Selection of the Valid Gravitation Theory from Observations of Black Hole Images$${}^{\sharp}$$

The Einstein–Euler–Heisenberg (EEH) black hole model represents an extension of classical black hole solutions in general relativity by incorporating quantum electrodynamic (QED) corrections. These corrections are introduced through the inclusion of the Euler–Heisenberg Lagrangian, which accounts for the nonlinear effects of QED in the presence of strong electromagnetic fields. This study investigates the observational properties of a thin accretion disk surrounding the electrically charged rotating EEH black hole. By exploring the influence of the spin parameter and charge on key dynamical quantities – such as the energy, angular momentum, angular velocity, and the innermost stable circular orbit (ISCO) of a test particle – it becomes possible to analyze the radiative flux, temperature distribution, and differential luminosity of the thin accretion disk in the spacetime of the charged rotating EEH black hole. The results are compared to those of Kerr and Kerr–Newman black holes in General relativity, revealing that QED corrections are found to increase the ISCO radius. Specifically, for a fixed electric charge, an increasing spin parameter leads to a larger ISCO radius compared to the standard Kerr black holes, as a result of additional electromagnetic corrections introduced by the Euler–Heisenberg theory. Conversely, when the spin parameter is held constant, an increase in the electric charge reduces the ISCO radius. Additionally, thin accretion disks around charged EEH rotating black holes exhibit higher temperatures and greater efficiency when the spin parameter is fixed and the electric charge is increased. However, for a constant electric charge, increasing the spin parameter results in an accretion disk that is cooler and has lower radiant efficiency. These findings highlight the potential of accretion disk processes as valuable tools for probing Euler–Heisenberg theory through astrophysical observations.

ABSTRACTMotivated by the fact that the universe is dominated by dark matter and dark energy, we consider rotating black holes surrounded by perfect fluid dark matter and study the accretion process in thin disc around such black holes. Here, we are interested in how the presence of dark matter affects the properties of the electromagnetic radiation emitted from a thin accretion disc. For this purpose, we use the Novikov–Thorne model and obtain the electromagnetic spectrum of an accretion disc around a rotating black hole in perfect fluid dark matter and compare with the general relativistic case. The results indicate that for small values of dark matter parameter we considered here, the size of the innermost stable circular orbits would decrease and thus the electromagnetic spectrum of the accretion disc increases. Therefore, discs in the presence of perfect fluid dark matter are hotter and more luminous than in general relativity. Finally, we construct thin accretion disc images around these black holes using the numerical ray-tracing technique. We show that the inclination angle has a remarkable effect on the images, whereas the effect of dark matter parameter is small.

