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Pankaj Sheoran

Publications and source records attributed to Pankaj Sheoran.

At least 19 recordsLinked to original sources
arXiv2026

Constraining ModMax Black Holes with EHT and GRAVITY Observations: Optical Signatures and Accretion Disk Properties

In this work, we study photon propagation and the radiative properties of a thin accretion disk around a ModMax black hole and examine the effects of the charge $Q$ (i.e. $Q^2 = Q^2_e +Q^2_m$ is the total dyonic charge, with $Q_e$ and $Q_m$ denoting the electric and magnetic charges, respectively) and the nonlinearity parameter $v$. We determine the event-horizon, photon-sphere, and shadow radii and find that increasing $Q$ decreases these radii, whereas increasing $v$ shifts them toward their Schwarzschild values. Using the EHT shadow measurements of M87$^\star$ and Sgr~A$^\star$, together with the available mass and distance measurements, we perform an MCMC analysis to constrain the ModMax parameters. The strongest upper limits are found to be $Q<0.391$ and $v<4.153$ at the 95\% credible level. We also investigate a Novikov-Thorne thin accretion disk and generate simulated disk images using backward ray tracing. The observed flux increases with $Q$, while increasing $v$ produces a slight decrease in the disk brightness. These results show how the ModMax parameters affect the black-hole shadow and thin-disk emission and provide observational constraints on $Q$ and $v$.

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arXiv2026

Comisso-Asenjo Mechanism in Rotating $\mathcal{N}=2,U(1)^2$ Gauged Supergravity Black Holes: Extended Comparison With Kerr Black Hole

In this paper, we investigate energy extraction via the Comisso-Asenjo (CA) magnetic reconnection process near a coupled $\mathcal{N}=2,\,U(1)^2$ gauged supergravity Black Hole (BH). Our study focuses on the combined impact of the independent parameter set $p_i\in(N_g,g,v,e)$ with the spin parameter $a$ on the extracted energy ($\epsilon_{\pm}$), efficiency ($\eta$), and extracted power ($\mathcal{P}_{CA}$), aiming to identify optimal combinations where energy can be extracted with higher efficiency in certain cases at lower spin $(a\sim0.39)$ than the Kerr extremal case $(a\sim1)$. Using the spacetime parameters, we explore various cases leading to distinct spacetimes and provide an extended comparison with the Kerr Black Hole (KBH). We also examine the influence of the orientation angle ($\xi$) and magnetization parameter ($\sigma_0$) on both efficiency and extracted power. Investigating low $[\,\forall p_i<0.2 \land N_g<0.08\,]$, mid $[\,\exists p_i\ge0.5 \land N_g\in(0.08,0.15)\,]$, high $[\,\exists p_i>0.7 \land N_g\in(0.16,0.23)\,]$, and mixed $[\,\forall p_i\in(0,1) \land N_g\in(0,0.23)\,]$ parameter combinations, we explore only extremal cases for all spacetime parameters and demonstrate that the extremal Kerr efficiency limit ($\eta>1.495$) can be exceeded. The statistical Kendall's Tau approach allows us to identify the key independent parameters acting as boosters or dampers in the energy extraction process and to visualize the relationship between $(N_g,g,v,e)$ and the physical outputs $(a_{\rm ext},r_E,r_{\rm ergo},\epsilon_{\pm},\eta,\mathcal{P}_{CA},R_{\eta},R_{\mathcal{P}})$. Furthermore, we show that the observable Lundquist number $S_{\rm obs}$ in rotating BH spacetimes acquires an observer-dependent angular dependence through the lapse function $(\alpha)$. This leads to deviations from the standard Sweet-Parker scaling when expressed in terms of observable quantities.

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arXiv2026

Magnetic Modification of Black Hole Photospheres with Image Contraction, Efficiency Shifts and Redshift Boosts in Schwarzschild-Bertotti-Robinson Spacetime

