non-Schwarzschild Black Hole Research Articles

Optical appearance of numerical black hole solutions in higher derivative gravity

The optical appearance of the numerically black hole solutions within the higher derivative gravity illuminated by an accretion disk context is discussed. We obtain solutions for non-Schwarzschild black holes with r0=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_0=1$$\\end{document}, r0=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_0=2$$\\end{document}, and r0=3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_0=3$$\\end{document}. Further analysis of spacetime trajectories reveals properties similar to Schwarzschild black holes, while the r0=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_0=2$$\\end{document} black hole exhibits significant differences. The results reveal the presence of a repulsive potential barrier for the black hole, allowing only particles with energies exceeding a certain threshold to approach it, providing a unique gravitational scenario for non-Schwarzschild black holes. Additionally, the optical images are derived through numerical simulations by discussing the trajectories of photons in the black hole spacetime. The distribution of radiation flux and the effects of gravitational redshift and Doppler shift on the observed radiation flux are considered. Interestingly, previous analyses of the optical appearance of black holes were conducted within the framework of analytic solutions, whereas the analysis of numerical black hole solutions first appears in our analysis.

Gravitationally decoupled non-Schwarzschild black holes and wormhole space–times

In this article, using gravitational decoupling by means of minimal geometric deformation approach, we obtain a new spherically symmetric and static black hole solution. To progress, we close the system by assuming that the average pressure of the theta -sector is vanishing. Also, we tackle the problem regarding how, for a given minimally deformed black hole solution, one can connect it to a wormhole space–time.

Quasiperiodic Oscillations and Dynamics of Test Particles around Quasi- and Non-Schwarzschild Black Holes

One of the open problems in black hole physics is testing spacetime around black holes through astrophysical observations in the strong field regime. In fact, black holes cannot produce radiation themselves in the electromagnetic spectrum. However, a black hole’s gravity plays an important role in the production of the radiation of the accretion disc around it. One may obtain valuable information from the electromagnetic radiation of accretion discs about the gravitational properties of the spacetime around black holes. In this work, we study particle dynamics in the spacetime of quasi- and non-Schwarzschild black holes. We compare the gravitational effects of the spacetime deformation parameters of both black hole solutions on the innermost stable circular orbit (ISCO) radius, position, energy, and angular momentum of test particles at the ISCO, together with the energy efficiency of the accretion disc in the thin Novikov–Thorn model. Furthermore, we study the frequencies of particle oscillations in the radial and angular directions along circular stable orbits around both deformed black holes. Furthermore, we investigate quasiperiodic oscillations around the black holes in the relativistic precession model. We show the dependence of the deviation parameters on the orbits of twin peak QPOs with the frequency ratio 3:2. In the obtained results, we compare the gravitational effects of deviation parameters with the spin of a rotating Kerr black hole. Finally, we obtain constraints on the values of the deviation parameter of the spacetime around the black hole at the center of the microquasars GRO J1655-40 and GRS 1915-105 and their mass, using the χ2 method.

Phase diagram of Einstein-Weyl gravity

Thanks to their interpretation as the first order correction of general relativity at high energies, quadratic theories of gravity have gained much attention in recent times. Particular attention has been drawn to the Einstein-Weyl theory, where the addition of the squared Weyl tensor to the action opens the possibility of having non-Schwarzschild black holes in the classical spectrum of the theory. Static and spherically symmetric solutions of this theory have been studied and classified in terms of their small scales behavior; however, a classification of these solutions in terms of the asymptotic gravitational field is still lacking. In this paper we address this point and present a phase diagram of the theory, where the different types of solutions are shown in terms of their mass and the strength of a Yukawa-like correction to the gravitational field. In particular we will show that, in the case of compact stars, different equations of state imply different Yukawa corrections to the gravitational potential, with possible phenomenological implications.

