Search Results (72)

We review some aspects of accretion disks physics, spacetime photon shell and photon orbits, related to retrograde (counter-rotating) motion in Kerr black hole (BH) spacetimes. In this brief review, we examine the counter-rotating components of the Kerr BH shadow boundary, under the influence of counter-rotating accretion tori, accreting flows and proto-jets (open critical funnels of matter, associated with the tori) orbiting around the central BH. We also analyze the redshifted emission arising from counter-rotating structures. Regions of the shadows and photon shell are constrained in their dependence of the BH spin and observational angle. The effects of the counter-rotating structures on these are proven to be typical of the fast-spinning BHs, and accordingly can be observed only in the restricted classes of the Kerr BH spacetimes. This review is intended as a concise guide to the main properties of counter-rotating fluxes and counter-rotating disks in relation to the photon shell and the BH shadow boundary. Our findings may serve as the basis for different theoretical frameworks describing counter-rotating accretion flows with observable imprints manifesting at the BH shadow boundary. The results can eventually enable the distinction of counter-rotating fluxes through their observable imprints, contributing to constraints on both the BH spin and the structure of counter-rotating accretion disks. In particular, photon trajectories and their impact parameters can manifest in the morphology of the BH shadow. Such features, when accessible through high-resolution imaging and spectral or polarization measurements, could provide a direct avenue for testing different theoretical models on accretion disk dynamics and their BH attractors. Full article

This work aims to maximize the Hawking emission temperature arising in the optical analog model of the event horizon of an astrophysical black hole. A weak probe wave interacts with an intense ultrashort optical pulse via the Kerr effect in a photonic crystal fiber. This interaction causes the probe wave to experience an effective spacetime geometry characterized by the presence of an optical event horizon, where the analogous Hawking radiation effect arises. Here we refer to the simulated or classical version of the analog of Hawking radiation. This study considers four distinct types of photonic crystal fibers with anomalous dispersion curves that allow for maximizing the effect. Our first three numerical simulations indicate that a Hawking emission temperature of up to 361 K can be achieved with a photonic crystal fiber with two zero-dispersion wavelengths, while the emission temperature values in the original investigation are lower than 244 K. And in the fourth, we can see that we have a configuration in which the temperature can be improved up to 1027 K. Moreover, these results also emphasize the feasibility of using analog models to test the quantum effects of gravity, such as Hawking radiation produced by typical black holes, whose magnitude is far below the temperature of the cosmic microwave background (2.7 K). Full article

Relativistic jets from active galactic nuclei (AGN) have been a topic of peak interest in the high-energy astrophysics community for their uniquely dynamic nature and incredible radiative power emanating from supermassive black holes and similarly accreting compact dense objects. An overall consensus on relativistic jet formation states that accelerated outflow at high Lorentz factors are generated by a complex relationship between the accretion disk of the system and the frame-dragging effects of the rotating massive central object. This paper will provide a basis for which circular polarization states, defined using a spin tetrad formalism, contribute to a description for the angular momentum flux in the jet emanating from the central engine. A representation of the Kerr spacetime is used in formulating the spin tetrad forms. A discussion on unresolved problems in jet formation and how we can use multi-method observations with polarimetry of AGN to direct future theoretical descriptions will also be given. Full article

In this paper, we consider massless scalar perturbations minimally coupled to gravity in the background spacetime of charged black holes in Yang–Mills theory with gravity’s rainbow modification. We calculate the corresponding quasinormal frequencies by employing the sixth-order Wentzel—Kramers—Brillouin (WKB) approximation for both asymptotically flat and de Sitter (dS) spacetimes. We show that the Yang–Mills modification of the Reissner–Nordström black holes leads to an increase in the real and imaginary parts of frequencies. Furthermore, we find that the perturbations in asymptotically flat spacetime decay faster with more oscillations compared to dS spacetime, and we study the effects of the rainbow functions on the oscillations. Interestingly, we reveal a novel feature of this black hole case study and show that, unlike typical black hole solutions such as Schwarzschild, RN, and Kerr, the higher multipole numbers live longer than the lower ones in both asymptotically flat and dS spacetimes. Furthermore, the reflection and transmission coefficients are explored for Einstein–Maxwell–Yang–Mills black holes, and the results are compared for flat and dS asymptotes. Full article