In this thesis, I present a number of studies intended to improve our understanding of black holes using gravitational waves. Although black holes are relatively well understood from a theory perspective, many questions remain about the nature of the black holes in our Universe. According to general relativity, astrophysical black holes are fully described by just their mass and spin. Yet, relying on electromagnetic-based observatories alone, we still know very little about the distribution of black hole masses or spins. Moreover, as merging black holes are invisible to these electromagnetic observatories, we cannot rely on them to provide us with information about the binary black hole merger rate or binary black hole formation channels. However, by observing gravitational wave signals from these inherently dark binaries, we will soon have some answers to these questions. Indeed, the Laser Interferometer Gravitational-Wave Observatory (LIGO) has already revealed a great deal of new information about binary black holes; giving us an early glimpse into their mass and spin distributions and placing the first constraints on the binary black hole merger rate. This thesis contributes to the goal of probing the nature of black holes with gravitational waves. Binary black holes can form as an isolated binary in the galactic field or through dynamical encounters in high-density environments. Dynamical formation can significantly alter the binary parameters, which then become imprinted on the gravitational waveform. By simulating varying black hole populations in high-density globular clusters, we identify a population of highly eccentric binary black hole mergers that are characteristic of dynamical formation. Although these systems would circularize by the time they are visible in LIGO's frequency band, the future Laser Interferometer Space Antenna (LISA) is capable of distinguishing this population of eccentric mergers from the circular mergers expected of isolated field-formed binaries. As these dynamically formed binaries depend on the size of the underlying black hole population in globular clusters, we can utilize the dynamically formed merger rate to infer globular cluster black hole populations -- allowing us to reveal information about binary black hole birth environments. In order to properly estimate the parameters of binary black holes from detected gravitational wave signals, such as their masses and spins, high-accuracy waveforms are a needed. The highest accuracy waveforms are those produced by numerical relativity simulations, which solve the full Einstein equations. Using the Spectral Einstein Code (SpEC), we expand the reach of numerical relativity to simulate binary black holes with nearly extremal spins, i.e., black holes with spins near the maximal value χ = 1. These waveforms are used to calibrate existing waveform approximants used in LIGO data analyses. This ensures that the systematic errors in these approximants are small enough that if highly-spinning systems are observed, the spins are recovered without bias. Although rapidly spinning binaries have remained elusive thus far, these waveforms ensure that the highest-spin systems can be detected in the quest to uncover the spin distribution of black holes. The end state of a binary black hole merger is a newly born, single black hole that rings down like a struck bell, sending its last few ripples of gravitational waves out into the spacetime. Embedded in this 'ringdown' signal are a multitude of specific frequencies. Einstein's theory of general relativity precisely predicts the ringdown frequencies of a black hole with a given mass and spin. The statement that a black hole is entirely described by just these two parameters is known as the no-hair theorem. For black holes that obey the laws of general relativity (and consequently, the no-hair theorem), these frequencies serve as a fingerprint for the black hole. However, if the objects we observe are not Einstein's black holes, but instead something more exotic, the frequencies will not have this property and this would be a spectacular surprise. A minimum of two tones are required for this test, each with an associated frequency and damping time that depend only on the mass and spin. The conventional no-hair test relies on the so-called 'fundamental' tones of a black hole. A test relying on the fundamental modes is not expected to be feasible for another ~10-15 years, after detector sensitivity has improved significantly. However, by analyzing the ringdown of high-accuracy numerical relativity waveforms, we show that modes beyond the fundamental, known as 'overtones', are detectable in current detectors. The overtones are short-lived, but this is countered by the fact that they can initially be much stronger than the fundamental mode. By measuring two tones in the ringdown of GW150914 we perform a first test of the no-hair theorem. While the current constraints are rather loose, this first test serves as a proof of principle. This is just one example of the powerful tests that can be employed with overtones using present day detectors and the even more precise tests that can be accomplished with LISA in the future.

Research on the observational appearance of black holes, both in general relativity and modified gravity, has been in full swing since the Event Horizon Telescope Collaboration announced photos of M87* and Sagittarius A*. Nevertheless, limited attention has been given to the impact of tilted accretion disks on black hole images. This paper investigates the 230 GHz images of non-rotating hairy black holes illuminated by tilted, thin accretion disks in Horndeski gravity with the aid of a ray tracing method. The results indicate that reducing the scalar hair parameter effectively diminishes image luminosity and extends both the critical curve and the inner shadow. This trend facilitates the differentiation between hairy black holes and Schwarzschild black holes, especially in certain parameter spaces where the current Event Horizon Telescope array is capable of capturing such variations. Furthermore, we observe that the inclination of the tilted accretion disk can mimic the observation angle, consequently affecting image brightness and the morphology of the inner shadow. In specific parameter spaces, alterations in the tilt or position of the accretion disk can lead to a drift in the light spot within the images of hairy black holes. This finding may establish a potential correlation between the precession of the tilted accretion disk and image features. Additionally, through an examination of images depicting hairy black holes surrounded by two thin accretion disks, we report the obscuring effect of the accretion environment on the inner shadow of the black hole.

Astrophysical black holes could be nearly extremal (that is, rotating nearly as fast as possible); therefore, nearly extremal black holes could be among the binaries that current and future gravitational-wave observatories will detect. Predicting the gravitational waves emitted by merging black holes requires numerical-relativity simulations, but these simulations are especially challenging when one or both holes have mass m and spin S exceeding the Bowen–York limit of . We present improved methods that enable us to simulate merging, nearly extremal black holes (i.e., black holes with ) more robustly and more efficiently. We use these methods to simulate an unequal-mass, precessing binary black hole (BBH) coalescence, where the larger black hole has . We also use these methods to simulate a non-precessing BBH coalescence, where both black holes have , nearly reaching the Novikov–Thorne upper bound for holes spun up by thin accretion disks. We demonstrate numerical convergence and estimate the numerical errors of the waveforms; we compare numerical waveforms from our simulations with post-Newtonian and effective-one-body waveforms; we compare the evolution of the black hole masses and spins with analytic predictions; and we explore the effect of increasing spin magnitude on the orbital dynamics (the so-called ‘orbital hangup’ effect).