Charged Particle Motions near Non-Schwarzschild Black Holes with External Magnetic Fields in Modified Theories of Gravity

A small deformation to the Schwarzschild metric controlled by four free parameters could be referred to as a nonspinning black hole solution in alternative theories of gravity. Since such a non-Schwarzschild metric can be changed into a Kerr-like black hole metric via a complex coordinate transformation, the recently proposed time-transformed, explicit symplectic integrators for the Kerr-type spacetimes are suitable for a Hamiltonian system describing the motion of charged particles around the non-Schwarzschild black hole surrounded with an external magnetic field. The obtained explicit symplectic methods are based on a time-transformed Hamiltonian split into seven parts, whose analytical solutions are explicit functions of new coordinate time. Numerical tests show that such explicit symplectic integrators for intermediate time steps perform well long-term when stabilizing Hamiltonian errors, regardless of regular or chaotic orbits. One of the explicit symplectic integrators with the techniques of Poincaré sections and fast Lyapunov indicators is applied to investigate the effects of the parameters, including the four free deformation parameters, on the orbital dynamical behavior. From the global phase-space structure, chaotic properties are typically strengthened under some circumstances, as the magnitude of the magnetic parameter or any one of the negative deformation parameters increases. However, they are weakened when the angular momentum or any one of the positive deformation parameters increases.

Scattering by deformed black holes

Obtaining black hole solutions in alternative theories of gravity can be a difficult task due to cumbersome field equations that arise in many of such theories. In order to study the strong field regime in a model-free approach, one can consider deformed black hole solutions with additional parameters beyond mass, charge and angular momentum. We investigate the scattering and absorption of a massless scalar field by non-Schwarzschild black holes, considering the Johannsen and Psaltis parametrization. In particular, we study the scattering process by the classical (null geodesics analysis), semiclassical (glory approximation) and partial waves approaches. We present the formalism needed to compute the scattering and absorption of massless scalar waves by Schwarzschild-like black holes with a set of deformation parameters in addition to their mass and present a selection of our results. We compare our numerical results for the scattering cross section with the classical and semiclassical results, obtaining excellent agreement.

Quantifying closeness between black hole spacetimes: a superspace approach

The set of all metrics that can be placed on a given manifold defines an infinite-dimensional ‘superspace’ that can itself be imbued with the structure of a Riemannian manifold. Geodesic distances between points on Met(M) measure how close two different metrics over M are to one another. Restricting our attention to only those metrics that describe physical black holes, these distances may therefore be thought of as measuring the level of geometric similarity between different black hole structures. This allows for a systematic quantification of the extent to which a black hole, possibly arising as an exact solution to a theory of gravity extending general relativity in some way, might be ‘non-Kerr’. In this paper, a detailed construction of a superspace for stationary black holes with an arbitrary number of hairs is carried out. As an example application, we are able to strengthen a recent claim made by Konoplya and Zhidenko about which deviation parameters describing a hypothetical, non-Schwarzschild black hole are likely to be most relevant for astrophysical observables.

Spherically symmetric solutions in higher-derivative theories of gravity

Higher-order theories of gravity have received much attention from several areas including quantum gravity, string theory and cosmology. This paper proposes a higher-order gravity whose action includes all curvature scalar terms up to the second-order corrections of general relativity, namely, $R^{2}$, $R^{3}$ and $R\square R$. Then, we explore spherically symmetric and static solutions in the weak-field regime and black holes context. All solutions in the weak-field regime due to a point mass are deduced, and by making a stability analysis of these solutions, we restrict them to Yukawa-type solutions. In regard to black hole solutions, we use the Lichnerovicz method to investigate the possibility of existence of non-Schwarzschild black holes. The results obtained show that non-Schwarzschild solutions might exist. However, for reasonable values of the parameters of the theory, its horizon radii are extremely small making macroscopic black holes different from Schwarzschild unfeasible.

Charged black holes in the Einstein-Maxwell-Weyl gravity

In this paper, charged asymptotically flat black hole solutions are numerically constructed in the Einstein-Maxwell-Weyl gravity. These solutions can be interpreted as generalizations of two different groups of non-charged asymptotically flat spacetimes: Schwarzschild black hole (SBH) and non-Schwarzschild black hole (NSBH) solutions. In addition, we discuss the thermodynamic properties of two groups of charged black holes in detail, and show that these obey the first law of thermodynamics of black hole.