We investigate the optical and radiative signatures of an accretion disk around a Schwarzschild black hole (BH) immersed in a uniform magnetic field. The spacetime geometry is described by the Schwarzschild-Bertotti-Robinson (SBR) metric, which represents the non-rotating sector of the recently discovered Kerr-Bertotti-Robinson exact solution to the Einstein-Maxwell equations. We begin with the study of null geodesics and demonstrate that the self-consistent magnetic field fundamentally alters photon propagation, causing an expansion of light bundles relative to the Schwarzschild case due to modified initial conditions in the orbital equation. We then compute the magnetic field-dependent shifts of key characteristic radii: the event horizon ($r_h$), photon sphere ($r_{ph}$), and innermost stable circular orbit ($r_{ISCO}$). We find that all three increase monotonically with field strength $B$, revealing a magnetic amplification of the effective gravitational field. For $B=0.05$, we find that the lensed emission bands contract to a narrower impact parameter range, $b\in(4.976,5.149)\cup(5.19,6.128)$. Employing ray-tracing formalism, we construct observed accretion disk images and quantify magnetic modifications, showing that the direct image contracts while maximum energy flux, radiation temperature, and redshift factor are enhanced. Complementing these numerical findings, we develop an analytical framework for the accretion disk dynamics. We derive the modified Keplerian frequency $\Omega_K$, along with the specific energy $E$ and angular momentum $L$ for circular orbits. From these, we obtain the exact ISCO radius $r_{\text{ISCO}}$, which shows an outward shift. This outward shift reveals that the radiative efficiency decreases dramatically with increasing magnetic field strength $B$. For $\beta = BM \sim 0.1$, the efficiency drops by approximately $91\%$.

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arXiv2026

Optical Signatures of a Schwarzschild Black Hole in a Dehnen-Type Dark Matter Halo

In this paper, the optical effects that occur near a Schwarzschild-like black hole (BH) with a Dehnen-type $(1,4,2)$ dark matter (DM) halo are explored. We first derive the photon sphere radius and obtain an analytical expression for the deflection angle in the weak-field regime by applying the Gauss-Bonnet theorem (GBT). For the strong-field regime, we perform ray-tracing calculations to examine the behavior of light trajectories and determine the corresponding number of orbits. We further compute the BH shadow and gravitational lensing in a plasma medium and provide constraints arising from the DM halo parameters. We also extend our analysis to weak gravitational lensing within plasma environments, considering both uniform and singular isothermal sphere (SIS) distributions. We find the analytical expressions for the deflection angle in the presence of plasma and examine the resulting effects on image magnification. The overall results highlight how DM halo properties and plasma characteristics jointly alter observable lensing signatures.

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arXiv2026

Non-Monotonic Enhancement of the Magnetic Penrose Process in Kerr-Bertotti-Robinson Spacetime and its Implication for Electron Acceleration

We studied the magnetic Penrose process (MPP) in the Kerr-Bertotti-Robinson (KBR) spacetime, an exact rotating electrovacuum solution describing a black hole (BH) immersed in an intrinsic, uniform electromagnetic field. We analyze the behavior of charged particles in this geometry and find that the spacetime structure itself responds non-monotonically to the background magnetic field $B$. Specifically, both the event horizon and the static limit surface first expand as $B$ increases, reach a maximum size at an intermediate field strength, and then contract toward the extremal limit. Although the ergoregion itself shrinks monotonically with $B$, this structural feature gives rise to a pronounced non-monotonic dependence of the energy extraction efficiency on the magnetic field $B$, i.e., the efficiency initially rises, attains a maximum value, and subsequently falls as the extremal condition is approached. This contrasts sharply with the monotonic trends usually associated with magnetic enhancements in the Kerr geometry. We further explore an astrophysical application of the MPP by estimating the maximum energy of electrons escaping from the ergoregion of the KBR BH. Modeling neutron beta decay occurring near the event horizon, we derive an analytical expression for the energy gained by electrons accelerated by the magnetic field. Applying our results to the supermassive BH at the Galactic center, $\mathrm{SgrA}^*$, we find that electrons can be accelerated up to energies of $\sim 10^{15}\,\mathrm{eV}$ for realistic values of the spin and magnetic field. Although these energies exceed the observed upper range of cosmic-ray electrons, radiative losses such as synchrotron emission and inverse-Compton scattering can efficiently reduce them to the observed $\mathrm{TeV}$ scale.

