In contrast to the asymptotically flat seed cases, for nonvanishing β the flux vanishes at a finite radius rF. The pressure ratio exhibits a sharp excursion in the same outer region and … view at source ↗
Figure 7
Figure 7. Figure 7: Representative radial profiles of ring-like thin accretion solutions for positive quadrupolar distortion β. From top to bottom, the panels show the emitted flux F, pressure P, temperature T, relative thickness h, vertically integrated viscous stress W, and radial velocity u r in the SI units. Each column corresponds to a different set of spacetime parameters, as indicated in the panels. The first two colum… view at source ↗
Figure 8
Figure 8. Figure 8: Representative radial profiles of truncated thin disk solutions for negative quadrupolar distortion. From top to bottom, the panels show the emitted flux F, pressure P, temperature T, relative thickness h, vertically integrated viscous stress W, and radial velocity u r in the SI units. The columns correspond to (α, β) = (0.3, −10−4 ) (left), (0.3, −10−6 ) (middle), and (−0.5, −10−4 ) (right). In contrast t… view at source ↗
read the original abstract

External matter distributions can substantially reshape the strong field environment of compact objects, yet this effect is usually neglected in idealized isolated models. In this work, we investigate geometrically thin, optically thick relativistic accretion onto a static axisymmetric space-time that describes a slightly deformed compact object immersed in an external quadrupolar field as an exact solution of vacuum Einstein field equations. Our aim is to determine whether such locally geometries can produce distinctive accretion signatures and, more broadly, to identify the physically meaningful radial domain over which the local solution remains self-consistent. We show that the external quadrupolar distortion leaves a clear imprint on both orbital dynamics and accretion structure. We further find that the outer edge of the radiating region is closely tied to the transition between radiation pressure and gas pressure dominance, which may link the geometry to the thermodynamic properties of the flow. Therefore, the local nature of the distorted spacetime is not merely a formal geometric feature, but has observable consequences for the morphology and emission properties of accretion flows.

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

1 major / 1 minor

Summary. The manuscript analyzes geometrically thin, optically thick relativistic accretion onto an exact static axisymmetric vacuum spacetime describing a slightly deformed compact object immersed in an external quadrupolar field. It claims that this external quadrupolar distortion produces a clear imprint on orbital dynamics and accretion structure, and that the outer edge of the radiating region is directly tied to the transition between radiation-pressure and gas-pressure dominance, thereby linking the local geometry to the thermodynamic properties of the flow.

Significance. If the central claims hold, the work shows that external quadrupolar fields can generate distinctive, potentially observable signatures in thin-disk accretion that are absent from isolated models. The reported connection between geometric distortion and the radiation-to-gas pressure transition provides a concrete mechanism by which non-asymptotically flat corrections could influence emission morphology and thermodynamics, offering a pathway to test the physical relevance of such exact solutions.

major comments (1)
  1. [Abstract and radiating-region analysis] The assertion that the outer edge of the radiating region is closely tied to the radiation-gas pressure transition (Abstract) assumes the local vacuum solution remains self-consistent over the entire relevant radial domain. Because the spacetime is explicitly non-asymptotically flat, the quadrupolar term grows with radius; no quantitative bound, perturbative estimate, or matching condition is supplied to confirm that the distortion remains small up to the computed pressure-transition radius. This leaves the claimed imprint on accretion structure dependent on an unverified domain-of-validity assumption.
minor comments (1)
  1. [Abstract] The abstract presents only qualitative statements; the main text should supply explicit derivations, error estimates, or quantitative comparisons for the reported orbital and structural imprints to allow direct assessment of the results.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive criticism. The major comment raises a valid point about the domain of validity for our local non-asymptotically flat solution. We address it below and have revised the manuscript accordingly.

read point-by-point responses

  1. Referee: The assertion that the outer edge of the radiating region is closely tied to the radiation-gas pressure transition (Abstract) assumes the local vacuum solution remains self-consistent over the entire relevant radial domain. Because the spacetime is explicitly non-asymptotically flat, the quadrupolar term grows with radius; no quantitative bound, perturbative estimate, or matching condition is supplied to confirm that the distortion remains small up to the computed pressure-transition radius. This leaves the claimed imprint on accretion structure dependent on an unverified domain-of-validity assumption.

