Narrow Results

The thin shell collapse leading to the formation of charged rotating black holes in three dimensions is analyzed in the light of a recently developed Hamiltonian formalism for these systems. It is proposed to demand, as a way to reconcile the properties of an infinitely extended solenoid in flat space with a magnetic black hole in three dimensions, that the magnetic field should vanish just outside the shell. The adoption of this boundary condition results in an exterior solution with a magnetic field different from zero at a finite distance from the shell. The interior solution is also found and assigns another interpretation, in a different context, to the magnetic solution previously obtained by Clément and Hirschmann and Welch.

We study analytical properties of the holographic superconductors with Weyl corrections. We describe the phenomena in the probe limit neglecting backreaction of the spacetime. We observe that for the conformal dimension △₊ = 3, the minimum value of the critical temperature at which condensation sets, can be obtained directly from the equations of motion as , which is in very good agreement with the numerical value [Phys. Lett. B697, 153 (2011)]. This value of corresponds to the value of the Weyl's coupling γ = -0.06 in Table 1 of Phys. Lett. B697, 153 (2011). We calculate the for another Weyl's coupling γ = 0.02 and the conformal dimension △_- = 1. Further, we show that the critical exponent is . We observe that there is a linear relation between the charge density ρ and the chemical potential difference μ-μ_c qualitatively matches the numerical curves.

We examine the statistical nature of the charged anticharged nonextremal black holes in string theory. From the perspective of the intrinsic Riemannian geometry, the first principle of the statistical mechanics shows that the stability properties of general nonextremal nonlarge charged black brane solutions are divulged from the positivity of the corresponding principle minors of the space-state metric tensor. Under the addition of the Kaluza–Klein monopoles, a novel aspect of the Gaussian fluctuations demonstrates that the canonical fluctuations can be ascertained without any approximation. We offer the state-space geometric implication for the most general nonextremal black brane configurations in string theory.

We review the origins, motivations, and implications for cosmology and black holes, of our proposal that “dark energy” is not a quantum vacuum energy, but rather arises from a Weyl scaling invariant nonderivative component of the gravitational action.

We study analytical properties of the Stuckelberg holographic superconductors with Weyl corrections. We obtain the minimum critical temperature as a function of the mass of the scalar field m². We show that in limit of the which is close to the numerical estimate . Further we show that the mass of the scalar field is bounded from below by the where . This lower bound is weaker and different from the previous lower bound m² = -3 predicted by stability analysis. We show that in the Breitenlohner–Freedman bound, the critical temperature remains finite. Explicitly, we prove that here there exists a linear relation between 〈O_Δ〉 and the chemical potential.

We study the effect of an external magnetic field on the stability of circular motion of charged particles in the equatorial plane of a five-dimensional rotating black hole. Using the Hamilton–Jacobi formalism, we derive the effective potential for the radial motion of test particles around a five-dimensional magnetized Myers–Perry black hole. We show that there exist stable circular orbits in equatorial planes in the background of this metric.

We consider extended cosmological gravities with Ricci tensor and scalar squared terms in diverse dimensions. These theories admit solutions of Einstein metrics, including the Schwarzschild–Tangherlini AdS black holes, whose mass and entropy vanish at the critical point. We perform linearized analysis around the black holes and show that in general the spectrum consists of the usual spin-2 massless and ghost massive modes. We demonstrate that there is no exponentially-growing tachyon mode in the black holes. At the critical point, the massless spin-2 modes have zero energy whilst the massive spin-2 modes are replaced by the log modes. There always exist certain linear combination of massless and log modes that has negative energy. Thus the stability of the black holes requires that the log modes to be truncated out by the boundary condition.

We present a version of acoustic black holes by using the principle of the Josephson effect. We find that in the case where two superconductors A and B are separated by an insulating barrier, an acoustic black hole may be created in the middle region between the two superconductors. We discuss in detail how to describe an acoustic black hole in the Josephson junction and write the metric in the language of the superconducting electronics. Our final results infer that for big enough tunneling current and thickness of the junction, experimental verification of the Hawking temperature could be possible.