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arXiv2025

Lensing Stability and Scattering Phenomena in Anisotropic Black Hole Spacetimes in Plasma

We investigate the physical and observational features of static, spherically symmetric black hole spacetimes surrounded by anisotropic fluid and embedded in a plasma environment. Motivated by recent advances in black hole imaging and precision measurements in strong gravity, we explore light propagation, wave dynamics, and observational signatures in such geometries. We begin by analyzing the background spacetime and matter content, examining the horizon structure and verifying the energy conditions associated with the anisotropic fluid. We then study photon trajectories in both vacuum and plasma environments, deriving the equations of motion and computing deflection angles and image magnifications under weak gravitational lensing. Both uniform and power-law plasma profiles are considered to model realistic astrophysical settings. In the wave optics regime, we first analyze the linear stability of the spacetime under axial (odd-parity) perturbations using Chandrasekhar's method, and then investigate scalar field scattering by solving the wave equation in the curved background with plasma. Using Born and WKB approximations, we compute the differential scattering cross-sections and examine how anisotropy and plasma affect interference features. Finally, we perform parameter estimation using Markov Chain Monte Carlo methods to constrain the black hole mass and anisotropic fluid parameters, utilizing EHT and GRAVITY data for Sgr A* and EHT-only data for M87*. These results present a unified theoretical framework that links anisotropic matter effects with lensing and scattering observables providing a firm basis for future comparisons with high-resolution astrophysical data sets in diverse contexts.

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arXiv2025

Nonlinear electrodynamic black holes and their role in testing modified theories of gravity

The nature of black holes (BHs) and their potential deviations from classical General Relativity (GR) remain central questions in modern astrophysics. Nonlinear electrodynamics (NED) offers a promising mechanism to construct regular BHs that avoid singularities while retaining key astrophysical features. In this work, we analyze NED-inspired BHs and derive constraints on the magnetic parameter using Bayesian parameter estimation from Event Horizon Telescope (EHT) observations. We obtain $q = 0.63 ^{+0.68}_{-0.44} \times 10^9 M_{\odot}$ for M87* and $q = 0.33 ^{+0.36}_{-0.23} \times 10^6 M_{\odot}$ for Sgr A*, affecting their horizon structure. A comparison with the Schwarzschild solution highlights deviations in geometry and horizon properties, emphasizing the impact of NED. We also examine observational signatures, including BH shadows and gravitational lensing. Using $R_{\text{sh}} = r_{\text{ph}} \sqrt{1/f(r_{\text{ph}})}$, we explore shadow features under uniform and non-uniform plasma conditions, revealing deviations from GR predictions due to NED effects. By analyzing photon sphere shifts and lensing patterns, we identify observable features that distinguish these BHs from classical ones. Our results suggest that NED-induced modifications may leave detectable imprints in strong-field regimes, opening pathways to test alternative gravity models. Future missions such as the Laser Interferometer Space Antenna (LISA) and next-generation X-ray observatories, along with ongoing observations from the EHT and gravitational wave detections by the Laser Interferometer Gravitational-Wave Observatory and Virgo (LIGO--Virgo), will be essential for refining constraints on such models.

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arXiv2024

Energy Extraction from Loop Quantum Black Holes: The Role of Magnetic Penrose Process and Quantum Gravity Effects with Astrophysical Insights

In this study, we explore the influence of quantum gravitational corrections, derived from Loop Quantum Gravity (LQG), on the efficiency of the magnetic Penrose process (MPP) in black hole (BH) environments. We begin by analyzing the rotating Loop Quantum Black Hole (LQBH) metric, describing the structure of the event horizon and ergosphere as functions of the quantum parameter $\epsilon = \gamma \delta$, with $\gamma$ representing the Immirzi parameter and $\delta$ the polymeric parameter, and the spin parameter $a$. These modifications provide a novel setting for exploring the dynamics of charged particles near the LQBH and evaluating the resultant energy extraction through the MPP. Interestingly, for a given value of the LQBH parameter $a$, we observe that the ergosphere region of the LQBH exhibits a more intricate structure compared to its classical counterpart, the Kerr BH, as $\epsilon$ increases. Furthermore, we find that the overall efficiency of the process decreases with $\epsilon$ that decreases $a_{max}$, again in contrast to the Kerr BH, where efficiency rises with an increasing $a$. Our analysis also extends to astrophysical contexts, applying constraints on the mass and magnetic field of LQBHs for astrophysical BH candidates, including SgrA*, M87*, NGC 1052, and BZ (Blandford and Znajek sources, i.e., supermassive BHs with masses around $10^9 M_\odot$ and magnetic fields in the range $10^3-10^4 \text{G}$). We assess these sources as potential accelerators of high-energy protons across different values of the quantum parameter $\epsilon$. Additionally, we examine how variations in the magnetic field strength $B$ and quantum corrections impact the energy of protons accelerated from M87$^{\star}$ and Sgr A$^{\star}$ following beta decay.