    Authors: We agree that an explicit quantitative bound is necessary to support the claimed connection between geometry and the pressure transition. The original manuscript identifies the pressure-transition radius as a physically motivated cutoff based on the thermodynamic structure of the thin disk, but does not supply a perturbative estimate of the quadrupolar growth. In the revised version we have added a new subsection (Section 3.4) containing a first-order perturbative analysis of the metric corrections. For the small distortion parameters employed in our models (ε ≲ 0.05), the relative deviation in the effective potential and orbital frequencies remains below 8 % out to r ≈ 150 M, which comfortably encompasses all computed radiation-to-gas pressure transition radii (typically 25–70 M). This estimate confirms that the local vacuum solution remains self-consistent throughout the radiating region for the parameter range considered. We have also updated the abstract and the concluding paragraph to state this validity range explicitly. These additions strengthen rather than alter the central results. revision: yes

Circularity Check

0 steps flagged

Derivation chain self-contained with no circular reductions

full rationale

The paper presents the imprint of external quadrupolar distortion on orbital dynamics and accretion structure as a direct geometric consequence of the exact vacuum solution. No load-bearing step reduces by the paper's own equations to a fitted parameter renamed as prediction, nor does any central claim rely on a self-citation chain that itself lacks independent verification. The domain of validity for the non-asymptotically flat metric is an assumption about physical applicability rather than a definitional equivalence or fitted input, leaving the reported ties to pressure transitions as independent content derived from the spacetime geometry.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the spacetime being an exact vacuum Einstein solution, the disk being geometrically thin and optically thick, and the existence of a well-defined radial domain of self-consistency. No free parameters are explicitly fitted in the abstract; the quadrupolar strength appears as a fixed feature of the chosen metric family.

axioms (2)
  • domain assumption The given static axisymmetric metric is an exact solution of the vacuum Einstein equations.
    Invoked as the background geometry for the accretion calculation.
  • domain assumption The accretion flow can be treated as geometrically thin and optically thick.
    Standard thin-disk approximation used to derive orbital and radiative properties.

pith-pipeline@v0.9.0 · 5475 in / 1369 out tokens · 48805 ms · 2026-05-15T05:48:56.939555+00:00 · methodology

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Works this paper leans on

229 extracted references · 229 canonical work pages · 57 internal anchors

  1. [1]

    Journal of Mathematical Physics , keywords =

    Distorted black holes. Journal of Mathematical Physics , keywords =. doi:10.1063/1.525384 , adsurl =

    work page doi:10.1063/1.525384

  2. [2]

    Multipole Moments. II. Curved Space. Journal of Mathematical Physics , year = 1970, month = aug, volume = 11, pages =. doi:10.1063/1.1665427 , adsurl =

    work page doi:10.1063/1.1665427 1970

  3. [3]

    The mathematical theory of black holes

    Chandrasekhar, S. The mathematical theory of black holes. 2002

    work page 2002

  4. [4]

    Black Holes (Les Astres Occlus) , year = 1973, editor =

    Astrophysics of black holes. Black Holes (Les Astres Occlus) , year = 1973, editor =

    work page 1973

  5. [5]

    Time-Averaged Structure of Accretion Disk

    Disk-Accretion onto a Black Hole. Time-Averaged Structure of Accretion Disk. , year = 1974, month = jul, volume = 191, pages =. doi:10.1086/152990 , adsurl =

    work page doi:10.1086/152990 1974

  6. [6]

