Effect of null aether field on weak deflection angle of black holes

A. \"Ovg\"un; \.I. Sakall{\i}; J. Saavedra

REVIEW 2 major objections 4 minor 74 references

Effect of null aether field on weak deflection angle of black holes

T0 review · 2 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A null aether black hole bends light by an angle whose aether term adds to or subtracts from the Schwarzschild value, depending on the sign of $b_1$.

desk verdict The only new result, the plasma deflection angle, has a factor-of-three error in the plasma terms; the vacuum part is a correct but known re-derivation. read the letter →

arxiv 1908.04261 v2 pith:N6FPONXE submitted 2019-08-09 gr-qc hep-th

A. Övgün , İ. Sakall{i} , J. Saavedra This is my paper · ORCID

classification gr-qchep-th PACS 04.40.-b95.30.Sf98.62.Sb

keywords deflectionoflightGauss-Bonnettheoremgravitationallensingblackholenullaethertheoryweakangleplasmamedium

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper studies how light is bent when it passes near a black hole in null aether theory, a modified gravity in which a vector field fills spacetime and selects a preferred frame. Using the optical metric and the Gauss–Bonnet theorem, the authors compute the weak-field deflection angle of the null aether black hole and find $\hat{\alpha} \simeq \frac{3}{2}\frac{a_1^2 b_1 \pi}{u^2}+\frac{4\tilde{m}}{u}$, where $u$ is the impact parameter. The extra $b_1$ term is the aether's fingerprint: for $b_1<0$ it weakens the bending relative to Schwarzschild, for $b_1>0$ it strengthens it, and for $b_1=0$ the Schwarzschild result is recovered. In a homogeneous plasma the angle acquires additional terms proportional to $\omega_e^2/\omega_\infty^2$, so the effect becomes frequency dependent. This gives an analytic prediction for how Lorentz-symmetry breaking could appear in gravitational lensing, and it demonstrates that the bending can be read as a global topological effect through the Gauss–Bonnet theorem.

What carries the argument

The load-bearing object is the optical metric of the NAT spacetime used together with the Gauss–Bonnet theorem. The optical metric is the spatial metric obtained by setting $ds^2=0$ for light, so photon trajectories become geodesics of that metric; its Gaussian curvature $K$ measures how strongly the spatial geometry is curved. The Gauss–Bonnet theorem ties the integral of $K$ over a region bounded by the light ray and a circle at infinity to the boundary geodesic curvature and the Euler characteristic, yielding the deflection angle $\hat{\alpha}=-\int\int_D K\,dS$ in the asymptotically flat setting. The calculation is done in the weak-field limit by approximating the photon path as the straight line $r=u/\sin\phi$, which makes the integral analytic and produces the power-law terms in $1/u$ and $1/u^2$. For the plasma case the same machinery is reused with a refractive index $n(r)$ inserted into the optical metric, which modifies the Gaussian curvature and adds frequency-dependent terms.

What would settle it

Accurately measure the deflection angle of a well-modeled gravitational lens at several impact parameters and fit for a $1/u$ Schwarzschild term plus a $1/u^2$ aether term: if the $1/u^2$ coefficient is consistent with zero, then $b_1$ is zero or the $q=1$, $a_2=0$ subcase is not the one realized in nature.

Watch

Extended reading notes

Core claim

The central result is a closed-form weak deflection angle for the null aether black hole in the chosen asymptotically flat case $a_2=0$, $q=1$, with metric function $h(r)=1-\frac{2a_1^2 b_1}{r^2}-\frac{2\tilde{m}}{r}$ and aether field $\varphi(r)=a_1/\sqrt{r}$. From the optical metric the Gaussian curvature is approximately $K\approx -\frac{2\tilde{m}}{r^3}+\frac{6b_1(2\tilde{m}-r)a_1^2}{r^5}$; integrating it over the region outside the zeroth-order straight-line photon orbit $r=u/\sin\phi$ via the Gauss–Bonnet theorem yields Eq. (25), which the authors note agrees with the earlier result in the paper that introduced the NAT black hole. Depending on the sign of $b_1$, the aether field either suppresses or enhances light deflection compared with the Schwarzschild value $4\tilde{m}/u$, analogous to the charge effect in Reissner–Nordström. For a homogeneous plasma the deflection becomes $\hat{\alpha}\approx \frac{6\tilde{m}\,\omega_e^2}{u\,\omega_\infty^2}+\frac{4\tilde{m}}{u}+\frac{5a_1^2b_1\omega_e^2\pi}{2u^2\omega_\infty^2}+\frac{3a_1^2b_1\pi}{2u^2}$, which reduces to the vacuum result when the plasma frequency vanishes.

Load-bearing premise

The paper's deflection formula rests on the hand-picked restriction to $q=1$ and $a_2=0$ within the null aether black hole solution; if the theory selects different values, the aether contribution to the bending angle would change or vanish.

