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Black hole solutions in general relativity come with pathologies such as singularity and mass inflation instability, which are believed to be cured by a yet-to-be-found quantum theory of gravity. Without such consistent description, one may model theory-agnostic phenomenological black holes that bypass the aforesaid issues. These so-called regular...
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... for fixed values of (M, a * , θ i , D), there can be a range of e-values for which the shadow will be inconsistent with the angular size θ d [60,61] as observed by EHT, check Table 1. For this purpose, let us first consider the , we have shown below the variation in shadow size using contour plots Fig. 4. From these plots, it is very easy to identify the disallowed regions which are inconsistent with EHT observations. ...Citations
... The frequencies and damping times associated with these oscillations serve as key characteristics of QNMs, providing essential information about the internal structure and properties of the BH. Departures from GR are anticipated to leave a discernible mark on the QNM spectra, serving as a distinct means of investigating quantum gravity effects [27][28][29][30][31][32][33][34][35][36][37][38][39]. ...
This paper explores the properties of the quasinormal modes (QNMs) of a regular black hole (BH) characterized by a Minkowski core and sub-Planckian curvature. When focusing on a special case, this regular BH exhibits identical large-scale behavior with the Hayward BH and some loop quantum gravity corrected (LQG-corrected) BH. A notable characteristic of the QNMs in this regular BH is the pronounced outburst of overtones when compared to the Schwarzschild BH (SS-BH). This outburst can be attributed to the deviation from the SS-BH in the near-horizon geometry region due to the quantum gravity effect. Furthermore, we compare the QNM properties of the regular BH with those of the Hayward BH and the LQG-corrected BH. A similar phenomenon of overtone outburst is observed in the modes of the overtone. As a conclusion, the QNMs may be a powerful tool for detecting the quantum gravity effect and distinguishing different BH models.
... Refs. [86][87][88][89][90][91][92] and the formalism devised in Ref. [93], which has also been generalized to cosmological settings [67][68][69]). Therefore, exploring possible connections with these approaches would represent a fascinating topic. ...
We investigate a Schwarzschild metric exhibiting a signature change across the event horizon, which gives rise to what we term a Lorentzian-Euclidean black hole. The resulting geometry is regularized by employing the Hadamard partie finie technique, which allows us to prove that the metric represents a solution of vacuum Einstein equations. In this framework, we introduce the concept of atemporality as the dynamical mechanism responsible for the transition from a regime with a real-valued time variable to a new one featuring an imaginary time. We show that this mechanism prevents the occurrence of the singularity and, by means of the regularized Kretschmann invariant, we discuss in which terms atemporality can be considered as the characteristic feature of this black hole.
... For black hole spacetimes in modified gravity theories, studies on the deflection angle of light using GBT are also reported in [22][23][24][25]. Additionally, after the successful release of the black hole images by the EHT, exploring the shadow cast by a black hole has attracted the scientific minds [26][27][28][29][30][31][32][33][34][35]. Such investigations can also aid in differentiating the features of various gravity theories [22,24,36]. ...
In this paper, we have explored the optical characteristics, namely the shadow and the deflection angle, inherent to the solution of a 4D-AdS-Einstein–Gauss–Bonnet black hole. This solution, which finds its inspiration in noncommutative geometry, had previously been established in our previous work. The radius of the shadow was determined using the Hamilton-Jacobi method and the Carter separation. Our results revealed that the presence of noncommutativity in the background of spacetime impacts the variation of the shadow radius. More specifically, we have demonstrated that an increase in the parameter O induces a decrease in the radius of the shadow. In a similar way, analogous observations have been made by studying the variation of the electric charge Q. The noncommutative parameter O
and the electric charge Q have been constrained regarding the EHT observation data of the M87* and Sgr A* black holes. Furthermore, the angle of deflection, which is the outcome of lensing by the black hole, has been derived following the Ishihara et al. approach for a receiver and source positioned at finite distances from the black hole in an asymptotically non-flat spacetime. The impact of the noncommutative parameter O and the charge Q of the black hole are hence analyzed, and our results depict that these parameters have a significant influence on the angle at which light is deflected by the gravitational field of the black hole.
... The BH shadows are unique images produced by the light deflected near the event horizon, creating the perfect opportunity to study the connection between various spacetimes and geometries. This includes analysis of the dark sector and the dark matter candidates [36,[47][48][49][50][51][52][53] as well as the discussion of the QNMs closely linked to the radius of the BH shadows [11,[54][55][56][57]. Hence, through geometric optics, our work explores the intricate relationship between the BH geometry, QNMs, and the modified Yukawa potential following recent trends [46,[58][59][60][61][62][63][64][65][66][67][68][69][70][71]. ...