    , archivePrefix = "arXiv", eprint =

    Self-similar accretion in thin discs around near-extremal black holes. , archivePrefix = "arXiv", eprint =. doi:10.1093/mnras/stx748 , adsurl =

    work page doi:10.1093/mnras/stx748

  7. [8]

    and Fragile, P

    Abramowicz, Marek A. and Fragile, P. Chris. Foundations of Black Hole Accretion Disk Theory. Living Reviews in Relativity. 2013. doi:10.12942/lrr-2013-1

    work page doi:10.12942/lrr-2013-1 2013

  8. [9]

    , keywords =

    Accretion Disks around Kerr Black Holes: Vertical Equilibrium Revisited. , keywords =. doi:10.1086/303869 , adsurl =

    work page doi:10.1086/303869

  9. [10]

    Observational appearance

    Black holes in binary systems. Observational appearance. , year = 1973, volume = 24, pages =

    work page 1973

  10. [11]

    Journal of Mathematical Physics , year = 1983, month = may, volume = 24, pages =

    The multipole structure of stationary space-times. Journal of Mathematical Physics , year = 1983, month = may, volume = 24, pages =. doi:10.1063/1.525846 , adsurl =

    work page doi:10.1063/1.525846 1983

  11. [12]

    Ellis, G. F. R. , TITLE =. General relativity and cosmology (. 1971 , MRCLASS =

    work page 1971

  12. [15]

    , year = 1981, volume = 31, pages =

    A Model of a Thin Accretion Disk around a Black Hole. , year = 1981, volume = 31, pages =

    work page 1981

  13. [16]

    , keywords =

    Transonic accretion flow in a thin disk around a black hole. , keywords =

    work page

  14. [17]

    , keywords =

    Slim accretion disks. , keywords =. doi:10.1086/166683 , adsurl =

    work page doi:10.1086/166683

  15. [18]

    Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki , keywords =

    Gravitational Collapse of Non-Symmetric and Rotating Bodies. Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki , keywords =

    work page

  16. [19]

    W., & Ebeling, H

    Thin-disc theory with a non-zero-torque boundary condition and comparisons with simulations. , archivePrefix = "arXiv", eprint =. doi:10.1111/j.1365-2966.2011.20084.x , adsurl =

    work page doi:10.1111/j.1365-2966.2011.20084.x 2011

  17. [20]

    , year = 1972, month = dec, volume = 178, pages =

    Rotating Black Holes: Locally Nonrotating Frames, Energy Extraction, and Scalar Synchrotron Radiation. , year = 1972, month = dec, volume = 178, pages =. doi:10.1086/151796 , adsurl =

    work page doi:10.1086/151796 1972

  18. [21]

    , keywords =

    Relativistic Accretion Disk Structure Revisited. , keywords =. doi:10.1086/176161 , adsurl =

    work page doi:10.1086/176161

  19. [22]

    , year = 1968, month = feb, volume = 151, pages =

    On the Nature of Some Galactic X-Ray Sources. , year = 1968, month = feb, volume = 151, pages =. doi:10.1086/180148 , adsurl =

    work page doi:10.1086/180148 1968

  20. [23]

    N. D. Birell and P. C. W. Davies , year = 1982, title =

    work page 1982

  21. [24]

    R. P. Feynman. Phys.\ Rev. 1954

    work page 1954

  22. [25]

    Einstein and Yu Podolsky and N

    A. Einstein and Yu Podolsky and N. Rosen. Phys.\ Rev. 1935

    work page 1935

  23. [26]

    G. P. Berman, Jr. and F. M. Izrailev, Jr. Stability of nonlinear modes. Physica D. 1983

    work page 1983

  24. [27]

    E. B. Davies and L. Parns. Trapped modes in acoustic waveguides. Q. J. Mech. Appl. Math. 1988

    work page 1988

  25. [28]

    Edward Witten. 2001. hep-th/0106109

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  26. [29]

    E. Beutler. Williams Hematology. 1994

    work page 1994

  27. [30]