Editorial extensions

If this is right

For $b_1>0$, a ray passing a null aether black hole is bent more strongly than by a Schwarzschild black hole of the same mass; for $b_1<0$ it is bent less, and the two agree only at $b_1=0$.
In a homogeneous plasma the deflection is frequency dependent, so lensing observations across different frequencies would see image positions shift unless the plasma term is negligible.
The plasma contribution increases the bending angle, but for the representative ratio $\omega_e/\omega_\infty=6\times10^{-3}$ the authors judge it too small for near-future observation.
Setting the plasma frequency to zero in Eq. (33) returns exactly the vacuum formula (25), so the plasma result is a strict extension of the vacuum calculation.
Because the angle comes from integrating the Gaussian curvature, the result reinforces the view that the bending of light in this setting is a global, topological effect.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Because the clean $1/u^2$ aether term follows from the hand-set value $q=1$, other allowed values of $q$ would make the aether correction scale differently with impact parameter, so measuring that power law could select the NAT parameter $q$.
Observations would constrain the product $a_1^2b_1$ rather than the individual couplings, since the aether contribution enters the deflection only through that combination at leading order.
Applying the same optical-metric Gauss–Bonnet method to a rotating NAT black hole, which the authors list as future work, would give a deflection dependent on spin and allow a direct comparison with Kerr lensing.
A non-homogeneous plasma would introduce radius-dependent refractive-index integrals; the homogeneous-plasma formula here is the zeroth-order version of that more general lensing calculation.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague,

The one thing you should know: the only genuinely new calculation in this paper, the plasma deflection angle (Eq. 33), has a factor-of-three error in the plasma terms. The vacuum formula (Eq. 25) is explicitly a re-derivation of Eq. (115) of the NAT black hole paper [17], so the paper's contribution rests entirely on the plasma extension.

The vacuum part is done carefully. The Gaussian curvature (17) and the GBT integration give the expected leading terms, and the authors are honest that they match [17]. The restriction to a2=0, q=1 is stated, though not justified physically; that is a limitation but not a fatal one.

The problem is the plasma section. The optical metric (28) has area element sqrt(det g_opt) = r n^2 h^{-3/2} dr dφ, which to leading order is r(1-c) dr dφ with c=ω_e^2/ω_∞^2. The paper uses dS = r dr dφ (as in Eq. 24), which drops that (1-c). This inflates the plasma corrections. In the Schwarzschild limit, Eq. (33) gives 6 m c/u; the standard result is 2 m c/u. The factor of 3 traces directly to that area-element mistake. The new aether-plasma term 5a1^2 b1 c π/(2u^2) is therefore also unreliable. The authors would need to recompute the entire plasma deflection with the correct measure.

There is also a minor issue: the paper calls Eq. (25) 'second order', but it mixes a first-order mass term with a second-order aether term. That is imprecise, not damaging.

Who is this for? Someone working on GBT methods for lensing in modified gravity might find the vacuum derivation pedagogically useful, but the known result is in [17]. The plasma result, if corrected, could be a small addition. As written, the new content is wrong.

I would send it to referees rather than desk-reject: the error is concrete and fixable, the method is standard, and the audience exists. But I would expect the referee to flag the area-element problem and require a corrected plasma calculation before acceptance.

Referee Report

2 major / 4 minor

Summary. The manuscript uses the Gauss-Bonnet theorem to compute the weak-field deflection angle for a static spherically symmetric black hole in null aether theory (NAT). The authors specialize the general solution to a2=0 and q=1 (Eqs. (13)-(14)), derive the optical metric Gaussian curvature (17), and obtain the deflection angle α ≈ 4m̃/u + (3/2) a1² b1 π/u² in Eq. (25), in agreement with Eq. (115) of Ref. [17]. They then generalize the calculation to a homogeneous plasma, obtaining Eq. (33) with additional terms proportional to ω_e²/ω_∞². The paper concludes that the sign of b1 controls whether the aether enhances or reduces bending relative to Schwarzschild and that the plasma contribution is too small to be observed in the near future.

Significance. The vacuum calculation is a useful application of the GBT method and is correct at leading order: I independently reproduced Eq. (25) from Eqs. (17) and (24), and the agreement with Eq. (115) of Ref. [17] is a strong consistency check. The plasma part is the only genuinely new result, but it is not reliable as written because the GBT integrand uses the vacuum area element rather than the full determinant of the plasma optical metric; this affects the coefficient of every plasma term. Until that is corrected, the paper's quantitative plasma claim, including the new aether-plasma cross term, is unsubstantiated. The qualitative statement that the plasma increases the deflection is likely correct, and the special-case vacuum result remains valid.

major comments (2)

[III.B, Eqs. (28)-(33)] The GBT area element used in Eq. (32) is dS = r dr dφ, but the optical metric (28) has determinant √(det g_opt) = n² r h^{-3/2}, with n² = 1 - (ω_e²/ω_∞²) h. At leading order in the plasma frequency this measure contains a factor 1 - ω_e²/ω_∞², which is not negligible. In the Schwarzschild limit a1 = 0, Eq. (33) gives α ≈ 4m̃/u + 6m̃ c/u, with c = ω_e²/ω_∞², whereas the standard homogeneous-plasma Schwarzschild result is α ≈ 4M/u + 2M c/u to first order in c and M, equivalently (4M/u)(1 + c/[2(1-c)]) in the leading-in-M approximation. The factor of 3 arises precisely from omitting the n² factor in the measure; Eq. (29) already contains the n-dependent Gaussian curvature, so using the vacuum measure double-counts the plasma contribution. The same omission changes the aether-plasma term 5 a1² b1 c π/(2u²) in Eq. (33); with the correct measure this term must be recomputed and its coefficient will change. Please redo the integration in Section III.B with the full determinant of Eq. (28); the vacuum result (25) is not affected because the omitted h^{-3/2} pieces are higher order in m̃/u.
[II, Eqs. (6)-(14)] The calculation is restricted to the subfamily a2 = 0, q = 1, chosen by hand after Eq. (6). The general static NAT solution (4) contains an independent charge parameter a2 and an arbitrary q > 0; with a2 = 0 any q > 0 is asymptotically flat by Eq. (6), and the metric function for q ≠ 1 has a 1/r^{1+q} term that will enter the deflection angle differently. No physical or observational selection principle is given for q = 1. Because the abstract and title refer to 'the NAT black hole' without this restriction, the paper overstates the scope of its result. Please either justify the choice q = 1, a2 = 0, or explicitly restrict all claims and the title/abstract to this subfamily.