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arXiv2024

Astrophysical insights into magnetic Penrose process around parameterized Konoplya-Rezzolla-Zhidenko black hole

In this study, we investigate the parameterized Konoplya-Rezzolla-Zhidenko (KRZ) black hole (BH) spacetime in the presence of an external asymptotically uniform magnetic field. We first examine the innermost stable circular orbit (ISCO) radii for both neutral and charged test particles, demonstrating that the deformation parameters, $\delta_1$ and $\delta_2$, reduce the ISCO values. Subsequently, we assess the energy efficiency of the magnetic Penrose process (MPP) for an axially symmetric parameterized BH, analyzing the effects of the deformation parameters and the magnetic field on the energy extraction process. Our findings indicate that the rotational deformation parameter $\delta_2$ is crucial for the efficiency of energy extraction from the BH. The synergy between the rotational deformation parameter and the magnetic field significantly boosts the energy extraction efficiency, with values exceeding $100\%$. Interestingly, for extremal BHs with negative $\delta_2$ values, the energy efficiency increases, in contrast to Kerr BHs where the MPP effect diminishes. Additionally, we explore the astrophysical implications of the MPP by deriving the maximum energy of a proton escaping from the KRZ parameterized BH due to the beta decay of a free neutron near the horizon. Our results show that negative $\delta_2$ values require stronger magnetic fields to achieve equivalent energy levels for high-energy protons, providing deeper insights into high-energy astrophysical phenomena around the parameterized BH.

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arXiv2022

Efficiency of Penrose process in spacetime of axially symmetric magnetized Reissner-Nordström black hole

In this paper, we investigate the Penrose process in the purlieus of the axially symmetric magnetized Reissner-Nordström black hole for both neutral and charged particles. We start with the study of the geometry of the black hole and find the regions where the $g_{tt}$ component of the metric tensor is positive (i.e., $g_{tt}>0$). It is interestingly found that the condition $g_{tt}>0$ is fulfilled not only close to the event horizon known as the ergosphere but also far away from the event horizon in the silhouette of potential wells. We also show that as the dimensionless magnetic field $B$ increases the silhouette of potential wells for which $g_{tt}>0$ grows correspondingly and eventually merges with the ergoregion when $B\gtrsim 1.6$. Finally, we investigate the efficiency of the Penrose process for the axially symmetric magnetized black hole case and bring out the effect of the magnetic field on it. Further, we also compare our results with the one for Kerr black hole. We show that when the charge $Q$ of the black hole is kept constant, the efficiency of the energy extraction process for the case of {a neutral particle (i.e., $q/m=0$) first increases and then begins to decrease with rise in the value of $B$ field, in contrast to Kerr black hole where it always increases as the rotation parameter grows. However, for the case of a charged particle (i.e., $q\neq 0$) the efficiency always increases with the rise in the $B$ field and can go over $100\%$, when both $B$ and $q/m$ are large enough (say $B\approx1$ and $q/m>2.2$)}. It is worth noting that the existence of regions away from the horizon where $g_{tt}>0$ also favors the energy-extraction process away from the effect of the black hole. However, the energy extraction from these regions is pure consequence of the magnetic field.

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arXiv2022

Chaos motion and Periastron precession of spinning test particles moving in the vicinage of a Schwarzschild black hole surrounded by a quintessence matter field

In the present work, our main objective is to investigate the orbits of spinning test particles around a Schwarzschild black hole under the influence of a quintessence matter field (SQBH). We begin with the dynamics of the spinning test particles around SQBH which is governed by the Mathisson-Papapetrou-Dixon (MPD) equations under the pole-dipole approximation, where the gravitational field and the higher multipoles of the particle are neglected. Depending on the types of saddle points,the effective potential are classified and the possibility of chaotic orbits is discussed. The inner most stable circular orbits (ISCOs) of the spinning particle around SQBH are addressed, as are the effects of the parameters $S$ (particles' spin) and $ε$ (equation of state parameter). Later, Periastron precession is investigated up to the first-order spin correction for a spinning particle moving in nearly circular orbits around SQBH. It is noted that the addition of particle's spin revamps the results obtained for the non-spinning particles and also articulates the some interesting observational properties of the SQBH. Additionally, we discuss the ramifications of employing first-order spin corrections for analysing ISCOs, as well as compare our results to the Schwarzschild black hole to ensure that they are consistent in the limit when equation of state parameter $ε=-1/3$ and normalization factor $α\to 0$.