In this paper we compute the Arnowitt-Deser-Misner (ADM) mass, the angular\nmomentum and the charge of the Kerr black hole solution in the\nscalar-tensor-vector gravity theory [known as the Kerr-MOG (modified-gravity)\nblack hole configuration]; we study in detail as well several properties of\nthis solution such as the stationary limit surface, the event horizon, and the\nergosphere, and conclude that the new deformation parameter $\\alpha$ affects\nthe geometry of the Kerr-MOG black hole significantly in addition to the ADM\nmass and spin parameters. Moreover, the ADM mass and black hole event horizon\ndefinitions allow us to set a novel upper bound on the deformation parameter\nand to reveal the correct upper bound on the black hole spin. We further find\nthe geodesics of motion of stars and photons around the Kerr-MOG black hole. By\nusing them we reveal the expressions for the mass and the rotation parameter of\nthe Kerr-MOG black hole in terms of the red- and blueshifts of photons emitted\nby geodesic particles, i.e., by stars. These calculations supply a new and\nsimple method to further test the general theory of relativity in its strong\nfield limit: If the measured red- and blueshifts of photons exceed the bounds\nimposed by the general theory of relativity, then the black hole is not of Kerr\ntype. It could also happen that the measurements are allowed by the Kerr-MOG\nmetric, implying that the correct description of the dynamics of stars around a\ngiven black hole should be performed using MOG or another modified theory of\ngravity that correctly predicts the observations. In particular, this method\ncan be applied to test the nature of the putative black hole hosted at the\ncenter of the Milky Way in the near future.\n

Black holes in General Relativity are described by space-time metrics that are simpler in comparison to non-vacuum compact objects. However, given the universality of the gravitational pull, it is expected that dark matter accumulates around astrophysical black holes, which can have an impact in the overall gravitational field, especially at galactic centers, and induce non-negligible effects in their observational imprints. In this work, we study the optical appearance of a spherically symmetric black hole both when orbited by isotropically emitting light sources and when surrounded by a (geometrically and optically thin) accretion disk, while immersed in a dark matter halo. The black hole geometry plus the dark matter halo come as a solution of Einstein's field equations coupled to an anisotropic fluid whose density component follows a Hermquist-type distribution. We analyze in some depth the circular geodesic structure in both perturbative and non-perturbative regimes, investigating particular possible consequences for the structure of accretion disks. Despite this, however, even in situations in which the geodesic description differs profoundly from the isolated black hole case, we find minor modifications to the primary and secondary tracks of the isotropic orbiting sources, and to the width, location, and relative luminosity of the corresponding photon rings as compared to the Schwarzschild black hole at equal black hole mass and emission models. This shows that physical structures are crucial for understanding black hole images and points the limitations of drawing conclusions from more artificial imaging profiling. More profoundly, this fact points towards troubles distinguishing between both geometries using present observations of very-long baseline interferometry.

We study the gravitational lensing of acoustic charged black holes in strong and weak field limit approximations. For this purpose, we first numerically obtain the deflection limit coefficients and deflection angle in the strong field limit. We observe that the strong deflection angle α D increases with increasing magnitude of the charged parameter Q and that the strong deflection angle α D of an acoustic charged black hole with tuning parameter ξ = 4 is greater than that of a standard Reissner–Nordström black hole (ξ = 0). We also study the astrophysical consequences via strong gravitational lensing by taking the example of various supermassive black holes in the center of several galaxies and observe that the acoustic charged black hole could be quantitatively distinguished from standard Reissner–Nordström (ξ = 0) and standard Schwarzschild (ξ = 0, Q = 0) black holes. Furthermore, by using the Gauss–Bonnet theorem, we derive the weak deflection angle in the background of an acoustic charged black hole in the curved spacetime. We find that, for fixed values of the charged parameter Q and the tuning parameter (ξ = 0 or 4), the weak deflection angle σ D decreases with the impact parameter b. We also observe that the weak deflection angle σ D decreases with increasing magnitude of the charged parameter Q for a fixed value of the tuning parameter (ξ = 0 or 4). Our results suggest that the observational test for an acoustic charged black hole is indeed feasible, and it is generalized to the cases of acoustic Schwarzschild (Q = 0), standard Reissner–Nordström (ξ = 0), and standard Schwarzschild (ξ = 0, Q = 0) black holes.