minor comments (4)

[III.B, Eq. (33)] The fourth term, '3a2b1π/(2u²)', should read '3 a1² b1 π/(2u²)' to be consistent with Eq. (25) and with the preceding aether-plasma term.
[IV] The sentence 'in the existence of plasma (ωe = 0)' should read 'ωe ≠ 0' (or 'ωe > 0'), since the following discussion concerns a nonzero plasma frequency.
[III.A, after Eq. (24)] The phrase 'second order due to the weak lensing' is inaccurate because Eq. (25) contains a leading term of order 1/u and a next-to-leading term of order 1/u²; specify the expansion parameter (for example m̃/u and a1²b1/u²) or call these the leading and next-to-leading orders.
[II and III.A, Eq. (15)] The symbol r0 is used for the closest-approach distance in Eq. (15) and for the horizon radius earlier in Section II; please disambiguate the notation.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the deflection-angle results are computed from the NAT metric and standard Gauss-Bonnet optical geometry, with no fitted parameter or self-citation chain bearing the central claim.

full rationale

The paper's central results, Eqs. (25) and (33), are obtained by direct calculation from the input metric (13) rather than by assuming the target deflection angles. The vacuum deflection angle (25) follows from the Gaussian curvature (17) through the standard GBT weak-field integral (24); no parameter is fitted to lensing data, and the aether parameter b1 enters through the metric itself, not through a quantity defined in terms of the deflection angle. The plasma formula (33) is likewise derived from the optical metric (28) with refractive index (27), following the Crisnejo-Gallo method [33]; it is not a renamed fit. The statement that Eq. (25) is in agreement with Eq. (115) of Ref. [17] is an independent check by non-overlapping authors (Gurses, Heydarzade, Senturk), not a self-citation. Self-citations in the paper are methodological references to prior applications of the GBT and do not carry the load of the derivation. The only substantive concern that could be raised, namely the skeptical critique about the area element used in the plasma section, is an algebraic/correctness issue and not a circular-definition issue. Therefore no step in the derivation reduces, by construction or by self-citation, to its own input.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claim rests on a special subcase (a2=0, q=1) of the NAT black hole solution from [17] and on the standard Gibbons-Werner optical geometry for weak lensing. No new particles, fields, or entities are introduced by this paper; the plasma medium is a standard background, not an invented entity.

free parameters (2)

q = 1
Chosen by hand in Section II ('taking q=1') to simplify the NAT metric; the full solution allows any q > 0, and the deflection formula depends on this choice.
a2 = 0
Set to zero in Section II ('we shall consider the case of a2=0') to select an asymptotically flat branch; this restriction is not justified physically.

assumptions (4)

domain assumption The line element in Eq. (13), obtained by setting a2=0 and q=1 in the NAT solution of [17], is a valid asymptotically flat spacetime.
The paper relies on reference [17] for the solution and does not re-derive or validate it here.
domain assumption The weak deflection angle is given by the Gauss-Bonnet theorem on the optical metric (Eq. 16) with the photon trajectory approximated by the straight line r = u/sin phi.
This is the standard Gibbons-Werner method (Eq. 24 and the line before it); it assumes small deflection and asymptotic flatness.
domain assumption The plasma refractive index is n(r) = sqrt(1 - (omega_e^2/omega_infinity^2) f(r)) (Eq. 27), with f(r) the metric function.
Taken from the plasma lensing literature [33]; used in Section III.B.
standard math Gauss-Bonnet theorem (Eq. 1).
Standard differential geometry result, taken as given.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Effect of null aether field on weak deflection angle of black holes." pith.science (2026). https://pith.science/paper/N6FPONXE

@misc{pith2026190804261,
  author       = {Pith},
  title        = {Pith review of: Effect of null aether field on weak deflection angle of black holes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/N6FPONXE}},
  note         = {Machine review of arXiv:1908.04261}
}

read the original abstract

We study the light rays in a static and spherically symmetric gravitational field of null aether theory (NAT). To this end, we employ the Gauss-Bonnet theorem to compute the deflection angle by a NAT black hole in the weak limit approximation. Using the optical metrics of the NAT black hole, we first obtain the Gaussian curvature and then calculate the leading terms of the deflection angle. Our calculations show how gravitational lensing is affected by the NAT field. We also show once again that the bending of light stems from a global and topological effect.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

74 extracted references · 68 canonical work pages

[17]

