arXiv subjects

Shafqat Ul Islam

Publications and source records attributed to Shafqat Ul Islam.

At least 19 recordsLinked to original sources

arXiv2026

Probing Kalb-Ramond gravity with charged rotating black holes: constraints from EHT observations

The Event Horizon Telescope (EHT) has guided strong-field gravitational physics by providing the first direct images of the supermassive black holes M87* and Sagittarius A*. The EHT observations offer unprecedented opportunities to test modified gravity theories against general relativity (GR). Motivated by this, we investigate charged rotating black holes in KR gravity, a framework motivated by string theory that incorporates spontaneous Lorentz symmetry breaking. The spacetime geometry is characterized by a Lorentz--violating parameter $\ell$ and electric charge $Q$, which modify the Kerr--Newman metric through a radial-dependent mass function. We compute black hole shadows and derive constraints on $\ell$ and $Q$ using EHT observations of M87* and Sgr A*. For angular shadow diameter $θ_{\rm sh}$ of M87* at inclination $θ_o=17^\circ$ and fixed $Q=0.2$, the EHT-allowed range $θ_{\rm sh}\in(35.1,\,40.5)\,μ\mathrm{as}$ constrains the Lorentz--violating parameter to approximately $-0.019\lesssim\ell\lesssim0.075$ and $-0.076\lesssim\ell\lesssim0.029$ across the admissible spin interval. For angular shadow diameter $θ_{\rm sh}$ of Sgr A* at inclination $θ_o=50^\circ$ and fixed $Q=0.2$, the corresponding EHT-allowed range $θ_{\rm sh}\in(41.7,\,55.7)\,μ\mathrm{as}$ permits approximately $-0.075\lesssim\ell\lesssim0.110$ and $-0.124\lesssim\ell\lesssim0.076$ across the admissible spin interval. Our analysis reveals that the Lorentz-violating parameter suppresses the shadow radius by a factor $\sqrt{1-\ell}$, while charge introduces additional distortions. Using the angular shadow diameter measured by EHT, we obtain an upper bound $\ell \lesssim 0.19$ from Sgr A* data with the stellar dynamics mass prior.

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arXiv2025

Probing Lorentz Symmetry Violation through Lensing Observables of Rotating Black Holes

We find a Kerr-like black hole solution-a rotating Bumblebee black hole (RBBH) with a Lorentz-violating parameter $\ell$ and examine the strong lensing by it. The parameter $\ell$ changes the event horizon radius and photon sphere, resulting in a different lensing signature compared to the Kerr black hole of general relativity. Using the strong deflection limit formalism, we compute key observables such as the angular positions of relativistic images, their separation, magnification, and time delays for supermassive black holes Sgr A* and M87*. Our results show that the parameter $\ell$ has a profound influence on these observables, with $\ell > 0$ suppressing and $\ell < 0$ increasing the deflection angle compared to the Kerr case. We compare RBBH observables with those of Kerr black holes, using Sgr A* and M87* as lenses to observe the effect of the Lorentz symmetry-breaking parameter $\ell$. For Sgr A*, the angular position $θ_\infty$ in $\in~(18.25-33.3)~μas$, while for M87* $\in~(13.71-25.02)~μas$. The angular separation $s$, for supermassive black holes (SMBHs) Sgr A* and M87*, differs significantly, with values ranging $\in~(0.005-0.81)~μas$ for Sgr A* and $\in~(0.003-0.6)~μas$ for M87*. The relative magnitude $r_{\text{mag}}$ $\in~(3.04-8.15)~μas$. We also compared the time delays between the relativistic images in the SMBHs and found that RBBH can be quantitatively distinguished from Kerr black holes. Our analysis concludes that, within the 1$σ$ region, a significant portion of the parameter space agrees with the EHT results of M87* and Sgr A*. This demonstrates the feasibility of utilizing strong gravitational lensing to identify Lorentz symmetry violations in extreme gravity regimes. Weak lensing analysis and Einstein ring observations provide further constraints, producing an upper bound of $\ell \lesssim \mathcal{O}(10^{-6})$.