We generalize our recent work on k-essence sourcing Kerr–Schild spacetimes to the kinetic gravity braiding scalar field. For k-essence, in order for a perturbative Kerr–Schild-type solution to become exact, the k-essence Lagrangian must either be linear in the kinetic term (with the Kerr–Schild congruence autoparallel) or unrestricted, provided the scalar gradient along the congruence vanishes. A similar reasoning for the pure kinetic braiding contribution leads to either a vanishing Lagrangian or a scalar that is constant along the congruence. From the scalar dynamics we also derive an accompanying constraint. Finally, we discuss pp-waves, an example of Kerr–Schild spacetime generated by a constant k-essence along the Kerr–Schild congruence with a vanishing Lagrangian. This allows for the construction of a Fock-type space, consisting of a tower of Kerr–Schild maps first yielding a vacuum pp-wave from flat spacetime; next a k-essence-generated pp-wave from the vacuum pp-wave; and finally an arbitrary number of k-essence pp-waves with different retarded time-dependent metric functions. Full article

To meet the supergravity requirements of a black hole without a singularity, we propose some possible finite-sized core structures to avoid the confusing singularity problem. This research first studies the Coulomb repulsion between electrons at a distance of 10⁻¹⁵ m, where the inverse square of the distance is still workable, revealing that the energy of the entire observable universe is required to form a charged region with a radius of 50 m, including 1.4 × 10³¹ Coulomb electrons. Therefore, the existence of a singularity at the center of a black hole becomes physically unreasonable in this case. To avoid the singularity problem, we propose a finite-sized black hole core in which the inner core is composed of the vast majority of neutrons and a very small amount of ⁵⁶Fe. Under the conditions of a total charge of 1.648824 × 10²⁰ C and a total mass equivalent to the Sun, a finite-sized black hole is constructed through this finite-sized core model. We use this non-rotating but charged, compact, star-like structure, surrounded by counter-rotating and co-rotating electrons, to construct a Kerr–Newman black hole with a finite-sized core structure. Based on this model, we can obtain the same spacetime as that of a traditional Kerr–Newman black hole. Full article

A compact object illuminated by background radiation produces a dark silhouette. The edge of the silhouette or shadow (alternatively, the apparent boundary or the critical curve) is commonly determined by the presence of the photon sphere (or photon shell in the case of rotating spacetime), corresponding to the maximum of the effective potential for null geodesics. While this statement stands true for Kerr black holes, here we remark that the apparent boundary (as defined by Bardeen) forms under a more general condition. We demonstrate that a shadow forms if the effective potential of null geodesics has a positive finite upper bound and includes a region where photons are trapped or scattered. Our framework extends beyond conventional solutions, including but not limited to naked singularities. Furthermore, we clarify the difference between the apparent boundary of a dark shadow and the bright ring on the screen of a distant observer. These results provide a unified theoretical basis for interpreting observations from the Event Horizon Telescope (EHT) and guiding future efforts towards extreme-resolution observations of compact objects. Full article

An approach is presented to address singularities in general relativity using a complex Riemannian spacetime extension. We demonstrate how this method can be applied to both black hole and cosmological singularities, specifically focusing on the Schwarzschild and Kerr black holes and the Friedmann–Lemaître–Robertson–Walker (FLRW) Big Bang cosmology. By extending the relevant coordinates into the complex plane and carefully choosing integration contours, we show that it is possible to regularize these singularities, resulting in physically meaningful, singularity-free solutions when projected back onto real spacetime. The removal of the singularity at the Big Bang allows for a bounce cosmology. The approach offers a potential bridge between classical general relativity and quantum gravity effects, suggesting a way to resolve longstanding issues in gravitational physics without requiring a full theory of quantum gravity. Full article

