Narrow Results

In this study, we investigate the shadow of dynamic Phantom black hole (BH) and their observable implications with actual images of the BHs M87* and SgrA. Using the Hamilton–Jacobi formalism, we derive the null geodesic equations within the symmetry planes of spacetime, which facilitates the precise calculation of the radius of the BH shadow and its celestial coordinates. One can notice that the BH shadow’s radius exhibits a notable dependence on the BHs electric charge e and magnetic charge g. We observe that the magnetic charge g has a distinct effect on the shadow’s radius $R_s$ for the $\mathrm{\Lambda }<0$ BH spacetime compared to the asymptotically flat BH spacetime. For both spacetime configurations, an increase in the magnetic charge g correlates with an enlargement of the BH shadow’s radius. Furthermore, we introduce a plasma medium to assess the shadow’s sensitivity to variations in the plasma refractive index. This approach allows us to simulate the optical properties of the surrounding environment and its effect on the perceived size of the BH shadow. In addition, we examine how the magnetic charge affects the BHs energy emission rate, drawing a correlation with the shadow’s dimensions. We also compare the theoretical depiction of BH images with the actual images of M87* and SgrA*.

In our quest toward a theory of gravity beyond General Relativity, black holes with their strong gravitational fields represent an important testing ground. Among the numerous alternative theories of gravity, much work in recent years has focused on a set of scalar–tensor theories, where the scalar field couples to higher curvature terms. The properties of the resulting black holes in such theories may differ distinctly from those of the Schwarzschild and Kerr black holes as, for instance, revealed by their shadows or their gravitational wave spectra.

In the summer of 2023, the pulsar timing arrays (PTAs) announced a compelling evidence for the existence of a nanohertz stochastic gravitational wave background (SGWB). Despite this breakthrough, however, several critical questions remain unanswered: What is the source of the signal? How can cosmic variance be accounted for? To what extent can we constrain nanohertz gravity? When will individual supermassive black hole binaries become observable? And how can we achieve a stronger detection? These open questions have spurred significant interests in PTA science, making this an opportune moment to revisit the astronomical and theoretical foundations of the field, as well as the data analysis techniques employed. In this review, we focus on the theoretical aspects of the SGWB as detected by PTAs. We provide a comprehensive derivation of the expected signal and its correlation, presented in a pedagogical manner, while also addressing current constraints. Looking ahead, we explore future milestones in the field, with detailed discussions on emerging theoretical considerations such as cosmic variance, the cumulants of the one- and two-point functions, subluminal gravitational waves, and the anisotropy and polarization of the SGWB.

In this work, we explore the thermodynamics of black holes using the Gouy–Stodola theorem, traditionally applied to mechanical systems relating entropy production to the difference between reversible and irreversible work. We model black holes as gravitational bubbles with surface tension defined at the event horizon, deriving the Bekenstein–Hawking entropy relation for nonrotating black holes. One extends this approach to rotating black holes, incorporating the effects of angular momentum, demonstrating that the Gouy–Stodola theorem can similarly derive the entropy–area law in this case. Additionally, we analyze the merging of two black holes, showing that the resultant total entropy exceeds the sum of the individual entropies, thereby adhering to the second law of thermodynamics. Our results suggest that gravitational surface tension is a key factor in black hole thermodynamics, providing a novel and coherent framework for understanding the entropy production in these extreme astrophysical objects.

This paper focuses on the examination of various thermodynamic properties of RN-AdS black hole surrounded by quintessence, which is considered as one of the most widely accepted models of dark energy. The investigation involves the determination of temperature, entropy, heat capacity, pressure, equation of state, and Gibbs free energy for this particular black hole. By employing the laws of thermodynamics pertaining to black holes and considering the influence of quintessence, the impact on these quantities is thoroughly analyzed. Additionally, graphical representations of these quantities are depicted, and based on the critical points obtained, the stability and phase transition of the system are assessed. The study further delves into the examination of stability, instability, and the Swallowtail behavior of the system. Notably, due to the discontinuity in the heat capacity, a phase transition occurs within the system, resembling Van der Waals-like phase transitions that transpire between small, intermediate, and large black holes.

We investigated Einstein–Gauss–Bonnet (EGB) 4D massive gravity coupled to nonlinear electrodynamics (NED) in an anti-de Sitter (AdS) background and found an exact magnetically charged black hole solution. The metric function was analyzed for different values of massive gravity parameters. The first law of black hole thermodynamics and generalized Smarr formula were verified, where we treated the cosmological constant as thermodynamic pressure. We defined vacuum polarization as the conjugate to NED parameter. To analyze the local stability of the black hole, we computed specific heat. We investigated the van der Waals-like/re-entrant phase transition of the black holes and estimated the critical points. We observed small black hole (SBH)/large black hole (LBH) and SBH/intermediate black hole (IBH)/LBH phase transitions. The Joule–Thomson coefficient, inversion, and isenthalpic curves were discussed. Finally, the minimum inversion temperature and the corresponding event horizon radius were obtained using numerical techniques.