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arXiv2025

Testing Strong Gravitational Lensing Effects of Supermassive Black Holes with String-Inspired Metric: Observational Signatures and EHT Constraints

We analyze gravitational lensing in the strong field limit for spherically symmetric string-inspired Euler-Heisenberg black holes, characterized by magnetic charge ($q$) and Einstein-Maxwell-dilaton coupling constants ($α, β$) from the low-energy limit of heterotic string theory. Our results show that the string coupling has a weak impact on the positions of relativistic images, deflection angles, photon orbit radii, and shadow sizes, making these black holes indistinguishable from the Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) black holes with the same mass and charge. Compared to Schwarzschild black holes, the string-inspired Euler-Heisenberg black holes exhibit smaller deflection angles, decreasing with increasing charge. Moreover, the time delay for Sgr A * and M87 * can reach $~11.477$ and $~17349.8$ minutes, respectively, at $q=0.1$ and $η=-1$, deviating from Schwarzschild black holes by $~0.0198$ and $~28.9$ minutes, which are not very significant. For Sgr A* and M87*, we determine $θ_\infty$ range within $(11.52, 26.33)~μas$, and $(9.17, 19.78)~μas$ respectively, with angular separations $s$ ranging from $(3.29-6.85)~nas$ for Sgr A* and $(2.47-5.15)~nas$ for M87*. EHT bounds on the $θ_{sh}$ of Sgr A* and M87* within the $1σ$ interval bound the $q$ as: for Sgr A* $0.54109\le q \le 0.7796 $ and for M87* $0< q \le 0.29107$, while in both the cases, we did not find any bound on the parameter $η$. We show that string-inspired Euler-Heisenberg black holes and EHT observations agree in the finite parameter space. A discussion on the effective metric has been included.

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arXiv2025

Shadows and parameter estimation of rotating quantum corrected black holes and constraints from EHT observation of M87* and Sgr A*

The scarcity of quantum gravity (QG) inspired rotating black holes limits the progress of testing QG through Event Horizon Telescope (EHT) observations. The EHT imaged the supermassive black holes, Sgr A* and M87*, revealing an angular shadow diameter of $d_{sh} = 48.7 \pm 7 μ$as with a black hole mass of $M = 4.0_{-0.6}^{+1.1} \times 10^6 M\odot$ for Sgr A*. For M87*, with a mass of $M = (6.5 \pm 0.7) \times 10^9 M_\odot$, the EHT measured an angular diameter of $θ_d = 42 \pm 3 μ$as. We present rotating quantum-corrected black hole (RQCBH) spacetimes with an additional QC parameter $α$ and constrain it by EHT observations. For angular shadow diameter ($d_{sh}$) of Sgr A* at $θ_o = 50^0$, the bounds are $0.0 \leq α\leq 1.443 M^2$ and $a \in (0, 0.8066 M)$. For $θ_o = 90^0$, the bounds are $0.0 \leq α\leq 1.447 M^2$ and $a \in (0, 0.894 M)$. While for M87* at inclination $θ_o = 17^0$, the bounds are $a \in (0, 0.8511 M)$ at $α=0$ and $a \in (0, 0.6157 M)$ at $α=0.8985 M^2$. For $θ_o = 90^0$, the bounds are $a \in (0, 0.8262 M)$ at $α=0$ and $a \in (0, 0.9799 M)$ at $α=0.4141 M^2$. These results show that $α$ significantly affects the shadows, offering key constraints on QG models. With EHT constraints from Sgr A and M87*, RQCBHs and Kerr black holes are indistinguishable in much of the EHT-constrained parameter space, making RQCBHs strong candidates for astrophysical black holes along with other BHs, e.g., regular black holes and other quantum-corrected solutions.

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arXiv2024

Photon orbits and phase transition for gravitational decoupled Kerr anti-de Sitter black holes

Interpreting the cosmological constant as the energy of the vacuum and using a gravitational decoupling approach leads to a new Kerr--anti-de Sitter (AdS) black hole. The metric of the new Kerr--AdS is simpler than the standard Kerr--AdS and exhibits richer geometry, where the effects of rotation appear as warped curvature. We investigate the relationship between unstable photon orbits and thermodynamic phase transitions in this new Kerr--AdS black hole background. We derive an exact expression for various thermodynamic properties, including mass ($M$), Hawking temperature ($T$), entropy ($S$), heat capacity ($C$), and free energy ($G$), by relating the negative cosmological constant to positive pressure through the equation $P = -Λ/(8 π) = 3/(8 πl^2)$, where $l$ represents the horizon radius, and by introducing its conjugate variable as the thermodynamic volume $V$. When $P < P_c$, black holes with $C_P > 0$ are thermodynamically stable, while those with $C_P \leq 0$ are unstable. Our analysis of the Gibbs free energy reveals a phase transition from small, globally unstable black holes to large, globally stable ones. Additionally, investigating the system's $P$-$V$ criticality and determining the critical exponents shows that our system shares similarities with a Van der Waals (vdW) fluid. In the reduced parameter space, we observe non-monotonic behavior of the photon sphere radius and the critical impact parameter when the pressure is below its critical value. Furthermore, we present the distribution of critical points in parameter space and derive a fitting formula for the coexistence curve.