We extend a result by one of the authors, established for nonvacuum Einstein gravity, to minimally coupled k-essence scalar–tensor theories. First, we prove that in order to source a Kerr–Schild-type spacetime, the k-essence Lagrangian should be at most quadratic in the kinetic term. This is reduced to linear dependence when the Kerr–Schild null congruence is autoparallel. Finally, we show that solutions of the Einstein equations linearized in Kerr–Schild-type perturbations are also required to solve the full nonlinear system of Einstein equations, selecting once again k-essence scalar fields with linear Lagrangians in the kinetic term. The only other k-essence sharing the property of sourcing perturbative Kerr–Schild spacetimes, which are also exact, is the scalar field constant along the integral curves of the Kerr–Schild congruence, with the otherwise unrestricted Lagrangian. Full article

This is the Part II paper of our series of papers on a gauge-invariant perturbation theory on the Schwarzschild background spacetime. After reviewing our general framework of the gauge-invariant perturbation theory and the proposal of gauge-invariant treatments for $l=0,1$-mode perturbations on the Schwarzschild background spacetime in the Part I paper, we examine the linearized Einstein equations for even-mode perturbations. We discuss the strategy to solve the linearized Einstein equations for these even-mode perturbations including $l=0,1$ modes. Furthermore, we explicitly derive the $l=0,1$-mode solutions to the linearized Einstein equations in both the vacuum and the non-vacuum cases. We show that the solutions for $l=0$-mode perturbations includes the additional Schwarzschild mass parameter perturbation, which is physically reasonable. Then, we conclude that our proposal of the resolution of the $l=0,1$-mode problem is physically reasonable due to the realization of the additional Schwarzschild mass parameter perturbation and the Kerr parameter perturbation in the Part I paper. Full article

This article is Part I of our series of full papers on a gauge-invariant “linear” perturbation theory on the Schwarzschild background spacetime which was briefly reported in our short papers by the present author in 2021. We first review our general framework of the gauge-invariant perturbation theory, which can be easily extended to the “higher-order” perturbation theory. When we apply this general framework to perturbations on the Schwarzschild background spacetime, gauge-invariant treatments of $l=0,1$ mode perturbations are required. On the other hand, in the current consensus on the perturbations of the Schwarzschild spacetime, gauge-invariant treatments for $l=0,1$ modes are difficult if we keep the reconstruction of the original metric perturbations in our mind. Due to this situation, we propose a strategy of a gauge-invariant treatment of $l=0,1$ mode perturbations through the decomposition of the metric perturbations by singular harmonic functions at once and the regularization of these singularities through the imposition of the boundary conditions to the Einstein equations. Following this proposal, we derive the linearized Einstein equations for any modes of $l\ge 0$ in a gauge-invariant manner. We discuss the solutions to the odd-mode perturbation equations in the linearized Einstein equations and show that these perturbations include the Kerr parameter perturbation in these odd-mode perturbations, which is physically reasonable. In the Part II and Part III papers of this series of papers, we will show that the even-mode solutions to the linearized Einstein equations obtained through our proposal are also physically reasonable. Then, we conclude that our proposal of a gauge-invariant treatment for $l=0,1$-mode perturbations is also physically reasonable. Full article