In this paper, we investigate the gravitational lensing effects in the weak and strong field limits of a static black hole with conformally coupled scalar field. In the weak field limit, with the use of Gauss–Bonnet theorem we calculate the deflection angle of the light. It is found that comparing to Schwarzschild and Reissner–Nordstro¨\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ddot{\ ext {o}}$$\\end{document}m (RN) black holes in general relativity, the weak deflection angle can be enhanced/suppressed by the scalar hair. In the strong field limit, we first compute the light deflection angle via calculating the lensing coefficients, all of which increase as the values of electric and scalar charges increase. Then we evaluate the lensing observables in strong field regime by supposing the hairy black hole as the candidate of M87* and SgrA* supermassive black holes, respectively. We find that the scalar hair has significant influences on various observables. In particular, the lensing observables of the charged black hole with positive scalar hair and RN black hole have degeneracy, which will be broken by the case with negative scalar hair. Our theoretical findings imply that it is feasible to employ the gravitational lensing effects as a probe of Einstein–Maxwell theory with negative scalar field differentiating from general relativity, once the future astrophysical observation is precise enough.

We revisit the classic system of a spherically symmetric black hole in general relativity (i.e., a Schwarzschild black hole) surrounded by a geometrically thin accretion disk. Our purpose is to examine whether one can determine three parameters of this system (i.e., black hole mass $M$, distance between the black hole and an observer ${r}_{o}$, inclination angle $i$) solely by observing the accretion disk and the black hole shadow. A point in our analysis is to allow ${r}_{o}$ to be finite, which is set to be infinite in most relevant studies. First, it is shown that one can determine the values of $({r}_{o}/M,i)$, where $M/{r}_{o}$ is the so-called angular gravitational radius, from the size and shape of shadow. Then, it is shown that if one additionally knows the accretion rate $\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{M}$ (respectively, mass $M$) by any independent theoretical or observational approach, one can determine the values of $(M,{r}_{o},i)$ [respectively, $(\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{M},{r}_{o},i)$] without degeneracy, in principle, from the value of flux at any point on the accretion disk.

By considering the celestial light source and the thin disk source, we employ the backward ray-tracing method to carefully study the shadow, inner shadow and observational images of the non-singular rotating black holes in loop quantum gravity. The results show that the increase of quantum parameter λ causes the shadow to shrink, while increases the deviation from circularity. And, the shadow’s angular diameter of M87* impose stronger constraints on the observed properties of the no-singulgar rotating black holes by comparing with SgrA*. For a celestial light source, the parameter λ indeed influences the distortion of light around black hole shadow, but this effect is relatively small and only becomes noticeable when extremely close to the shadow. When a thin accretion disk around black hole, it turns out that for an observer at any position, the parameter λ has little effect on the shape of the inner shadow. However, it decreases the size of the inner shadow, reduces the observed light intensity, and narrows the redshifted shadow images, regardless of whether the accretion disk is prograde or retrograde. Meanwhile, it is true that the thin disk images of black hole cannot effectively reflect the internal structure of black hole. Finally, we can conclude that a key observational feature of these non-singular rotating black holes is that the larger the black hole’s spin parameter, the smaller the upper limit of λ’s effect. And, the parameter λ decreases the gravitational field’s strength, thereby weakens the observed images. This could provide a possible way to constraining black hole parameters, identifying quantum gravity effects, and distinguishing loop quantum gravity black holes, even if it cannot be used to distinguish the non-singular properties of black hole.

We consider a timelike 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 center-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 $\overline{a}$ and $\overline{b}$ 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 $\overline{a}$, $\overline{b}$, 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*. Considering rotating EBI black holes as the lens, we find the angular position of images for Sgr A* and M87* and observe that the deviations of the angular position from that of the analogous Kerr black hole are not more than $2.44\text{ }\text{ }\ensuremath{\mu}\mathrm{as}$ for Sgr A* and $1.83\text{ }\text{ }\ensuremath{\mu}\mathrm{as}$ for M87*, which are unlikely to get resolved by the current EHT observations.