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arXiv2024

Investigating Rotating Black Holes in Bumblebee Gravity: Insights from EHT Observations

The EHT observation revealed event horizon-scale images of the supermassive black holes Sgr A* and M87* and these results are consistent with the shadow of a Kerr black hole as predicted by general relativity. However, Kerr-like rotating black holes in modified gravity theories can not ruled out, as they provide a crucial testing ground for these theories through EHT observations. It motivates us to investigate the Bumblebee theory, a vector-tensor extension of the Einstein-Maxwell theory that permits spontaneous symmetry breaking, resulting in the field acquiring a vacuum expectation value and introducing Lorentz violation. We present rotating black holes within this bumblebee gravity model, which includes an additional parameter $\ell$ alongside the mass $M$ and spin parameter $a$ - namely RBHBG. Unlike the Kerr black hole, an extremal RBHBG, for $\ell<0$, refers to a black hole with angular momentum $a>M$. We derive an analytical formula necessary for the shadow of our rotating black holes, then visualize them with varying parameters $a$ and $\ell$, and also estimate the black hole parameters using shadow observables viz. shadow radius $R_s$, distortion $δ_s$, shadow area $A$ and oblateness $D$ using two well-known techniques. We find that $\ell$ incrementally increases the shadow size and causes more significant deformation while decreasing the event horizon area. Remarkably, an increase in $\ell$ enlarges the shadow radius irrespective of spin or inclination angle $θ_0$.

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arXiv2023

Strong Gravitational Lensing by Loop Quantum Gravity Motivated Rotating Black Holes and EHT Observations

We investigate gravitational lensing in the strong deflection regime by loop quantum gravity (LQG)-motivated rotating black hole (LMRBH) metrics with an additional parameter $l$ besides mass $M$ and rotation $a$. The LMRBH spacetimes are regular everywhere, asymptotically encompassing the Kerr black hole as a particular case and, depending on the parameters, describe black holes with one horizon only (BH-I), black holes with an event horizon and a Cauchy horizon (BH-II), black holes with three horizons (BH-III), or black holes with no horizons (NH) spacetime. It turns out that as the LQG parameter $l$ increases, the unstable photon orbit radius $x_{ps}$, the critical impact parameter $u_{ps}$, the deflection angle $α_D(θ)$ and angular position $θ_{\infty}$ also increases. Meanwhile, the angular separation $s$ decreases, and relative magnitude $r_{mag}$ increases with increasing $l$ for prograde motion but they show opposite behaviour for the retrograde motion. For Sgr A*, the angular position $θ_{\infty}$ is $\in$ (16.4, 39.8) $μ$as, while for M87* $\in$ (12.33, 29.9) $μ$as. The angular separation $s$, for SMBHs Sgr A* and M87*, differs significantly, with values ranging $\in$ (0.008-0.376) $μ$as for Sgr A* and $\in$ (0.006-0.282) $μ$as for M87*. We estimate the time delay between the first and second relativistic images using twenty supermassive galactic centre black holes as lenses. Our analysis concludes that, within the $1 σ$ region, a significant portion of the BH-I and BH-II and for a small portion of BH-III parameter space agrees with the EHT results of M87* and Sgr A* whereas NH is completely ruled out. We discover that the EHT results of Sgr A* place more stringent limits on the parameter space of LMRBH black holes than those established by the EHT results of M87*.