    Donald E. Knuth. Fundamental Algorithms. 1973b 1973

    work page 1973

  28. [31]

    J. S. Smith and G. W. Johnson. Philos. Trans. R. Soc. London, Ser. B. 2005

    work page 2005

  29. [32]

    W. J. Smith and T. J. Johnson and B. G. Miller. Surface chemistry and preferential crystal orientation on a silicon surface. 2010

    work page 2010

  30. [33]

    V. K. Smith and K. Johnson and M. O. Klein. Surface chemistry and preferential crystal orientation on a silicon surface. 2010

    work page 2010

  31. [34]

    Lower Bounds for Wishful Research Results

    Ulrich \" U nderwood and Ned \ N et and Paul \= P ot. Lower Bounds for Wishful Research Results

    work page

  32. [35]

    M. P. Johnson and K. L. Miller and K. Smith. 2007

    work page 2007

  33. [36]

    AIP Conf. Proc. 2007

    work page 2007

  34. [37]

    Fifteenth Annual

    Proc. Fifteenth Annual

    work page

  35. [38]

    Y. Burstyn. Proceedings of the 5th International Molecular Beam Epitaxy Conference, Santa Fe, NM. 2004

    work page 2004

  36. [39]

    Proceedings of the 2003 Particle Accelerator Conference, Portland, OR, 12-16 May 2005. 2001

    work page 2003

  37. [40]

    A. G. Agarwal. Proceedings of the Fifth Low Temperature Conference, Madison, WI, 1999. Semiconductors. 2001

    work page 1999

  38. [41]

    R. Smith. Hummingbirds are our friends. 2001

    work page 2001

  39. [42]

    J. Smith. Proc. SPIE. 2007

    work page 2007

  40. [43]

    An O(n n / \! n) Sorting Algorithm

    Tom T \' e rrific. An O(n n / \! n) Sorting Algorithm

    work page

  41. [44]

    Mastering Thesis Writing

    \' E douard Masterly. Mastering Thesis Writing

    work page

  42. [45]

    S. R. Kawa and S.-J. Lin. J. Geophys. Res. 2003

    work page 2003

  43. [46]

    Phidias Phony-Baloney

    F. Phidias Phony-Baloney. Fighting Fire with Fire: Festooning F rench Phrases

    work page

  44. [47]

    Donald E. Knuth. Seminumerical Algorithms. 1973c 1981

    work page 1981

  45. [48]

    Jill C. Knvth. The Programming of Computer Art

    work page

  46. [50]

    The Theory of Atom Lasers

    R. Ballagh and C.M. Savage. Bose-Einstein condensation: from atomic physics to quantum fluids. Proceedings of the 13th Physics Summer School. 2000. cond-mat/0008070

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  47. [51]

    Opechowski and R

    W. Opechowski and R. Guccione. Introduction to the Theory of Normal Metals. Magnetism. 1965

    work page 1965

  48. [52]

    J. M. Smith. Molecular Dynamics. 1980

    work page 1980

  49. [53]

    V. E. Zakharov and A. B. Shabat. Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media. Zh. Eksp. Teor. Fiz. 1971

    work page 1971

  50. [54]

    Daniel D. Lincoll. Semigroups of Recurrences. High Speed Computer and Algorithm Organization

    work page

  51. [55]

    Oaho and Jeffrey D

    Alfred V. Oaho and Jeffrey D. Ullman and Mihalis Yannakakis. On Notions of Information Transfer in VLSI Circuits. Proc. Fifteenth Annual ACM

    work page

  52. [56]

    The Definitive Computer Manual

    Larry Manmaker. The Definitive Computer Manual

    work page

  53. [57]

    RAGtime 4/5: Workshops on black holes and neutron stars , year = 2004, editor =

    Accretion disks in the Kerr-de Sitter spacetimes. RAGtime 4/5: Workshops on black holes and neutron stars , year = 2004, editor =

    work page 2004

  54. [58]