In this study, we investigate the properties of a thin accretion disk around a static spherically symmetric black hole in 4D Einstein–Gauss–Bonnet gravity, with an additional coupling constant, $\alpha$, appearing in the spacetime metric. Using the Novikov–Thorne accretion disk model, we examine the thermal properties of the disk, finding that increasing $\alpha$ reduces the energy, angular momentum, and effective potential of a test particle orbiting the black hole. We demonstrate that $\alpha$ can mimic the spin of a Kerr black hole in general relativity up to $a\simeq$ 0.23 M for the maximum value of $\alpha$. Our analysis of the thermal radiation flux shows that larger $\alpha$ values increase the flux and shift its maximum towards the central black hole, while far from the black hole, the solution recovers the Schwarzschild limit. The impact of $\alpha$ on the radiative efficiency of the disk is weak but can slightly alter it. Assuming black-body radiation, we observe that the disk’s temperature peaks near its inner edge and is higher for larger $\alpha$ values. Lastly, the electromagnetic spectra reveal that the disk’s luminosity is lower in Einstein–Gauss–Bonnet gravity compared to general relativity, with the peak luminosity shifting toward higher frequencies, corresponding to the soft X-ray band as $\alpha$ increases. Full article

We present a novel approach for the construction of interior solutions for the Kerr metric, extending J. Ovalle’s foundational work through ellipsoidal coordinate transformations. By deriving a physically plausible interior solution that smoothly matches the Kerr exterior metric, we analyze the energy conditions across various rotation parameters. Our findings reveal anisotropic fluid properties and energy condition behaviors in specific space-time regions, providing insights into the strong-field regime of rotating black holes. The proposed solution offers a more realistic description of rotating black hole interiors, with implications for understanding compact astrophysical objects. Full article

We compute the generalized spin precession frequency (${\Omega }_p$) of a test gyroscope in a stationary spacetime, specifically for a Kerr–MOG black hole within the framework of scalar–tensor–vector gravity (STVG), also known as modified gravity (MOG). A comprehensive analysis of the generalized spin frequency was conducted for non-extremal Kerr–MOG black hole, extremal Kerr–MOG black hole, and naked singularity or superspinar, in comparison to non-extremal Kerr black hole, extremal Kerr black hole, and Kerr naked singularity or Kerr superspinar. The generalized spin frequency we derived can be expressed in terms of the black hole mass parameter, the angular momentum parameter, and the MOG parameter. Additionally, we distinguish between non-extremal black hole, extremal black hole, and naked singularity through the computation of the aforementioned precession frequency. Furthermore, we calculate the generalized spin frequency for various angular coordinates, ranging from the polar to the equatorial plane. Lastly, we determine three fundamental epicyclic frequencies, the Keplerian frequency, the radial epicyclic frequency, and the vertical epicyclic frequency, to differentiate these three types of objects. We also compute the periastron frequency and nodal frequency. Utilizing these frequency profiles allows for the distinction of these three compact objects. Full article

Supermassive black holes (SMBHs) are observed in active galactic nuclei interacting with their environments, where chaotical, discontinuous accretion episodes may leave matter remnants orbiting the central attractor in the form of sequences of orbiting toroidal structures, with strongly different features as different rotation orientations with respect to the central Kerr BH. Such ringed structures can be characterized by peculiar internal dynamics, where co-rotating and counter-rotating accretion stages can be mixed and distinguished by tori interaction, drying–feeding processes, screening effects, and inter-disk jet emission. A ringed accretion disk (RAD) is a full general relativistic model of a cluster of toroidal disks, an aggregate of axi-symmetric co-rotating and counter-rotating disks orbiting in the equatorial plane of a single central Kerr SMBH. In this work, we discuss the time evolution of a ringed disk. Our analysis is a detailed numerical study of the evolving RAD properties formed by relativistic thin disks, using a thin disk model and solving a diffusion-like evolution equation for an RAD in the Kerr spacetime, adopting an initial wavy (ringed) density profile. The RAD reaches a single-disk phase, building accretion to the inner edge regulated by the inner edge boundary conditions. The mass flux, the radial drift, and the disk mass of the ringed disk are evaluated and compared to each of its disk components. During early inter-disk interaction, the ring components spread, destroying the internal ringed structure and quickly forming a single disk with timescales governed by ring viscosity prescriptions. Different viscosities and boundary conditions have been tested. We propose that a system of viscously spreading accretion rings can originate as a product of tidal disruption of a multiple stellar system that comes too close to an SMBH. Full article