Black holes have the ability to generate infinite number of images of any given source. These relativistic images are formed by light rays winding around the black hole several times. The phenomenology associated with these images is very rich, since these features are very sensitive to the metric structure of the black hole. Here, we review some aspects of gravitational lensing by black holes and consider some fundamental aspects related to alternative solutions, which do not reproduce Schwarzschild in the asymptotic limit and are supported by exotic matter.

We argue that, when certain higher-curvature corrections are added to the four-dimensional Einstein–Hilbert action, black holes become stable below certain mass. We show this to be the case for an infinite family of ghost-free theories involving terms of arbitrarily high order in curvature. The thermodynamic behavior of the new black holes is universal for arbitrary values of the couplings, with the only exception of the Schwarzschild solution itself, which is recovered when all the couplings are set to zero. For this class of theories, the issue of non-unitary evolution is inexistent, as black holes never evaporate completely.

In the present work, we compute the spectrum of quasinormal frequencies of four-dimensional (4D) charged black holes (BHs) in Einstein-power-Maxwell (EpM) theory. In particular, we study scalar perturbations adopting the sixth-order WKB approximation. We analyze in detail, the behavior of the spectrum depending on the charge of the BH, the quantum number of angular momentum and the overtone number. In addition, a comparison is made between the results obtained here and the results valid for charged BHs in other theories as well as for the Reissner–Nordström BH. Finally, we have provided an analytical expression for the quasinormal spectrum in the eikonal limit.

We investigate some models of compact objects in the general relativity theory with cosmological constant $\mathrm{\Lambda }$, based on two density profiles, one of them attributed to Stewart and the other one to Durgapal and Bannerji, proposed in the literature to model “neutron stars”. For them, a nonlocal equation of state with cosmological constant is obtained as a consequence of the chosen metric. In another direction, we obtain a solution for configurations with null radial pressure. The first model (based on Stewart’s density profile) turned out to be the most interesting, since surprisingly it admits the presence of dark energy in the interior of the star, in the outermost layers, for a certain range of mass–radius ratio $\gamma$. This dark energy is independent of the cosmological constant, since it is a consequence of the tangential pressure of the fluid be sufficiently negative. Still in this case, for other values of $\gamma$, all the energy conditions are satisfied. Another advantage of this model, as well as that based on the density profile of Durgapal and Bannerji, is the existence of intervals of $\gamma$ compatible with physically acceptable models for $\mathrm{\Lambda }<0$, $\mathrm{\Lambda }=0$ and $\mathrm{\Lambda }>0$, which also allowed us to analyze the influence of $\mathrm{\Lambda }$ on the behavior of the fluid with respect to the energy conditions. The other configuration studied here, $P_r=0$, only allows solutions for $\mathrm{\Lambda }<0$, in order to ensure a positive mass for the object and to satisfy all the energy conditions in a specific range of $\gamma$.

We show the appearance of geometric phase in a Dirac particle traversing in nonrelativistic limit in a time-independent gravitational field. This turns out to be similar to the one originally described as a geometric phase in magnetic fields. We explore the geometric phase in the Kerr and Schwarzschild geometries, which have significant astrophysical implications. Nevertheless, the work can be extended to any spacetime background including that of time-dependent. In the Kerr background, i.e. around a rotating black hole, geometric phase reveals both the Aharonov–Bohm effect and Pancharatnam–Berry phase. However, in a Schwarzschild geometry, i.e. around a nonrotating black hole, only the latter emerges. We expect that our assertions can be validated in both the strong gravity scenarios, like the spacetime around black holes, and weak gravity environment around Earth.

We construct the gravitational energy–momentum tensor in general relativity through the Noether theorem. In particular, we explicitly demonstrate that the constructed quantity can vary as a tensor under the general coordinate transformation. Furthermore, we verify that the energy–momentum conservation is satisfied because one of the two indices of the energy–momentum tensor should be in the local Lorentz frame. It is also shown that the gravitational energy and the matter one cancel out in certain space-times.