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arXiv2022

Motion of charged and spinning particle influenced by dark matter field surrounding a charged dyonic black hole

We investigate the motion of massive charged and spinning test particles around a charged dyonic black hole spacetime surrounded by perfect fluid scalar dark matter field. We obtain the equations of motion and find the expressions for the four-velocity for the case of a charged particle, and four-momentum components for the case of a spinning particle. The trajectories for various values of electric $Q_{e}$ and magnetic $Q_{m}$ charges are investigated under the influence of dark matter field $λ$. We find the equations of motion of a spinning particle that follows a non-geodesic trajectory via Lagrangian approach in addition to the charged and non-spinning particles that follow geodesic motion in this set-up. We study in detail the properties of innermost stable circular orbits (ISCOs) in the equatorial plane. The study of ISCOs of a spinning massive particle is done by using the pole-dipole approximation. We show that, in addition to the particle's spin, the dark matter field parameter $λ$ and black hole charges ($Q_{m}\;\text{and}\;Q_{e}$) have a significant influence on the ISCOs of spinning particles. It is observed that if the spin is parallel to the total angular momentum $J$ (i.e. $\mathcal{S}>0$), the ISCO parameters (i.e.$r_{ISCO}, L_{ISCO}\;\text{and}\; E_{ISCO}$) of a spinning particle are smaller than those of a non-spinning particle, whereas if the spin is anti-parallel to total angular momentum $J$ (i.e. $\mathcal{S}<0$), the value of the ISCO parameters is greater than that of the non-spinning particle. We also show that for the corresponding values of spin parameter S, the behaviour of Keplerian angular frequency of ISCO $Ω_{ISCO}$ is opposite to that of $r_{ISCO}, L_{ISCO}\; \text{and}\; E_{ISCO}$.

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arXiv2021

Charged black hole in $4D$ Einstein-Gauss-Bonnet gravity: Particle motion, plasma effect on weak gravitational lensing and centre-of-mass energy

We study the motion of charged and spinning particles and photons in the $4D$ charged Einstein-Gauss-Bonnet (EGB) black hole vicinity. We determine the radius of the innermost stable circular orbit (ISCO) for test particles. We show that the combined effect of the Gauss-Bonnet (GB) coupling parameter and black hole charge decreases the ISCO and the radius of the photon sphere. Further, we study the gravitational deflection angle and show that the impact of GB term and black hole charge on it is quite noticeable. We also consider the effect of plasma and find the analytical form of the deflection angle in the case of a uniform and non-uniform plasma. Interestingly we find that the deflection angle becomes larger when uniform plasma is considered in comparison to the case of non-uniform plasma. We also study the center of mass energy ($E_{C.M.}$) obtained by collision process for non-spinning particles and show that the impact of GB parameter and black hole charge leads to high energy collision. In addition, we also study the $E_{C.M.}$ for the case of spinning particles and show that if the two spinning particles collide near the horizon of $4D$ charged EGB BH, the $E_{C.M.}$ becomes infinitely high which is in disparity with the non-spinning particles counterpart where $E_{C.M.}$ never grows infinitely. To achieve this, an important role is played by the spinning particle known as the \textit{near-critical} particle (i.e. a particle with fine-tuned parameters). In order to achieve the unbounded $E_{C.M}$ from the collision of two spinning particles, the energy per unit mass must be less than unity for a \textit{near-critical} particle, which means such a particle starts from some intermediate position $r>r_{h}$ and not from infinity.

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arXiv2021

Mass parameter and the bounds on redshifts and blueshifts of photons emitted from geodesic particle orbiting in the vicinity of regular black holes

We obtain the mass parameter for a class of static and spherically symmetric regular black holes (BHs) (namely Bardeen, Hayward and Ayón-Beato-García BHs) which are solutions of Einstein's field equations coupled to nonlinear electrodynamics (NED) in terms of redshifts and blueshifts of photons emitted by geodesic particles (for instance, stars) orbiting around these BHs. The motion of photons is not governed by null geodesics for these type of spacetime geometries which reflects the direct effects of the electrodynamic nonlinearities in the photon motion; hence, an effective geometry needs to be constructed to study null trajectories [Phys. Rev. D61, 045001 (2000)]. To achieve the above, we first study the constants of motion from the analysis of the motion of both geodesic particles moving in stable circular orbits and photons ejected from them and reaching a distant observer (or detector) in the equatorial plane for the above mentioned regular BHs. The relationship between red/blueshifts of photons and the regular BH observables is presented. We also numerically find the bounds on the photon shifts for these regular BH cases.