A Modiﬁed Gravity Theory: Null Aether,

M. G ¨ urses and C ¸ . S ¸ ent ¨ urk, “A Modiﬁed Gravity Theory: Null Aether,” Commun. Theor. Phys. 71, 312 (2019)

work page 2019
[1]

( 7) and ( 8) become h(r) = 1 − 2G2Q2b1 r2 ( r0 r ) q− 1 − 2 ˜m r , (9) φ(r) = GQ r ( r0 r ) (q− 1)/ 2

Setting a1 = GQr(q− 1)/ 2 0 , where Q is the NAT “charge”, Eqs. ( 7) and ( 8) become h(r) = 1 − 2G2Q2b1 r2 ( r0 r ) q− 1 − 2 ˜m r , (9) φ(r) = GQ r ( r0 r ) (q− 1)/ 2 . (10) At the location of r0, we have h(r0) = 1 − 2G2Q2b1 r2 0 − 2 ˜m r0 = 0, (11) φ(r0) = GQ r0 . (12) It is worth noting that the horizon condition ( 11) is independent of the parameter q....

work page
[2]

On the gravitational ﬁeld of a mass po int according to Einstein’s theory ,

K. Schwarzschild, “On the gravitational ﬁeld of a mass po int according to Einstein’s theory ,” Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys. ) 1916, 189 (1916)

work page 1916
[3]

Black Hole Shadows , Photon Rings, and Lensing Rings,

S. E. Gralla, D. E. Holz and R. M. Wald, “Black Hole Shadows , Photon Rings, and Lensing Rings,” Phys. Rev . D 100, 024018 (2019)

work page 2019
[4]

Constraining a black hole companion for M87* through imaging by the Event Horizon Telescope,

M. Safarzadeh, A. Loeb and M. Reid, “Constraining a black hole companion for M87* through imaging by the Event Horizon Telescope,” Mon. Not. Roy . Astron. Soc. 488, L90 (2019)

work page 2019
[5]

Black holes in Einstein-aether and Horava-Lifshitz gravity ,

E. Barausse, T. Jacobson and T. P . Sotiriou, “Black holes in Einstein-aether and Horava-Lifshitz gravity ,” Phys. Re v . D 83, 124043 (2011)

work page 2011
[6]

Horava gravity versus thermo dynamics: The Black hole case,

D. Blas and S. Sibiryakov , “Horava gravity versus thermo dynamics: The Black hole case,” Phys. Rev . D 84, 124043 (2011)

work page 2011
[7]

Black Holes in Einstein-Aethe r Theory ,

C. Eling and T. Jacobson, “Black Holes in Einstein-Aethe r Theory ,” Class. Quant. Grav . 23, 5643 (2006) Erratum: [Class. Quant. Grav .27, 049802 (2010)]

work page 2006

Show all 74 references

[8]

Rotating black h oles in three-dimensional Horava gravity ,

T. P . Sotiriou, I. V ega and D. V ernieri, “Rotating black h oles in three-dimensional Horava gravity ,” Phys. Rev . D 90, 044046 (2014)

2014
[9]

A no-go theorem for slowl y rotating black holes in Horava-Lifshitz gravity ,

E. Barausse and T. P . Sotiriou, “A no-go theorem for slowl y rotating black holes in Horava-Lifshitz gravity ,” Phys. R ev . Lett. 109, 181101 (2012) Erratum: [Phys. Rev . Lett. 110, 039902 (2013)]

2012
[10]

Slowly rotating black ho les in Horava-Lifshitz gravity ,

E. Barausse and T. P . Sotiriou, “Slowly rotating black ho les in Horava-Lifshitz gravity ,” Phys. Rev . D 87, 087504 (2013)

2013
[11]

Black holes in Lorentz- violating gravity theories,

E. Barausse and T. P . Sotiriou, “Black holes in Lorentz- violating gravity theories,” Class. Quant. Grav . 30, 244010 (2013)

2013
[12]

Renormalization of Horava gravi ty ,

A. O. Barvinsky , D. Blas, M. Herrero-Valea, S. M. Sibiry akov and C. F. Steinwachs, “Renormalization of Horava gravi ty ,” Phys. Rev . D93, 064022 (2016)

2016
[13]

Universal horizon s in maximally symmetric spaces,

J. Bhattacharyya and D. Mattingly , “Universal horizon s in maximally symmetric spaces,” Int. J. Mod. Phys. D 23, 1443005 (2014)

2014
[14]

Spherical solutions in Einst ein-aether theory: Static aether and stars,

C. Eling and T. Jacobson, “Spherical solutions in Einst ein-aether theory: Static aether and stars,” Class. Quant. Grav .23, 5625 (2006) Erratum: [Class. Quant. Grav . 27, 049801 (2010)]

2006
[15]

Grifﬁths, Introduction to Elementary Particles, 2n d, Revised Edition(John Wiley and Sons, M ¨ orlenbach, 2008)

D. Grifﬁths, Introduction to Elementary Particles, 2n d, Revised Edition(John Wiley and Sons, M ¨ orlenbach, 2008)

2008
[16]

Asymptotically Safe Standard Mod el Extensions?,

G. M. Pelaggi, A. D. Plascencia, A. Salvio, F. Sannino, J . Smirnov and A. Strumia, “Asymptotically Safe Standard Mod el Extensions?,” Phys. Rev . D 97, 095013 (2018)