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arXiv2023

Rotating Kiselev Black Holes in $f(R,T)$ Gravity

Exact solutions describing rotating black holes can provide significant opportunities for testing modified theories of gravity, which are motivated by the challenges posed by dark energy and dark matter. Starting with a spherical Kiselev black hole as a seed metric, we construct rotating Kiselev black holes within the $f(R,T)$ gravity framework using the revised Newman-Janis algorithm - the $f(R,T)$ gravity-motivated rotating Kiselev black holes (FRKBH), which encompasses, as exceptional cases, Kerr ($K=0$) and Kerr-Newman ($K=Q^2$) black holes. These solutions give rise to distinct classes of black holes surrounded by fluids while considering specific values of the equation-of-state parameter, $w$, for viable choices for the $f(R,T)$ function. From the parameter space or domain of existence of black holes defined by $a$ and $γ$ for FKRBH, we discover that when $a_1 a_2$), we encounter two distinct critical values $γ=γ_{E1}, \; γ_{E2}$ with $γ_{E1}>γ_{E2}$ (or $γ=γ_{E3},\; γ_{E4}$ with $γ_{E3}>γ_{E4}$. We delve into the horizon and global structure of FKRBH spacetimes and examine their dependence on parameters $w$ and $γ$. This exploration is motivated by the remarkable effects of $f(R,T)$ gravity, which gives rise to diverse and intricate spacetime structures within the domain where black holes exist.

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arXiv2023

Investigating Loop Quantum Gravity with EHT Observational Effects of Rotating Black holes

A mathematically consistent rotating black hole model in loop quantum gravity (LQG) is yet lacking. The scarcity of rotating black hole solutions in LQG substantially hampers the development of testing LQG from observations, e.g., from the Event Horizon Telescope (EHT) observations. The EHT observation revealed event horizon-scale images of the supermassive black holes Sgr A* and M87*. The EHT results are consistent with the shadow of a Kerr black hole of general relativity. We present LQG-motivated rotating black hole (LMRBH) spacetimes, which are regular everywhere and asymptotically encompass the Kerr black hole as a particular case. The LMRBH metric describes a multi-horizon black hole in the sense that it can admit up to three horizons, such that an extremal LMRBH, unlike the Kerr black hole, refers to a black hole with angular momentum $a>M$. The metric, depending on the parameters, describes (1) black holes with only one horizon (BH-I), (2) black holes with an event horizon and a Cauchy horizons (BH-II), (3) black holes with three horizons (BH-III) or (4) no-horizon (NH) spacetime, which, we show, is almost ruled out by the EHT observations. We constrain the LQG parameter with the aid of the EHT shadow observational results of M87* and Sgr A*,respectively, for an inclination angle of $17^0$ and $50^0$. In particular, the VLTI bound for the Sgr A*, $δ\in (-0.17,0.01)$, constrains the parameters ($a,l$) such that for $0< l\leq 0.347851M\; (l\leq 2\times 10^6$ km), the allowed range of $a$ is $(0,1.0307M)$. Together with the EHT bounds of Sgr A$^*$ and M87$^*$ observables, our analysis concludes that a substantial part of BH-I and BH-II parameter space agrees with the EHT results of M87* and Sgr A*. While the EHT M87* results totally rule out the BH-III, but not that by Sgr A*.

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arXiv2022

Loop Quantum Gravity motivated multihorizon rotating black holes

With a semiclassical polymerization in the loop quantum gravity (LQG), the interior of Schwarzschild black holes provides a captivating single-horizon regular black hole spacetime. The shortage of rotating black hole models in loop quantum gravity (LQG) substantially restrains the progress of testing LQG from observations. Motivated by this, starting with a spherical LQG black hole as a seed metric, we construct a rotating spacetime using the revised Newman-Janis algorithm, namely, the LQG-motivated rotating black holes (LMRBH), which encompasses Kerr ($l=0$) black holes as an exceptional case. We discover that for any random $l>0$, unlike Kerr black hole, an extremal LMRBH refers to a black hole with angular momentum $a>M$. The rotating metric, in parameter space, describes (1) black holes with an event and Cauchy horizons, (2) black holes with three horizons, (3) black holes with only one horizon or (4) no horizon spacetime. We also discuss the horizon and global structure of the LMRBH spacetimes and its dependence on $l/M$ that exhibits rich spacetime structures in the ($M,\;a,\;l$) parameter space.