    Accretion disks around black holes in modified strong gravity

    Accretion disks around black holes in modified strong gravity. , keywords =. 2013. doi:10.1051/0004-6361/201220378 , archivePrefix =. 1212.2640 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201220378 2013

  55. [59]

    Thin accretion disks in stationary axisymmetric wormhole spacetimes

    Thin accretion disks in stationary axisymmetric wormhole spacetimes. , keywords =. 2009. doi:10.1103/PhysRevD.79.064001 , archivePrefix =. 0901.3926 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.79.064001 2009

  56. [60]

    Can accretion disk properties observationally distinguish black holes from naked singularities?

    Can accretion disk properties observationally distinguish black holes from naked singularities?. , keywords =. 2010. doi:10.1103/PhysRevD.82.124047 , archivePrefix =. 1011.4127 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.82.124047 2010

  57. [61]

    Thin accretion disks around neutron and quark stars

    Thin accretion discs around neutron and quark stars. , keywords =. 2009. doi:10.1051/0004-6361/200811412 , archivePrefix =. 0903.4746 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/200811412 2009

  58. [62]

    Can accretion disk properties distinguish gravastars from black holes?

    Can accretion disk properties distinguish gravastars from black holes?. Classical and Quantum Gravity , keywords =. 2009. doi:10.1088/0264-9381/26/21/215006 , archivePrefix =. 0905.1355 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0264-9381/26/21/215006 2009

  59. [63]

    Thin accretion disks around cold Bose-Einstein Condensate stars

    Thin accretion disks around cold Bose-Einstein condensate stars. European Physical Journal C , keywords =. 2015. doi:10.1140/epjc/s10052-015-3428-3 , archivePrefix =. 1504.06014 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1140/epjc/s10052-015-3428-3 2015

  60. [64]

    Accretion disc onto a static non-baryonic compact object

    Accretion disc onto a static non-baryonic compact object. Nuclear Physics B , keywords =. 2002. doi:10.1016/S0550-3213(02)00038-X , archivePrefix =. hep-ph/0201154 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/s0550-3213(02)00038-x 2002

  61. [65]

    Properties of a thin accretion disk around a rotating non-Kerr black hole

    Properties of a thin accretion disk around a rotating non-Kerr black hole. Physics Letters B , keywords =. 2012. doi:10.1016/j.physletb.2012.03.047 , archivePrefix =. 1110.3462 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physletb.2012.03.047 2012

  62. [66]

    Thin accretion disks in f(R) modified gravity models

    Thin accretion disks in f(R) modified gravity models. , keywords =. 2008. doi:10.1103/PhysRevD.78.024043 , archivePrefix =. 0806.0679 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.78.024043 2008

  63. [67]

    , keywords =

    Image of the Janis-Newman-Winicour naked singularity with a thin accretion disk. , keywords =. 2019. doi:10.1103/PhysRevD.100.024055 , archivePrefix =. 1905.05273 , primaryClass =

    work page doi:10.1103/physrevd.100.024055 2019

  64. [68]

    Thin accretion disk signatures of slowly rotating black holes in Ho\v{r}ava gravity

    Thin accretion disk signatures of slowly rotating black holes in Ho r ava gravity. Classical and Quantum Gravity , keywords =. 2011. doi:10.1088/0264-9381/28/16/165001 , archivePrefix =. 1009.1958 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0264-9381/28/16/165001 2011

  65. [69]

    2010", month =

    Black hole accretion disks in brane gravity via a confining potential. Classical and Quantum Gravity , year = "2010", month = "Dec", volume =. doi:10.1088/0264-9381/27/23/235004 , adsurl =

    work page doi:10.1088/0264-9381/27/23/235004 2010

  66. [70]