2018
[18]

NAT Black Hole s,

M. Gurses, Y . Heydarzade and C. Senturk, “NAT Black Hole s,” Eur. Phys. J. C 79, 11, 942 (2019)

2019
[19]

Applications of the Gaus s-Bonnet theorem to gravitational lensing,

G. W. Gibbons and M. C. Werner, “Applications of the Gaus s-Bonnet theorem to gravitational lensing,” Class. Quant. Grav . 25, 235009 (2008)

2008
[20]

Gravitational lensing in the Kerr-Rande rs optical geometry ,

M. C. Werner, “Gravitational lensing in the Kerr-Rande rs optical geometry ,” Gen. Rel. Grav . 44, 3047 (2012)

2012
[21]

Weak ﬁeld deﬂection angle by regular black holes wi th cosmic strings using the Gauss-Bonnet theorem,

A. ¨Ovg ¨ un, “Weak ﬁeld deﬂection angle by regular black holes wi th cosmic strings using the Gauss-Bonnet theorem,” Phys. Rev . D99, 104075 (2019)

2019
[22]

Gravitational bending angle of light for ﬁnite distance an d the Gauss-Bonnet theorem,

A. Ishihara, Y . Suzuki, T. Ono, T. Kitamura and H. Asada, “Gravitational bending angle of light for ﬁnite distance an d the Gauss-Bonnet theorem,” Phys. Rev . D 94, 084015 (2016)

2016
[23]

Light deﬂection and GaussBonnet theorem: deﬁnition of total deﬂection angle and its applications,

H. Arakida, “Light deﬂection and GaussBonnet theorem: deﬁnition of total deﬂection angle and its applications,” G en. Rel. Grav .50, 48 (2018)

2018
[24]

Deﬂection angle of lig ht for an observer and source at ﬁnite distance from a rotatin g wormhole,

T. Ono, A. Ishihara and H. Asada, “Deﬂection angle of lig ht for an observer and source at ﬁnite distance from a rotatin g wormhole,” Phys. Rev . D 98, 044047 (2018)

2018
[25]

Gravitomagnetic bend ing angle of light with ﬁnite-distance corrections in stati onary axisymmetric spacetimes,

T. Ono, A. Ishihara and H. Asada, “Gravitomagnetic bend ing angle of light with ﬁnite-distance corrections in stati onary axisymmetric spacetimes,” Phys. Rev . D 96, 104037 (2017)

2017
[26]

Light deﬂection by charged wormhol es in Einstein-Maxwell-dilaton theory ,

K. Jusuﬁ, A. ¨Ovg ¨ un and A. Banerjee, “Light deﬂection by charged wormhol es in Einstein-Maxwell-dilaton theory ,” Phys. Rev . D96, n084036 (2017) Addendum: [Phys. Rev . D 96, 089904 (2017)]

2017
[27]

Exact traversable wormhol e solution in bumblebee gravity ,

A. ¨Ovg ¨ un, K. Jusuﬁ and I. Sakalli, “Exact traversable wormhol e solution in bumblebee gravity ,” Phys. Rev . D 99, 024042 (2019). 7

2019
[28]

Gravitational Lensing by Rotating Wormholes,

K. Jusuﬁ and A. ¨Ovg ¨ un, “Gravitational Lensing by Rotating Wormholes,” Phys. Rev . D97, 024042 (2018)

2018
[29]

Light Deﬂection by a Quantum Improved Kerr Black Ho le Pierced by a Cosmic String,

K. Jusuﬁ and A. ¨Ovg ¨ un, “Light Deﬂection by a Quantum Improved Kerr Black Ho le Pierced by a Cosmic String,” Int. J. Geom. Meth. Mod. Phys. (2019) 1950116

2019
[30]

Light Deﬂection by a Rotating Global Monopole Spacetime,

K. Jusuﬁ, M. C. Werner, A. Banerjee, and A. ¨Ovg ¨ un, “Light Deﬂection by a Rotating Global Monopole Spacetime,” Phys. Rev . D 95, no. 10, 104012 (2017)

2017
[31]

Effect of Lorentz Symmetry Breaking on the Deﬂecti on of Light in a Cosmic String Spacetime,

K. Jusuﬁ, I. Sakalli, and A. ¨Ovg ¨ un, “Effect of Lorentz Symmetry Breaking on the Deﬂecti on of Light in a Cosmic String Spacetime,” Phys. Rev . D 96, no. 2, 024040 (2017)

2017
[32]

Deﬂection angle of li ght for an observer and source at ﬁnite distance from a rotati ng global monopole,

T. Ono, A. Ishihara, and H. Asada, “Deﬂection angle of li ght for an observer and source at ﬁnite distance from a rotati ng global monopole,” Phys. Rev . D 99, no. 12, 124030 (2019)

2019
[33]

Gravitational lensing by wormholes supported by electromagnetic, scalar, and quantum effects,

K. Jusuﬁ, A. ¨Ovg ¨ un, A. Banerjee and I. Sakalli, “Gravitational lensing by wormholes supported by electromagnetic, scalar, and quantum effects,” Eur. Phys. J. Plus 134, no. 9, 428 (2019)

2019
[34]

Weak lensing in a plasma mediu m and gravitational deﬂection of massive particles using th e Gauss-Bonnet theorem. A uniﬁed treatment,