In this research paper, we discuss the energy–momentum-squared gravity model ${ℱ}({ℛ},{{𝒯}}^2)$ coupled with perfect fluid. We obtain the equation of state for the perfect fluid in ${ℱ}({ℛ},{{𝒯}}^2)$-gravity model. Furthermore, we deal with the energy–momentum-squared gravity model ${ℱ}({ℛ},{{𝒯}}^2)$ coupled with perfect fluid, which admits the Ricci solitons with a conformal vector field. We provide a clue in this series to determine the density and pressure in the radiation and phantom barrier periods, respectively. In addition, we investigate the different energy conditions, black holes and singularity conditions for perfect fluid attached to ${ℱ}({ℛ},{{𝒯}}^2)$-gravity in terms of Ricci soliton. Finally, we derive the Schrödinger equation for energy–momentum-squared gravity model ${ℱ}({ℛ},{{𝒯}}^2)$ coupled with perfect fluid.

In this paper, we extend the vacuum Schwarzschild solution to obtain new black hole solutions within the framework of the Rastall theory of gravity using minimal gravitational decoupling technique. Through the addition of an extra source which induces anisotropy in static spherically symmetric configuration, the field equations are obtained which are then decomposed into two simpler arrays by virtue of a deformation strictly on the radial metric component. The first of these sets corresponds to the seed source (which we take as the vacuum) and is specified by the metric components of the Schwarzschild spacetime. For the second set, a solution is determined by imposing a constraint on the anisotropic extra source via a linear equation of state. For specified values of the Rastall and decoupling parameters, two extended solutions are obtained. The nature of the matter that constitutes the extra source is investigated through the energy conditions. We also study the asymptotic behavior of both solutions by analyzing the deformed radial metric component. It turns out that the additional source in both solutions is exotic due to the violation of the dominant energy conditions. The asymptotic flatness is preserved only for the solution corresponding to the conformally symmetric extra source.

In this paper, we study the inverse scattering of massive charged Dirac fields in the exterior region of (de Sitter)–Reissner–Nordström black holes. Firstly, we obtain a precise high-energy asymptotic expansion of the diagonal elements of the scattering matrix (i.e. of the transmission coefficients) and we show that the leading terms of this expansion allow to recover uniquely the mass, the charge and the cosmological constant of the black hole. Secondly, in the case of nonzero cosmological constant, we show that the knowledge of the reflection coefficients of the scattering matrix on any interval of energy also permits to recover uniquely these parameters.

We consider the stationary metrics that have both the black hole and the ergoregion. The class of such metric contains, in particular, the Kerr metric. We study the Cauchy problem with highly oscillatory initial data supported in a neighborhood inside the ergoregion with some initial energy $E_0$. We prove that when the time variable $x_0$ increases this solution splits into two parts: one with the negative energy $-E_1$ ending at the event horizon in a finite time, and the second part, with the energy $E_2=E_0+E_1>E_0$, escaping, under some conditions, to the infinity when $x_0\to +\infty$. Thus we get the superradiance phenomenon. In the case of the Kerr metric the superradiance phenomenon is “short-lived”, since both the solutions with positive and negative energies cross the outer event horizon in a finite time (modulo $O(\frac{1}{k})$) where $k$ is a large parameter. We show that these solutions end on the singularity ring in a finite time. We study also the case of naked singularity.

In this paper, we establish the asymptotic behavior along outgoing and incoming radial geodesics, i.e. the peeling property for the tensorial Fackerell–Ipser and spin $\pm 1$ Teukolsky equations on Schwarzschild spacetime. Our method combines a conformal compactification with vector field techniques to prove the two-side estimates of the energies of tensorial fields through the future and past null infinity ${\mathcal{ℐ}}^{\pm }$ and the initial Cauchy hypersurface ${\mathrm{\Sigma }}_0=\{t=0\}$ in a neighborhood of spacelike infinity $i_0$ far away from the horizon and future timelike infinity. Our results obtain the optimal initial data which guarantees the peeling at all orders.