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arXiv2022

Testing strong gravitational lensing effects by supermassive compact objects with regular spacetimes

We compare and contrast gravitational lensing, in the strong-field limit, by photon sphere in spherically symmetric regular electrically charged (REC) black holes ($0 b_E$). Here, $b$ is additional parameter due to charge and the value $b=b_E \approx 0.226$ corresponds to an extremal black hole with degenerate horizons. Interestingly, the spacetime admits photon sphere for $0<b\leq b_P \approx 0.247$ and an anti-photon sphere only for $b_E < b \leq b_P$. With no-horizon spacetime, images by lensing from the inside of the photon sphere ($u<u_{ps}$) can also appear. Interestingly, for the case $u<u_{ps}$ the deflection angle $α_D$ increases with $u$. We analyse the lensing observables by modelling compact objects Sgr A*, M87*, NGC4649, and NGC1332 as black holes and no-horizon spacetimes. The angular position $θ_{\infty}$ and photon sphere radius $x_{ps}$ decrease with increasing parameter $b$. Our findings suggest that the angular separations ($s$) and magnification ($r$) of relativistic images inside the photon sphere may be higher than those outside. Moreover, the time delay for Sgr A* and M87* can reach $\sim$ 8.8809 min and $\sim$ 12701.8 min, respectively, at $b = 0.2$, deviating from Schwarzschild black holes by $\sim$ 2.615 min and $\sim$ 4677 min. These deviations are insignificant for Sgr A* because it is too small, but they are sufficient for astronomical observation of M87* and some other black holes. With EHT bounds on $θ_{sh}$ of Sgr A* and M 87*, within $1 σ$ region, placing bounds on the parameter $b$, our analysis concludes that the REC black holes agree with the EHT results in finite space, whereas the corresponding REC no-horizon spacetimes are completely ruled out.

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arXiv2022

Strong gravitational lensing by Bardeen black holes in 4D EGB gravity: constraints from supermassive black holes

Observation indicates that many nearby galaxies host supermassive central black holes. Modelling Bardeen models in four-dimensional Einstein-Gauss-Bonnet (4D EGB) gravity, with additional parameters $\tildeα$ and charge $q$, as central black holes in various galaxies, we investigate gravitational lensing properties in strong deflection limits. Interestingly, the spherical photon orbit radius $x_m$, the critical impact parameter $u_m$, the lensing coefficient $\bar{b}$, the deflection angle $α_D(θ)$, angular position $θ_{\infty}$ are decreasing with $q$ and $α$ whereas the other lensing coefficient $\bar{a}$ and angular separation $s$ have opposite behaviour. Taking the supermassive black holes Sgr A* and M87* as the lens, we also compare observable signatures of 4D EGB Bardeen black holes with those of the Schwarzschild black holes. The angular position $θ_\infty$ for Sgr A* $\in$ (23.1853, \; 25.56427) $μ$as, whereas for M87* it is $\in$ ( 17.941,\; 19.7819) $μ$as. Further, the angular separation $s$, which is an increasing function of $\tildeα$ and $q$ for Sgr A* and M87* differs significantly, respectively, in (0.031997,0.14895) $μ$as and (0.0247, 0.1152) $μ$as. The deviations of the lensing observables $Δθ_{\infty}$ and $Δs$ for 4D EGB Bardeen black hole ($\tildeα=0.9,~q=0.09$) from the Schwarzschild black hole, respectively, can reach up to $2.3789~μ$as and $0.11695~μ$as for Sgr A* , $1.84084~μ$as and $0.0905~μ$as for M87*. On the other hand, the relative magnification $\in$ (4.65751,\; 6.82173). Considering twenty-two massive central black holes as lens, we also estimate the time delay $ΔT^s_{2,1}$ between the first and second relativistic image to find that, e.g., the time delay for Sgr A* and M87*, respectively, can reach $\sim9.86088$~min and $\sim16023.93$~min.

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arXiv2021

Investigating strong gravitational lensing effects by suppermassive black holes with Horndeski gravity