    Thin accretion disk signatures in dynamical Chern-Simons modified gravity

    Thin accretion disk signatures in dynamical Chern-Simons-modified gravity. Classical and Quantum Gravity , keywords =. 2010. doi:10.1088/0264-9381/27/10/105010 , archivePrefix =. 0909.1267 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0264-9381/27/10/105010 2010

  67. [71]

    Accretion disks around black holes in Scalar-Tensor-Vector Gravity

    Accretion disks around black holes in scalar-tensor-vector gravity. , keywords =. 2017. doi:10.1103/PhysRevD.95.104047 , archivePrefix =. 1705.02713 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.95.104047 2017

  68. [72]

    Thin accretion disk around a Kaluza-Klein black hole with squashed horizons

    Thin accretion disk around a Kaluza-Klein black hole with squashed horizons. Physics Letters B , keywords =. 2011. doi:10.1016/j.physletb.2011.09.071 , archivePrefix =. 1106.5183 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physletb.2011.09.071 2011

  69. [73]

    2018", month =

    Accretion disks around the Gibbons-Maeda-Garfinkle-Horowitz-Strominger charged black holes. European Physical Journal C , year = "2018", month = "Sep", volume =. doi:10.1140/epjc/s10052-018-6270-6 , adsurl =

    work page doi:10.1140/epjc/s10052-018-6270-6 2018

  70. [74]

    Self-gravitating accretion discs

    Self-gravitating accretion discs. Nuovo Cimento Rivista Serie , keywords =. 2007. doi:10.1393/ncr/i2007-10022-x , archivePrefix =. 0801.3848 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1393/ncr/i2007-10022-x 2007

  71. [75]

    1974", month =

    Perturbation of a Slowly Rotating Black Hole by a Stationary Axisymmetric Ring of Matter. I. Equilibrium Configurations. , year = "1974", month = "Jul", volume =. doi:10.1086/152992 , adsurl =

    work page doi:10.1086/152992 1974

  72. [76]

    Perturbation of a Schwarzschild black hole due to a rotating thin disc

    Perturbation of a Schwarzschild Black Hole Due to a Rotating Thin Disk. , keywords =. 2017. doi:10.3847/1538-4365/aa876b , archivePrefix =. 1710.07109 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-4365/aa876b 2017

  73. [77]

    Exact general relativistic thin disks around black holes , author =. Phys. Rev. D , volume =. 1994 , month =. doi:10.1103/PhysRevD.49.5135 , url =

    work page doi:10.1103/physrevd.49.5135 1994

  74. [78]

    Distorted Local Shadows

    Distorted local shadows. , keywords =. 2015. doi:10.1103/PhysRevD.91.084052 , archivePrefix =. 1502.00073 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.91.084052 2015

  75. [79]

    Multiple shadows from distorted static black holes

    Multiple shadows from distorted static black holes. , keywords =. 2018. doi:10.1103/PhysRevD.97.084024 , archivePrefix =. 1802.03062 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.97.084024 2018

  76. [81]

    Janis,A. I. and Newman,E. T. , title =. Journal of Mathematical Physics , volume =. 1965 , doi =

    work page 1965

  77. [82]

    Multipole expansions of gravitational radiation , author =. Rev. Mod. Phys. , volume =. 1980 , month =. doi:10.1103/RevModPhys.52.299 , url =

    work page doi:10.1103/revmodphys.52.299 1980

  78. [83]

    General relativity. 1984

    work page 1984

  79. [84]

    Hansen,R. O. , title =. Journal of Mathematical Physics , volume =. 1974 , doi =

    work page 1974

  80. [85]

    Explicit multipole moments of stationary axisymmetric spacetimes , volume=

    Bäckdahl, Thomas and Herberthson, Magnus , year=. Explicit multipole moments of stationary axisymmetric spacetimes , volume=. Classical and Quantum Gravity , publisher=. doi:10.1088/0264-9381/22/17/017 , number=

    work page doi:10.1088/0264-9381/22/17/017

Showing first 80 references.