Quasinormal modes of Dirac field in the Einstein\u2013Dilaton\u2013Gauss\u2013Bonnet and Einstein\u2013Weyl gravities

Quasinormal modes of Dirac field in the background of a non-Schwarzschild black holes in theories with higher curvature corrections are investigated in this paper. With the help of the semi-analytic WKB approximation and further using of Padé approximants as prescribed in Matyjasek and Opala (Phys Rev D 96(2):024011. arXiv:1704.00361 [gr-qc], 2017) we consider quasinormal modes of a test massless Dirac field in the Einstein–Dilaton–Gauss–Bonnet (EdGB) and Einstein–Weyl (EW) theories. Even though the effective potential for one of the chiralities has a negative gap we show that the Dirac field is stable in both theories. We find the dependence of the modes on the new dimensionless parameter p (related to the coupling constant in each theory) for different values of the angular parameter ell and show that the frequencies tend to linear dependence on p. The allowed deviations of qausinormal modes from their Schwarzschild limit are one order larger for the Einstein–Weyl theory than for the Einstein–Dilaton–Gauss–Bonnet one, achieving the order of tens of percents. In addition, we test the Hod conjecture which suggests the upper bound for the imaginary part of the frequency of the longest lived quasinormal modes by the Hawking temperature multiplied by a factor. We show that in both non-Schwarzschild metrics the Dirac field obeys the above conjecture for the whole range of black-hole parameters.

Hawking radiation of non-Schwarzschild black holes in higher derivative gravity: A crucial role of grey-body factors

The higher derivative gravity includes corrections of the second order in curvature and allows for both Schwarzschild and non-Schwarzschild asymptotically flat black-hole solutions. Here we find the grey-body factors and energy emission rates for Hawking radiation of test Dirac and electromagnetic fields in the vicinity of such a non-Schwarzschild black hole. The temperature and mass of the black hole monotonically decrease from its Schwarzschild value to zero when the coupling constant is increased up to its extremal value. Nevertheless, for small and moderate values of the coupling constant the Hawking radiation is enhanced, and only in the regime of large coupling it is suppressed, as one could expect. The reason for such counter-intuitive behavior is the important role of the grey-body factors: for small and moderate couplings the temperature falls relatively slowly, while the effective potentials for black holes of the same mass become considerably lower, allowing for much higher transmission rates. We have also estimated the lifetime of such black holes and shown that the range of black-hole masses at which ultra-relativistic emission of massive electrons and positrons starts is shifted towards smaller black-hole masses when the coupling constant is large.

Characterizing black hole metrics in quadratic gravity

The recent discovery of non-Schwarzschild black hole spacetimes has opened new directions of research in higher-derivative gravitational theories. However, despite intense analytical and numerical efforts, the link with the linearized theory is still poorly understood. In this work we address this point for the Einstein-Weyl Lagrangian, whose weak field limit is characterized by the standard massless graviton and a spin-2 ghost. We show that the strength of the Yukawa term at infinity determines the thermal properties of the black hole and the structure of the singularity near $r=0$. Moreover, inspired by recent results in the Asymptotic Safety scenario we investigate the consequences of an imaginary ghost mass. In this case we find a countable set of solutions all characterized by spatial oscillations of typical wavelength determined by the mass of the spin-2 field.

Quasinormal modes of the four-dimensional black hole in Einstein\u2013Weyl gravity

In this paper we consider quasi-normal modes of test scalar and electromagnetic fields in the background of a non-Schwarzschild black hole in the Einstein–Weyl gravity. We find the dependence of the modes on the new parameter p, which is related to the coupling constant alpha , for different values of the angular parameter l and show that when l is increasing, the frequencies tend to linear dependence on p. We have also examined the case of a massive scalar field for which we have shown that the arbitrarily long lived modes (called quasi-resonances) exist in the spectrum.

Gregory-Laflamme instability of black hole in Einstein-scalar-Gauss-Bonnet theories

We investigate the stability analysis of Schwarzschild black hole in Einstein-scalar-Gauss-Bonnet (ESGB) theory because the instability of Schwarzschild black hole without scalar hair implies the Gauss-Bonnet black hole with scalar hair. The linearized scalar equation is compared to the Lichnerowicz-Ricci tensor equation in the Einstein-Weyl gravity. It turns out that the instability of Schwarzschild black hole in ESGB theory is interpreted as not the tachyonic instability, but the Gregory-Laflamme instability of black string. In the small mass regime of $1/\lambda<1.174/r_+$, the Schwarzschild solution becomes unstable and a new branch of solution with scalar hair bifurcates from the Schwarzschild one. This is very similar to finding a newly non-Schwarzschild black hole in Einstein-Weyl gravity.