We study gravitational lensing in strong-field limit by a static spherically symmetric black hole in quartic scalar field Horndeski gravity having additional hair parameter $q$, evading the no-hair theorem. We find an increase in the deflection angle $α_D$, photon sphere radius $x_{ps}$, and angular position $θ_{\infty}$ that increases more quickly while angular separation $s$ more slowly, but the ratio of the flux of the first image to all other images $r_{mag}$ decreases rapidly with increasing magnitude of the hair $q$. We also discuss the astrophysical consequences in the supermassive black holes at the centre of several galaxies and note that the black holes in Horndeski gravity can be quantitatively distinguished from the Schwarzschild black hole. Notably, we find that the deviation $Δθ_{\infty}$ of black holes in Horndeski gravity from their general relativity (GR) counterpart, for supermassive black holes Sgr A* and M87, for $q=-1$ respectively, can reach as much as $25.192~μ$as and $18.92~μ$as while $Δs$ is about $1.121~μ$as for Sgr A* and $0.8424~μ$as for M87*. The ratio of the flux of the first image to all other images suggest that the Schwarzschild images are brighter than those of the black holes in Horndeski gravity, wherein the deviation $|Δr_{mag}|$ is as much as 3.082. The results suggest that observational tests of hairy black holes in Horndeski gravity are indeed feasible.

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arXiv2021

Strong gravitational lensing by rotating Simpson--Visser black holes

We investigate strong field gravitational lensing by rotating Simpson-Visser black hole, which has an additional parameter ($0\leq l/2M \leq1$), apart from mass ($M$) and rotation parameter ($a$). A rotating Simpson-Visser metric correspond to (i) a Schwarzschild metric for $l/2M=a/2M=0$ and $ M \neq 0 $, (ii) a Kerr metric for $l/2M=0$, $|a/2M|< 0.5$ and $ M \neq 0 $ (iii) a rotating regular black hole metric for $|a/2M|< 0.5$, $ M \neq 0 $ and $l/2M$ in the range $0 0.5$ and $l/2M\neq 0$. We find a decrease in the deflection angle $α_D$ and also in the ratio of the flux of the first image and all other images $ r_{mag}$. On the other hand, angular position $θ_{1}$ increases more slowly and photon sphere radius $x_{m}$ decreases more quickly, but angular separation $s$ increases more rapidly, and their behaviour is similar to that of the Kerr black hole. The formalism is applied to discuss the astrophysical consequences in the supermassive black holes and find that the rotating Simpson-Visser black holes can be distinguished from the Kerr black hole via gravitational lensing. The deviation of the lensing observables $Δθ_1$ and $Δs$ of rotating Simpson Visser black holes from Kerr black hole for $0<l/2M <0.6$ ($a/2M=0.45$), for supermassive black holes Sgr A* and M87, respectively, are in the range $0.0422-0.11658~μ$as and $0.031709-0.08758~μ$as while $|Δr_{mag}|$ is in the range $0.2037 - 0.95668$. It is difficult to distinguish the two black holes because the departure are in $\mathcal{O}(μ$as), which are unlikely to get resolved by the current EHT observations. We also derive a two-dimensional lens equation and formula for deflection angle in the strong field limit by focusing on trajectories close to the equatorial plane.

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arXiv2021

Particle acceleration around rotating Einstein-Born-Infeld black hole and plasma effect on gravitational lensing

We consider a time-like geodesics in the background of rotating Einstein-Born-Infeld (EBI) black hole to examine the horizon and ergosphere structure. The effective potential that governs the particle's motion in the spacetime and the innermost stable circular orbits (ISCO) is also studied. A qualitative analysis is conducted to find the redshifted ultrahigh centre-of-mass (CM) energy as a result of a two-particle collision specifically near the horizon. The recent Event Horizon Telescope (EHT) triggered a surge of interest in strong gravitational lensing by black holes, which provide a new tool comparing the black hole lensing in general relativity and alternate gravity theories. Motivated by this, we also discussed both strong and weak-field gravitational lensing in the space-time discretely for a uniform plasma and a singular isothermal sphere. We calculated the light deflection coefficients $\bar{a}$ and $\bar{b}$ in the strong field limits, and their variance with the rotational parameter $a$ for different plasma frequency as well as in vacuum. For EBI black holes, we found that plasma's presence increases the photon sphere radius, the deflection angle, the deflection coefficients $\bar{a}$, $\bar{b}$, the angular positions and the angular separation between the relativistic images. It is also shown that with increasing spin the impact of plasma on a strong gravitational lensing becomes smaller as the spin parameter grows in the prograde orbit ($a>0$). For extreme black holes, the strong gravitational effects in the homogenous plasma are similar to those of in a vacuum. We investigate strong gravitational lensing effects by supermassive black holes Sgr A* and M87*...