The line profiles like that of the fluorescent Fe K or Co K lines in the X-ray spectra of the active galactic nuclei (AGN) reflect characteristics of the central regions of these objects. These lines can be formed in the accretion disks around central supermassive black holes and their shapes are connected with the central black hole spin and the accretion disk inclination angle to the line-of-the-sight. If an AGN is a source of a gravitational lens system with microlensing events, one can get an additional important information about both the accretion disk parameters and gravitational lens parameters as well. Microlensing processes were observed in such gravitational lens systems, as PKS 1830-211, B0218+357, RX J1131-1231 i HE1104-1805, Q2237+0305 and we can suspect to observe there also the spectral appearances of microlensing. Here we performed the numerical simulations of the microlensed relativistic spectral line profiles formed in the AGN accretion disks. Using the inear caustic model we show that the time dependence of the profile is determined essentially by the angle between to the disk axis and the caustic. This gives us an opportunity to assess this orientation. Microlens caustics magnify some parts of the accretion disk more prominently than others. Due to the Doppler effects and differences in the rotation direction this leads to the frequency-dependent magnification which distorts the profile of a relativistic spectral line. Such deformations are variable with time due to relative motions of the source and the microlens, and they can give us possibility to obtain some additional information about the disk brightness profile and caustic orientation relatively to the disk. Here we consider the thin disk model, Schwarzschild black hole, and the linear caustic approximation as well. The numerical simulations of the relativistic emission line profiles distorted by strong gravitational microlensing effect were performed for several different orientations of the linear caustic relatively to the disk, as well as several inclinations of the disk to the line-of-the-sight. Basic presumptions for the numerical modeling were the following: (a) AGN is a source in the gravitational lens system and it its inner parts the luminescent emission lines with relativistic profiles are being emitted; (b) this line is formed in the thin accretion disk quite far away from the central black hole and can be calculated with no taking into account the relativistic effects; (c) the caustic can be considered as a linear one. We show that the relative orientation of the caustic and the disk can be determined from emission lines profiles. Our numerical simulations demonstrate that the difference between profiles corresponding to different caustic orientations appears to be more prominent during the first half of the strong microlensing event, namely, before the crossing the disk center, and this dependence is irrespective to the accretion disk brightness profile. We show that for the spectral accuracy level high enough we have a perspective to determine the caustic orientation from the observational data.

Shadows and strong gravitational lensing by Van der Waals black hole in homogeneous plasma

Since the Event Horizon Telescope (EHT) collaboration released horizon-scale images of the supermassive black holes Sgr~A* and M87*, a new observational window for probing black hole spacetimes in the strong-gravity regime has opened. As an important class of Kerr black hole mimickers, rotating Simpson-Visser (SV) black holes exhibit a degeneracy with Kerr black holes at the level of shadow size, making it difficult to distinguish them using shadow observations alone.Motivated by this issue, we present a systematic investigation of the radiative properties and optical appearance of rotating SV black holes surrounded by a thin accretion disks, and mainly analyze the influence of the regularization parameter $g$ on related observables. The results show that although the kinetic quantities and the location of the innermost stable circular orbit (ISCO) depend on the regularization parameter $g$, the radiative efficiency of the rotating SV black hole is the same as its Kerr counterpart. Within the Novikov-Thorne thin-disk model, the radiative flux, effective temperature, and spectral luminosity are studied, and by adopting observational parameters relevant to Sgr~A* and M87*, concrete examples of the rotating SV black holes are calculated and compared with that of the Kerr black holes. The results show that the parameter $g$ suppresses the maximum values of these quantities. In addition, using a backward ray-tracing technique, we numerically simulate the optical appearance of rotating SV black holes and analyze the corresponding intensity images,
redshift and observed flux distributions. Our results show that these quantities are affected by $g$. In particular, as $g$ increases, the observed intensity is significantly suppressed and the photon ring region has remarkable increase in its width. Our findings suggest that accretion-disk-related observables may provide important avenues to distinguish rotating SV black holes and Kerr black holes, and offer theoretical guidance for future high-resolution observations.