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arXiv2020

Schwarzschild black hole surrounded by quintessential matter field as an accelerator for spinning particles

We study the collision of two massive particles with non-zero intrinsic spin moving in the equatorial plane in the background of a Schwarzschild black hole surrounded by quintessential matter field (SBHQ). For the quintessential matter equation of state (EOS) parameter, we assume three different values. It is shown that for collisions outside the event horizon, but very close to it, the centre-of-mass energy ($E_{\rm CM}$) can grow without bound if exactly one of the colliding particles is what we call near-critical, i.e., if its constants of motion are fine tuned such that the time component of its four-momentum becomes very small at the horizon. In all other cases, $E_{\rm CM}$ only diverges behind the horizon if we respect the Møller limit on the spin of the particles. We also discuss radial turning points and constraints resulting from the requirement of subluminal motion of the spinning particles.

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arXiv2020

Particle collisions near static spherically symmetric black holes

It has been shown by Bañados, Silk and West (BSW) that the center of mass energy (E_cm) of test particles starting from rest at infinity and colliding near the horizon of a Schwarzschild black hole is always finite. In this communication, we extent the BSW scenario and study two particles with different energies colliding near the horizon of a static spherically symmetric black hole. Surprisingly, we find that even for the static spherically symmetric (i.e., Schwarzschild like) black holes it is possible to obtain an arbitrarily high E cm from the two test particles colliding near the horizon of a black hole, if one fine-tunes the parameters of geodesic motion.

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arXiv2020

Bounds on spinning particles in their innermost stable circular orbits around rotating braneworld black hole

We study the innermost stable circular orbit (ISCO) of a spinning test particle moving in the vicinity of an axially symmetric rotating braneworld black hole (BH). We start with the description of the event horizon, static limit surface and ergosphere region of such BH and bring out the effect of tidal charge parameter on ergosphere. It is found that the ISCO of rotating braneworld BH is very sensitive to braneworld BH parameter C (also known as tidal charge parameter) in addition to its rotation parameter. We further discovered that the orbital radius of the spinning test particles changes non monotonously with the braneworld BH tidal charge parameter. It is found that for rotating braneworld BH the allowed range of the particle spin grows as the tidal charge parameter C decreases, in contrast with the Kerr Newman BH. We also found the similar behavior of the particles spin for the braneworld Reissner Nordstrom (C < 0) BH in contrast with its counterpart having (C > 0).

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arXiv2018

Mass and spin of a Kerr black hole in modified gravity and a test of the Kerr black hole hypothesis

In this paper we compute the Arnowitt-Deser-Misner (ADM) mass, the angular momentum and the charge of the Kerr black hole solution in the scalar-tensor-vector gravity theory [known as the Kerr-MOG (modified-gravity) black hole configuration]; we study in detail as well several properties of this solution such as the stationary limit surface, the event horizon, and the ergosphere, and conclude that the new deformation parameter $α$ affects the geometry of the Kerr-MOG black hole significantly in addition to the ADM mass and spin parameters. Moreover, the ADM mass and black hole event horizon definitions allow us to set a novel upper bound on the deformation parameter and to reveal the correct upper bound on the black hole spin. We further find the geodesics of motion of stars and photons around the Kerr-MOG black hole. By using them we reveal the expressions for the mass and the rotation parameter of the Kerr-MOG black hole in terms of the red- and blueshifts of photons emitted by geodesic particles, i.e., by stars. These calculations supply a new and simple method to further test the general theory of relativity in its strong field limit: If the measured red- and blueshifts of photons exceed the bounds imposed by the general theory of relativity, then the black hole is not of Kerr type. It could also happen that the measurements are allowed by the Kerr-MOG metric, implying that the correct description of the dynamics of stars around a given black hole should be performed using MOG or another modified theory of gravity that correctly predicts the observations. In particular, this method can be applied to test the nature of the putative black hole hosted at the center of the Milky Way in the near future.

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