G. Crisnejo and E. Gallo, “Weak lensing in a plasma mediu m and gravitational deﬂection of massive particles using th e Gauss-Bonnet theorem. A uniﬁed treatment,” Phys. Rev . D 97, 124016 (2018)

2018
[35]

Finite distance c orrections to the light deﬂection in a gravitational ﬁeld wi th a plasma medium,

G. Crisnejo, E. Gallo, and A. Rogers, “Finite distance c orrections to the light deﬂection in a gravitational ﬁeld wi th a plasma medium,” Phys. Rev . D 99, 124001 (2019)

2019
[36]

Gravitati onal lensing in dispersive media and deﬂection angle of char ged massive particles in terms of curvature scalars and energy-momentu m tensor,

G. Crisnejo, E. Gallo, and J. R. Villanueva, “Gravitati onal lensing in dispersive media and deﬂection angle of char ged massive particles in terms of curvature scalars and energy-momentu m tensor,” Phys. Rev . D 100, no. 4, 044006 (2019)

2019
[37]

Hawking Radiation and Deﬂecti on of Light from Rindler Modiﬁed Schwarzschild Black Hole,

I. Sakalli and A. Ovgun, “Hawking Radiation and Deﬂecti on of Light from Rindler Modiﬁed Schwarzschild Black Hole,” EPL 118, no. 6, 60006 (2017)

2017
[38]

Weak Gravitational lensing by phantom black holes and phantom wormholes using the Gauss-Bonnet theorem,

A. ¨Ovg ¨ un, G. Gyulchev , and K. Jusuﬁ, “Weak Gravitational lensing by phantom black holes and phantom wormholes using the Gauss-Bonnet theorem,” Annals Phys. 406, 152 (2019)

2019
[39]

Effect of the cosmological constant on the deﬂecti on angle by a rotating cosmic string,

K. Jusuﬁ and A. ¨Ovg ¨ un, “Effect of the cosmological constant on the deﬂecti on angle by a rotating cosmic string,” Phys. Rev . D 97, 064030 (2018)

2018
[40]

Deﬂection of light by rotating regular black holes using the Gauss-Bonnet theorem,

K. Jusuﬁ, A. ¨Ovg ¨ un, J. Saavedra, Y . Vasquez, and P . A. Gonzalez, “Deﬂection of light by rotating regular black holes using the Gauss-Bonnet theorem,” Phys. Rev . D 97, 124024 (2018)

2018
[41]

Light deﬂection by Damour-Solodukhin wormholes and Gauss-Bonnet theorem,

A. ¨Ovg ¨ un, “Light deﬂection by Damour-Solodukhin wormholes and Gauss-Bonnet theorem,” Phys. Rev . D 98, 044033 (2018)

2018
[42]

Gravitational lensing un der the effect of Weyl and bumblebee gravities: Application s of GaussBonnet theorem,

A. ¨Ovg ¨ un, K. Jusuﬁ, and I. Sakalli, “Gravitational lensing un der the effect of Weyl and bumblebee gravities: Application s of GaussBonnet theorem,” Annals Phys. 399, 193 (2018)

2018
[43]

Deﬂection angle of photon through dark matter by black holes and wormholes using the Gauss-Bonnet theorem,

A. ¨Ovg ¨ un, “Deﬂection angle of photon through dark matter by black holes and wormholes using the Gauss-Bonnet theorem,” Universe 5, 115 (2019)

2019
[44]

Weak gravitational le nsing by Kerr-MOG Black Hole and Gauss-Bonnet theorem,

A. ¨Ovg ¨ un, I. Sakalli, and J. Saavedra, “Weak gravitational le nsing by Kerr-MOG Black Hole and Gauss-Bonnet theorem,” Annals Phys. 411, 167978 (2019)

2019
[45]

Shadow cast and Deﬂect ion angle of Kerr-Newman-Kasuya spacetime,

A. ¨Ovg ¨ un, I. Sakalli, and J. Saavedra, “Shadow cast and Deﬂect ion angle of Kerr-Newman-Kasuya spacetime,” JCAP 1810, 041 (2018)

2018
[46]

The effect of the Brane-Dicke coupling parameter o n weak gravitational lensing by wormholes and naked singularities,

W. Javed, R. Babar, and A. ¨Ovg ¨ un, “The effect of the Brane-Dicke coupling parameter o n weak gravitational lensing by wormholes and naked singularities,” Phys. Rev . D 99, 084012 (2019)

2019
[47]

Effect of the Dilaton Field on Deﬂection Angle of Ma ssive Photons by Black Holes in Einstein-Maxwell-Dilaton-Axion,

W. Javed, R. Babar, and A. ¨Ovg ¨ un, “Effect of the Dilaton Field on Deﬂection Angle of Ma ssive Photons by Black Holes in Einstein-Maxwell-Dilaton-Axion,” Theory . Phys. Rev . D100, no. 10, 104032 (2019)

2019
[48]

Deﬂection Angle of Photon from Magnetized Black Ho le and Effect of Nonlinear Electrodynamics,

W. Javed, J. Abbas, and A. ¨Ovg ¨ un, “ Deﬂection Angle of Photon from Magnetized Black Ho le and Effect of Nonlinear Electrodynamics,” Eur. Phys. J. C 79, no. 8, 694 (2019)

2019
[49]