This paper investigates the contribution of the nonsingular Yukawa-modified potential in the context of four-dimensional Einstein-Gauss-Bonnet (EGB) gravity modeling by a static and spherically symmetric black hole solution. These Yukawa-type corrections are essentially described along two parameters, β and λ, affecting Newton's law of gravity at large distances, and a deformation parameter ℓ 0 , which is essential at short distances. Primarily, the strongest effect is encoded in β, which alters the total mass of the black hole with additional mass proportional to βM, imitating the effects of dark matter at large distances from the black hole. In contrast, the effect due to λ is small for as-trophysical values. On the other hand, the EGB gravity is ruled by the Gauss-Bonnet (GB) coupling constant α, a fundamental parameter of the theory. We pay particular attention to thermodynamic stability, critical orbits, geodesics and quasinormal modes. The results demonstrate stability of the black hole solution for a range of values of the GB coupling constant α. Furthermore, this study investigates the null geodesic motion, namely the shadow behavior, providing intriguing results in relation to the size of the black hole shadow. *
... The BH shadows are unique images produced by the light deflected near the event horizon, creating the perfect opportunity to study the connection between various spacetimes and geometries. This includes analysis of the dark sector and the dark matter candidates [36,[47][48][49][50][51][52][53] as well as the discussion of the QNMs closely linked to the radius of the BH shadows [11,[54][55][56][57]. Hence, through geometric optics, our work explores the intricate relationship between the BH geometry, QNMs, and the modified Yukawa potential following recent trends [46,[58][59][60][61][62][63][64][65][66][67][68][69][70][71]. ...
This paper investigates the contribution of the nonsingular Yukawa-modified potential in the context of four-dimensional Einstein-Gauss-Bonnet (EGB) gravity modeling by a static and spherically symmetric black hole solution. These Yukawa-type corrections are essentially described along two parameters, β and λ, affecting Newton's law of gravity at large distances, and a deformation parameter ℓ 0 , which is essential at short distances. Primarily, the strongest effect is encoded in β, which alters the total mass of the black hole with additional mass proportional to βM, imitating the effects of dark matter at large distances from the black hole. In contrast, the effect due to λ is small for as-trophysical values. On the other hand, the EGB gravity is ruled by the Gauss-Bonnet (GB) coupling constant α, a fundamental parameter of the theory. We pay particular attention to thermodynamic stability, critical orbits, geodesics and quasinormal modes. The results demonstrate stability of the black hole solution for a range of values of the GB coupling constant α. Furthermore, this study investigates the null geodesic motion, namely the shadow behavior, providing intriguing results in relation to the size of the black hole shadow. *
... These black holes may have survived due to their topological stability and can provide clues about the observables in early universe. They belong to Bardeen type space-time [9] and its generalizations [10][11][12][13][14][15][16][17][18][19][20][21][22]. ...
We consider the rotating generalization of the Bardeen black hole solution in the presence of cloud of strings (CoS). The parameter space for which the black hole horizon exists is determined. We also study the static limit surface and the ergo-region in the presence of the CoS parameter. We consider photon orbits and obtain the deformation of black hole shadows due to rotation for various values of the CoS parameter. The shadow deformation is used to determine the black hole spin for different values of the black hole parameters.
... Finally, we mention that the present paper focuses just on a static and spherically symmetric BH that evolves to its regular state when the charge or horizon radius goes to its extreme value -a regular but non-rotating BH. Next, we plan to investigate the evolution of rotating BHs [97], especially the issue of how a singular rotating BH evolves to its regular counterpart, together with the relevant topics, such as the superradiance of rotating BHs [98]. To this end, the Newman-Janis algorithm (NJA) [99,100] will be applied to Eqs. (1) and (22) in order to construct the metrics of rotating BHs. ...
We propose a novel black hole model in which singular and regular black holes are combined as a whole and more precisely singular and regular black holes are regarded as different states of parameter evolution. We refer to them as singular and regular states , respectively. Furthermore, the regular state is depicted by the final state of parameter evolution in the model. We also present the sources that can generate such a black hole spacetime in the framework of F ( R ) gravity. This theory of modified gravity is adopted because it offers a possible resolution to a tough issue in the thermodynamics of regular black holes, namely the discrepancy between the thermal entropy and Wald entropy. The dynamics and thermodynamics of the novel black hole model are also discussed when a singular state evolves into a regular state during the change of charge or horizon radius from its initial value to its extreme value.
... Moreover, examine whether the Schwarzschild BH and the EYM BH have distinct shadows. Another reason for this research is that the EYM BH is a regular BH, and regular BHs solutions (both static and rotating), are thought to be one of the solutions to the problem of the existence of singularities in General Relativity [69][70][71][72][73][74]. Furthermore, the spacetime under consideration is classified as a non-minimal field theory. ...