In this paper, we present comparisons of the deflection angles of massless and massive particles in the Schwarzschild space-time. For the case of photons in a general static space-time, we construct a spatial 3D equation of motion for their path that leads to an implicit formula for the deflection angle. We then compare our results with well-known results of the literature in the Schwarzschild space-time. For the case of massive particles, we calculate the deflection angle only in the Schwarzschild space-time. The end result is that as the velocity of any massive particle diminishes, the deflection angle increases. To show the relevance of these comparisons, we constructed different black hole shadows for massive particles in order to be compared with a shadow made by photons.

We study the bound orbit conditions for equatorial and eccentric orbits around a Kerr black hole both in the parameter space (E, L, a) representing the energy, angular momentum of the test particle, and spin of the black hole, and also (e, μ, a) space representing the eccentricity, inverse-latus rectum of the orbit, and spin. We apply these conditions and implement the relativistic precession (RP) model to M82X-1, which is an Intermediate-mass black hole (IMBH) system, where two high-frequency Quasi-Periodic Oscillations (HFQPOs) and a low-frequency QPO were simultaneously observed. Assuming that the QPO frequencies can also be generated by equatorial and eccentric trajectories, we calculate the probability distributions to infer e, a, and periastron distance, r_p, of the orbit giving rise to simultaneous QPOs. We find that an eccentric orbit solution is possible in the region between innermost stable circular orbit (ISCO) and the marginally bound circular orbit (MBCO) for $e={0.2768}_{-0.0451}^{+0.0657},$a = 0.2897 ± 0.0087, and $r_p={4.6164}_{-0.1259}^{+0.0694}$.

We derive the conditions for a non-equatorial eccentric bound orbit to exist around a Kerr black hole in two-parameter spaces: the energy, angular momentum of the test particle, spin of the black hole, and Carter’s constant space (E, L, a, Q), and eccentricity, inverselatus rectum space (e, μ, a, Q). These conditions distribute various kinds of bound orbits in different regions of the (E, L) and (e, μ) planes, depending on which pair of roots of the effective potential forms a bound orbit. We provide a prescription to select these parameters for bound orbits, which are useful inputs to study bound trajectory evolution in various astrophysical applications like simulations of gravitational wave emission from extreme-mass ratio inspirals, relativistic precession around black holes, and the study of gyroscope precession as a test of general relativity.

We show that spinors propagating in curved gravitational background acquire an interaction with spacetime curvature, which leads to a quantum mechanical geometric effect. This is similar to what happens in the case of magnetic fields, known as Pancharatnam-Berry phase. As the magnetic and gravitational fields have certain similar properties, e.g. both contribute to curvature, this result is not difficult to understand. Interestingly, while spacetime around a rotating black hole offers Aharonov-Bohm and Pancharatnam-Berry both kinds of geometric effect, a static spacetime offers only the latter. In the bath of primordial black holes, such gravity induced effects could easily be measured due to their smaller radius.

Light rays passing close to a black hole experience very strong deflections and can give rise to infinite sequences of images for any given source. We show how these images can be analytically described for any kinds of static or rotating metrics. In the case of the Kerr metric, caustics become larger and larger for higher orders, and an exponentially large number of higher order images arises. We discuss how these results have been used in the popular movie “Interstellar”. Some perspectives for observations of the strong deflection phenomenology come from the black hole in the Galactic center, where high resolution observational efforts are being concentrated.

Recently, different methods succeeded in calculating the spin dynamics at higher orders in the post-Newtonian (PN) approximation. This is an essential step toward the determination of more accurate templates for gravitational waves, to be used in future gravitational wave astronomy. We focus on the extension of the ADM canonical formalism to spinning binary black holes. Using the global Poincarée invariance of asymptotically flat spacetimes as the most important guiding consistency condition, this extension can be constructed order by order in the PN approximation. We were able to reach a high order both in the spin power and the PN counting.