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arXiv2021

Strong field gravitational lensing by hairy Kerr black holes

Recent times witnessed a surge of interest in strong gravitational lensing by black holes due to the Event Horizon Telescope (EHT) results, which suggest comparing the black hole lensing in general relativity and modified gravity theories. This may help us to assess the phenomenological differences between these models. A Kerr black hole is also a solution to some alternative theories of gravity, while recently obtained modified Kerr black holes (hairy Kerr black holes), which evade the no-hair theorem, are due to additional sources from surrounding fluid, like dark matter, having conserved energy momentum tensor (EMT). These hairy Kerr black holes may also be solutions to an alternative theory of gravity. We generalize previous work on gravitational lensing by a Kerr black hole in the strong deflection limits to the hairy Kerr black holes, with a deviation parameter $α$ and a primary hair $\ell_0$. Interestingly, the deflection coefficient $\bar{a}$ increases and decreases with increasing $\ell_0$ and $α$ respectively. $\bar{b}$ shows opposite behaviour with $\ell_0$ and $α$. We also find that the deflection angle $α_D$, angular position $θ_{\infty}$ and $u_{m}$ decrease, but angular separation $s$ increases with $α$. We compare our results with those for Kerr black holes, and also apply the formalism to discuss the astrophysical consequences in the context of the supermassive black holes Sgr A* and M87*. We observe that the deviations of the angular positions from that of the Kerr black hole are not more than $2.6~μ$as for Sgr A* and $1.96~μ$as for M87*, which are unlikely to be resolved by the current EHT observations.

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arXiv2021

Parameters estimation and strong gravitational lensing of nonsingular Kerr-Sen black holes

The recent time witnessed a surge of interest in strong gravitational lensing by black holes is due to the Event Horizon Telescope (EHT) results, which suggest comparing the black hole lensing in both general relativity and heterotic string theory. That may help us to assess the phenomenological differences between these models. Motivated by this, we consider gravitational lensing by the nonsingular Kerr-Sen black holes, which encompass Kerr black holes as a particular case, to calculate the light deflection coefficients $p$ and $q$ in strong-field limits, while the former increases with increasing parameters $k$ and charge $b$, later decrease. We also find a decrease in the light deflection angle $α_D$, angular position $θ_{\infty}$ decreases more slowly and impact parameter for photon orbits $u_{m}$ more quickly, but angular separation $s$ increases more rapidly with parameters $b$ and $k$. We compare our results with those for Kerr black holes, and also the formalism is applied to discuss the astrophysical consequences in the case of the supermassive black holes NGC 4649, NGC 1332, Sgr A* and M87*. In turn, we also investigate the shadows of the nonsingular Kerr-Sen black holes and show that they are smaller and more distorted than the corresponding Kerr black holes and nonsingular Kerr black holes shadows. The inferred circularity deviation $ΔC\leq 0.10$, for the M87* black hole shadow, put constraints on the nonsingular Kerr-Sen black hole parameters ($a, k$) and ($a, b$). The maximum shadow angular diameter for $b=0.30M$ and $k=0.30M$ are, respectively, $θ_d=35.3461\,μ$as and $θ_d=35.3355\,μ$as. We also estimate the parameters associated with nonsingular Kerr-Sen black holes using the shadow observables.

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arXiv2020

Gravitational lensing by charged black hole in regularized $4D$ Einstein-Gauss-Bonnet gravity

Among the higher curvature gravities, the most extensively studied theory is the so-called Einstein-Gauss-Bonnet (EGB) gravity, whose Lagrangian contains Einstein term with the GB combination of quadratic curvature terms, and the GB term yields nontrivial gravitational dynamics in $ D\geq5$. Recently there has been a surge of interest in regularizing, a $ D \to 4 $ limit of, the EGB gravity, and the resulting regularized $4D$ EGB gravity valid in $4D$. We consider gravitational lensing by Charged black holes in the $4D$ EGB gravity theory to calculate the light deflection coefficients in strong-field limits $\bar{a}$ and $\bar{b}$, while the former increases with increasing GB parameter $α$ and charge $q$, later decrease. We also find a decrease in the deflection angle $α_D$, angular position $θ_{\infty}$ decreases more slowly and impact parameter for photon orbits $u_{m}$ more quickly, but angular separation $s$ increases more rapidly with $α$ and charge $q$. We compare our results with those for analogous black holes in General Relativity (GR) and also the formalism is applied to discuss the astrophysical consequences in the case of the supermassive black holes Sgr A* and M87*.

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