In this paper, we study the dynamics of a test particle around a regular black hole (BH) in a non-minimal Einstein-Yang-Mills (EYM) theory and examine the BH shadow. The EYM theory is a non-minimally coupled theory in which curvature couples to non-Abelian gauge fields. We investigate particle motion with parameters in EYM BH for massless and massive particles. This work provides the horizon structure, photon radius and inner stable circular orbit (ISCO) of a mass particle with EYM BH parameters. An analysis is provided of the effective potential as well as the possible orbits for test particles under various EYM BH parameters values. In timelike radial geodesics, we find that for smaller values of magnetic charge, particles following a timelike radial geodesic are more hasty in EYM BH, and hence arrive at the center faster than those traveling a Schwarzschild BH geodesic. However, at larger values of the magnetic charge, the inverse effect is observed. The effect of model parameters is investigated in order to study the ISCO, photon radius, orbit stability (Lyapunov exponent), and effective force on particles for the BH in the EYM theory. Finally, we investigate the BH shadow. We find that higher magnetic charge values and non-minimal coupling parameters result in smaller shadow radius values.
... If these roots have the same value, being therefore a double root, the corresponding horizon is extremal in the sense that the associated surface gravity vanishes. It is also possible to have intermediate situations in which both horizons have distinct positions, but one of them is extremal [31,32,73]. ...
A bstract
We illustrate that regular black holes and horizonless stars, typically considered as quite distinct families of black hole mimickers, are intimately intertwined. We show that any spherically symmetric regular black hole can be continuously deformed into a horizonless star under the mild conditions of non-negativity of gravitational energy (Misner-Sharp quasi-local mass), and an assumed linear relation between the latter and the Arnowitt-Deser-Misner (ADM) mass. We illustrate this general result by considering the family of geometries proposed by Hayward as the description of regular black holes, and we also describe the properties of the corresponding horizonless stars. The form of the associated effective stress-energy tensor shows that these horizonless stars can be identified as anisotropic gravastars with a soft surface and inner/outer light rings. We also construct dynamical geometries that could describe the evolution of regular black holes towards horizonless stars, and show that it is plausible that the effective stress-energy tensor in the first stages of evolution is generated by semiclassical effects, in agreement with independent works analyzing semiclassical backreaction.
... For many years, the research on BH physics has attracted the attention of physicists and astronomers. Different types of black holes, such as static BHs [38], dynamic BHs [39], spherically symmetric BHs [40], axially symmetric BHs [41], and exotic BHs [42], have been intensively discussed. The study of the thermodynamic laws of BH areas suggests that black holes, as special celestial bodies, seem to have thermal properties. ...
... there is one photon sphere. Equation (39) gives the location of the ISCO for photon: r ISCO−ph = −C 1 ± C 2 1 − 10C 2 3 . For the GBD theory, we derive that the relationship that the ISCO with the massive particles needs to satisfy: ...
... This constraint (56) can also be obtained by using Equation (39) and the consideration d 2 V e f f dr 2 ≥ 0. By substituting expression (5) into the above Equation (56), we show in Figure 7 the dependence of the parameter ω 2 on the circular orbit radius r. When the integral constants are taken as C 1 = −10 and C 2 = 15, we find that the stable region of circular orbits ω 2 ≥ 0 is: r 24.86. ...
The many problems faced by the theory of general relativity (GR) have always motivated us to explore the modified theory of GR. Considering the importance of studying the black hole (BH) entropy and its correction in gravity physics, we study the correction of thermodynamic entropy for a kind of spherically symmetric black hole under the generalized Brans–Dicke (GBD) theory of modified gravity. We derive and calculate the entropy and heat capacity. It is found that when the value of event horizon radius r+ is small, the effect of the entropy-correction term on the entropy is very obvious, while for larger values r+, the contribution of the correction term on entropy can be almost ignored. In addition, we can observe that as the radius of the event horizon increases, the heat capacity of BH in GBD theory will change from a negative value to a positive value, indicating that there is a phase transition in black holes. Given that studying the structure of geodesic lines is important for exploring the physical characteristics of a strong gravitational field, we also investigate the stability of particles’ circular orbits in static spherically symmetric BHs within the framework of GBD theory. Concretely, we analyze the dependence of the innermost stable circular orbit on model parameters. In addition, the geodesic deviation equation is also applied to investigate the stable circular orbit of particles in GBD theory. The conditions for the stability of the BH solution and the limited range of radial coordinates required to achieve stable circular orbit motion are given. Finally, we show the locations of stable circular orbits, and obtain the angular velocity, specific energy, and angular momentum of the particles which move in circular orbits.