Abdus Salam and quadratic curvature gravity: Classical solutions

In 1978, Salam and Strathdee suggested on the basis of Froissart boundedness that curvature-squared terms should be included in the gravitational Lagrangian. Despite the presence of ghosts in such theories, the subject has remained a persistent topic in approaches to quantum gravity and cosmology. In this article, the space of spherically symmetric solutions to such theories is explored, highlighting horizonless solutions, wormholes and non-Schwarzschild black holes.

Magnetized particle motion around non-Schwarzschild black hole immersed in an external uniform magnetic field

The motion of a magnetized particle orbiting around non-Schwarzschild black hole immersed in an external uniform magnetic field is considered. The influence of deformation parameter $h$ to effective potential of the radial motion of the magnetized particle around non-Schwarzschild black hole using Hamilton-Jacobi formalism is studied. We have obtained numerical values of area $\Delta \rho $ where magnetized particles can move which is expanding (narrowing) due to the effect of the negative (positive) deformation. Finally, we have studied the collision of two particles (magnetized-neutral, magnetized-magnetized, magnetized-charged) in non-Schwarzschild spacetime and got the center-of-mass energy $(E_{c.m})$ for the particles. Moreover, we have found the capture radius ( $r_{cap}$ ) – the distance from the central object to the point where particles collide and fall down to the central compact object. It is shown that non-Schwarzschild black holes could also act as particle accelerators with arbitrarily high center-of-mass energy.

Gravitational lensing by a non-Schwarzschild black hole in a plasma

We study gravitational lensing in the vicinity of a massive object described by non-Schwarzschild geometry surrounded by a homogeneous plasma. The expression for the deflection angle in a non-Schwarzschild space-time in the weak field regime in the presence of plasma have been derived. It has been shown that the obtained deflection angle depends on (i) the frequency of the electromagnetic wave, due to the dispersion properties of the plasma; (ii) the gravitational mass \(M\); and (iii) deformation parameter \(\epsilon\) of the gravitational lens. Moreover, the influence of deformation parameter of the gravitational lens and plasma frequency on the magnification of brightness of the source star has been studied in the case of microlensing.

Features and stability analysis of non-Schwarzschild black hole in quadratic gravity

Black holes are found to exist in gravitational theories with the presence of quadratic curvature terms and behave differently from the Schwarzschild solution. We present an exhaustive analysis for determining the quasinormal modes of a test scalar field propagating in a new class of black hole backgrounds in the case of pure Einstein-Weyl gravity. Our result shows that the field decay of quasinormal modes in such a non-Schwarzschild black hole behaves similarly to the Schwarzschild one, but the decay slope becomes much smoother due to the appearance of the Weyl tensor square in the background theory. We also analyze the frequencies of the quasinormal modes in order to characterize the properties of new back holes, and thus, if these modes can be the source of gravitational waves, the underlying theories may be testable in future gravitational wave experiments. We briefly comment on the issue of quantum (in)stability in this theory at linear order.

Spherically symmetric solutions in higher-derivative gravity

Extensions of Einstein gravity with quadratic curvature terms in the action arise in most effective theories of quantized gravity, including string theory. This article explores the set of static, spherically symmetric and asymptotically flat solutions of this class of theories. An important element in the analysis is the careful treatment of a Lichnerowicz-type ``no-hair'' theorem. From a Frobenius analysis of the asymptotic small-radius behavior, the solution space is found to split into three asymptotic families, one of which contains the classic Schwarzschild solution. These three families are carefully analyzed to determine the corresponding numbers of free parameters in each. One solution family is capable of arising from coupling to a distributional shell of matter near the origin; this family can then match onto an asymptotically flat solution at spatial infinity without encountering a horizon. Another family, with horizons, contains the Schwarzschild solution but includes also non-Schwarzschild black holes. The third family of solutions obtained from the Frobenius analysis is nonsingular and corresponds to ``vacuum'' solutions. In addition to the three families identified from near-origin behavior, there are solutions that may be identified as ``wormholes,'' which can match symmetrically onto another sheet of spacetime at finite radius.