Effect of the Quintessential Dark Energy on Weak De ﬂection Angle by Kerr-Newmann Black Hole,

W. Javed, J. Abbas and A. ¨Ovg ¨ un, “Effect of the Quintessential Dark Energy on Weak De ﬂection Angle by Kerr-Newmann Black Hole,” Annals Phys. 418, 168183 (2020)

2020
[50]

Effect of the Hair on Deﬂection Angle by Asymptotic ally Flat Black Holes in Einstein- Maxwell-Dilaton Theory ,

W. Javed, j. Abbas and A. ¨Ovg ¨ un, “Effect of the Hair on Deﬂection Angle by Asymptotic ally Flat Black Holes in Einstein- Maxwell-Dilaton Theory ,” Phys. Rev . D100, no. 4, 044052 (2019)

2019
[51]

Weak Deﬂection Angle of Extended Uncertainty Prin ciple Black Holes,

Y . Kumaran and A. ¨Ovg ¨ un, “Weak Deﬂection Angle of Extended Uncertainty Prin ciple Black Holes,” Chin. Phys. C 44, 025101 (2020)

2020
[52]

Gravitational deﬂection of rel ativistic massive particles by wormholes,

Z. Li, G. He and T. Zhou, “Gravitational deﬂection of rel ativistic massive particles by wormholes,” Phys. Rev . D 101, no. 4, 044001 (2020)

2020
[53]

Motion and trajectories of photons in a three-dime nsional rotating Hoˇ rava AdS black hole,

P . A. Gonzalez, M. Olivares, E. Papantonopoulos and Y . Vasquez, “Motion and trajectories of photons in a three-dime nsional rotating Hoˇ rava AdS black hole,” Phys. Rev . D101, no.4, 044018 (2020)

2020
[54]

Motion and collision of particles near DST Black holes,

P . A. Gonzalez, M. Olivares, Y . Vasquez, J. Saavedra andA. ¨Ovg ¨ un, “Motion and collision of particles near DST Black holes,” Eur. Phys. J. C 79, no. 6, 528 (2019)

2019
[55]

Motion and collision of particles in a rotating lin ear dilaton black hole,

P . A. Gonzalez, M. Olivares, E. Papantonopoulos and Y . Vasquez, “Motion and collision of particles in a rotating lin ear dilaton black hole,” Phys. Rev . D 97, no. 6, 064034 (2018)

2018
[56]

Particle colli sions near a three-dimensional warped AdS black hole,

R. Becar, P . A. Gonzalez and Y . Vasquez, “Particle colli sions near a three-dimensional warped AdS black hole,” Eur. Phys. J. C 78, no. 4, 335 (2018)

2018
[57]

Motion of magnetically charged parti cles in a magnetically charged stringy black hole spacetime,

P . A. Gonzalez, M. Olivares, E. Papantonopoulos, J. Saa vedra and Y . Vasquez, “Motion of magnetically charged parti cles in a magnetically charged stringy black hole spacetime,” Phys . Rev . D95, no. 10, 104052 (2017)

2017
[58]

Black hole explosions,

S. W. Hawking, “Black hole explosions,” Nature 248, 30 (1974)

1974
[59]

Particle Creation by Black Holes,

S. W. Hawking, “Particle Creation by Black Holes,” Comm un. Math. Phys. 43, 199 (1975) Erratum: [Commun. Math. Phys. 46, 206 (1976)]

1975
[60]

The Generalize d uncertainty principle and black hole remnants,

R. J. Adler, P . Chen, and D. I. Santiago, “The Generalize d uncertainty principle and black hole remnants,” Gen. Rel. Grav .33, 2101 (2001)

2001
[61]

Extended Uncertainty Principle Black H oles,

J. R. Mureika, “Extended Uncertainty Principle Black H oles,” Phys. Lett. B 789, 88 (2019). 8

2019
[62]

(Anti-)de Sitter black hole t hermodynamics and the generalized uncertainty principle,

B. Bolen and M. Cavaglia, “(Anti-)de Sitter black hole t hermodynamics and the generalized uncertainty principle, ” Gen. Rel. Grav .37, 1255 (2005

2005
[63]

Role of the scalar ﬁeld in gravitational lensing,

K. S. Virbhadra, D. Narasimha, and S. M. Chitre, “Role of the scalar ﬁeld in gravitational lensing,” Astron. Astroph ys. 337, 1 (1998)

1998
[64]

Principles of Gravitation al Lensing,

A. B. Congdon and C. Keeton, “Principles of Gravitation al Lensing,” Astronomy and Planetary Sciences, Springer In terna- tional Publishing (2018) 10.1007/978-3-030-02122-1

2018 doi
[65]

Principles of Astrophysics: Using Gravity and Stellar Physics to Explore the Cosmos (Undergraduate Le cture Notes in Physics),

C. Keeton, “Principles of Astrophysics: Using Gravity and Stellar Physics to Explore the Cosmos (Undergraduate Le cture Notes in Physics),” Springer (2014)

2014
[66]

Formalism for Testing Th eories of Gravity Using Lensing by Compact Objects. I: Stati c, Spherically Symmetric Case,

C. R. Keeton and A. O. Petters, “Formalism for Testing Th eories of Gravity Using Lensing by Compact Objects. I: Stati c, Spherically Symmetric Case,” Phys.Rev . D 72 (2005) 104006