For a wave equation with time-independent Lorentzian metric consider an initial-boundary value problem in $ℝ\times \mathrm{\Omega }$, where $x_0\in ℝ$ is the time variable and $\mathrm{\Omega }$ is a bounded domain in ${ℝ}^n$. Let $\mathrm{\Gamma }\subset \partial \mathrm{\Omega }$ be a subdomain of $\partial \mathrm{\Omega }$. We say that the boundary measurements are given on $ℝ\times \mathrm{\Gamma }$ if we know the Dirichlet and Neumann data on $ℝ\times \mathrm{\Gamma }$. The inverse boundary value problem consists of recovery of the metric from the boundary measurements. In the author’s previous works a localized variant of the boundary control method was developed that allows the recovery of the metric locally in a neighborhood of any point of $\mathrm{\Omega }$ where the spatial part of the wave operator is elliptic. This allows the recovery of the metric in the exterior of the ergoregion.

The goal of this survey paper is to recover the black holes. In some cases the ergoregion coincides with the black hole. In the case of two space dimensions we recover the black hole inside the ergoregion assuming that the ergosphere, i.e. the boundary of the ergoregion, is not characteristic at any point of the ergosphere.

We consider a static brane in the background of a topological black hole in arbitrary dimensions. For hyperbolic horizons, we find a solution only when the black hole mass assumes its minimum negative value. In this case, the tension of the brane vanishes, and the brane position coincides with the location of the horizon. For an elliptic horizon, we show that the massless mode of Randall–Sundrum is recovered in the limit of large black hole mass.

We numerically construct static and spherically symmetric electrically charged black hole solutions in Einstein–Born–Infeld gravity with massive dilaton. The numerical solutions show that the dilaton potential allows many more black hole causal structures than the massless dilaton. We find that depending on the black hole mass and charge and the dilaton mass, the black holes can have either one, two, or three horizons. The extremal solutions are also found. As an interesting peculiarity we note that there are extremal black holes with an inner horizon and with triply degenerated horizon.

We study string-loop corrections to magnetic black hole. Four-dimensional theory is obtained by compactification of the heterotic string theory on the manifold K3×T² or on a suitable orbifold yielding N=1 supersymmetry in 6D. The resulting 4D theory has N=2 local supersymmetry. Prepotential of this theory receives only one-string-loop correction. The tree-level gauge couplings are proportional to the inverse effective string coupling and decrease at small distances from the center of magnetic black hole, so that loop corrections to the gauge couplings are important in this region. We solve the system of Killing spinor equations (conditions for the supersymmetry variations of the fermions to vanish) and Maxwell equations. At the string-tree level, we reproduce the magnetic black hole solution which can also be obtained by solving the system of the Einstein–Maxwell equations and the equations of motion for the moduli. String-loop corrections to the tree-level solution are calculated in the first order in string coupling. The resulting corrections to the metric and dilaton are large at small distances from the center of the black hole. Possible smearing of the singularity at the origin by quantum corrections is discussed.

We discuss the conditions under which one can expect to have the usual identification of black hole entropy with the area of the horizon. We then construct an example in which the actual presence of the event horizon on a given hypersurface depends on a quantum event in which a certain quantum variable acquires a value and which occurs in the future of the given hypersurface. This situation indicates that there is something fundamental that is missing in the most popular of the current approaches towards the construction of a theory of quantum gravity, or, alternatively, that there is something fundamental that we do not understand about entropy in general, or at least in its association with black holes.

A five-dimensional rotating black string in a Randall–Sundrum brane world is considered. The black string intercepts the three-brane in a four-dimensional rotating black hole. The geodesic equations and the asymptotics in this background are discussed.

End state of gravitational collapse and the related cosmic censorship conjecture continue to be amongst the most important open problems in gravitation physics today. My purpose here is to bring out several aspects related to gravitational collapse and censorship, which may help towards a better understanding of the issues involved. Possible physical constraints on gravitational collapse scenarios are considered. It is concluded that the best hope for censorship lies in analyzing the genericity and stability properties of the currently known classes of collapse models which lead to the formation of naked singularities, rather than black holes, as the final state of collapse and which develop from a regular initial data.

It has been argued by several authors that the quantum mechanical spectrum of black hole horizon area must be discrete. This has been confirmed in different formalisms, using different approaches. Here we concentrate on two approaches, the one involving quantization on a reduced phase space of collective coordinates of a Black Hole and the algebraic approach of Bekenstein. We show that for non-rotating, neutral black holes in any spacetime dimension, the approaches are equivalent. We introduce a primary set of operators sufficient for expressing the dynamical variables of both, thus mapping the observables in the two formalisms onto each other. The mapping predicts a Planck size remnant for the black hole.

Black hole entropy and its relation to the horizon area are considered. More precisely, the conditions and specifications that are expected to be required for the assignment of entropy, and the consequences that these expectations have when applied to a black hole are explored. In particular, the following questions are addressed: When do we expect to assign an entropy?; when are entropy and area proportional? and, what is the nature of the horizon? It is concluded that our present understanding of black hole entropy is somewhat incomplete, and some of the relevant issues that should be addressed in pursuing these questions are pointed out.