2005
[67]

Effects of plasma on gravitational len sing,

X. Er and S. Mao, “Effects of plasma on gravitational len sing,” Mon. Not. Roy . Astron. Soc. 437 (2014) no.3, 2180

2014
[68]

Gravitationa l Lensing in Presence of Plasma: Strong Lens Systems, Black H ole Lensing and Shadow ,

G. S. Bisnovatyi-Kogan and O. Y . Tsupko, “Gravitationa l Lensing in Presence of Plasma: Strong Lens Systems, Black H ole Lensing and Shadow ,” Universe 3 (2017) no.3, 57

2017
[69]

G ravitational lensing by magnetized compact object in the pr es- ence of plasma,

B. Turimov , B. Ahmedov , A. Abdujabbarov and C. Bambi, “G ravitational lensing by magnetized compact object in the pr es- ence of plasma,” Int. J. Mod. Phys. D 28, no.16, 2040013 (2019)

2019
[70]

Periheli on precession and deﬂection of light in the general spherica lly symmetric spacetime,

Ya-Peng Hu, H. Zhang, J-Peng Hou, L-Zun Tang, “Periheli on precession and deﬂection of light in the general spherica lly symmetric spacetime,” Adv . High Energy Phys. 2014, 604321 (2014)

2014
[71]

Analytical formulas for gravita tional lensing,

P . Amore and S. Arceo, “Analytical formulas for gravita tional lensing,” Phys. Rev . D 73, 083004 (2006)

2006
[72]

Gravitationa l lensing in a non-uniform plasma,

G. S. Bisnovatyi-Kogan and O. Y . Tsupko, “Gravitationa l lensing in a non-uniform plasma,” Mon. Not. Roy . Astron. So c. 404, 1790 (2010)

2010
[73]

First-Princi ples Plasma Simulations of Black-Hole Jet Launching,

K. Parfrey , A. Philippov and B. Cerutti, “First-Princi ples Plasma Simulations of Black-Hole Jet Launching,” Phys . Rev . Lett. 122, 035101 (2019)

2019
[74]

Black hole shadow in a general rotating spac etime obtained through Newman-Janis algorithm,

R. Shaikh, “Black hole shadow in a general rotating spac etime obtained through Newman-Janis algorithm,” Phys. Rev . D 100, 024028 (2019). This figure "obs.png" is available in "png" format from: http://arxiv.org/ps/1908.04261v2

2019 arXiv

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [17]

A Modiﬁed Gravity Theory: Null Aether,

M. G ¨ urses and C ¸ . S ¸ ent ¨ urk, “A Modiﬁed Gravity Theory: Null Aether,” Commun. Theor. Phys. 71, 312 (2019)

work page 2019

[2] [1]

( 7) and ( 8) become h(r) = 1 − 2G2Q2b1 r2 ( r0 r ) q− 1 − 2 ˜m r , (9) φ(r) = GQ r ( r0 r ) (q− 1)/ 2

Setting a1 = GQr(q− 1)/ 2 0 , where Q is the NAT “charge”, Eqs. ( 7) and ( 8) become h(r) = 1 − 2G2Q2b1 r2 ( r0 r ) q− 1 − 2 ˜m r , (9) φ(r) = GQ r ( r0 r ) (q− 1)/ 2 . (10) At the location of r0, we have h(r0) = 1 − 2G2Q2b1 r2 0 − 2 ˜m r0 = 0, (11) φ(r0) = GQ r0 . (12) It is worth noting that the horizon condition ( 11) is independent of the parameter q....

work page

[3] [2]

On the gravitational ﬁeld of a mass po int according to Einstein’s theory ,

K. Schwarzschild, “On the gravitational ﬁeld of a mass po int according to Einstein’s theory ,” Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys. ) 1916, 189 (1916)

work page 1916

[4] [3]

Black Hole Shadows , Photon Rings, and Lensing Rings,

S. E. Gralla, D. E. Holz and R. M. Wald, “Black Hole Shadows , Photon Rings, and Lensing Rings,” Phys. Rev . D 100, 024018 (2019)

work page 2019

[5] [4]

Constraining a black hole companion for M87* through imaging by the Event Horizon Telescope,

M. Safarzadeh, A. Loeb and M. Reid, “Constraining a black hole companion for M87* through imaging by the Event Horizon Telescope,” Mon. Not. Roy . Astron. Soc. 488, L90 (2019)

work page 2019

[6] [5]

Black holes in Einstein-aether and Horava-Lifshitz gravity ,

E. Barausse, T. Jacobson and T. P . Sotiriou, “Black holes in Einstein-aether and Horava-Lifshitz gravity ,” Phys. Re v . D 83, 124043 (2011)

work page 2011

[7] [6]

Horava gravity versus thermo dynamics: The Black hole case,

D. Blas and S. Sibiryakov , “Horava gravity versus thermo dynamics: The Black hole case,” Phys. Rev . D 84, 124043 (2011)

work page 2011

[8] [7]

Black Holes in Einstein-Aethe r Theory ,

C. Eling and T. Jacobson, “Black Holes in Einstein-Aethe r Theory ,” Class. Quant. Grav . 23, 5643 (2006) Erratum: [Class. Quant. Grav .27, 049802 (2010)]

work page 2006