Schwarzschild Black Hole Research Articles

On the radiation field of a linearly accelerated charged particle in Born–Infeld theory

The electric potential and the electromagnetic field for a linearly accelerated Born–Infeld charged particle are obtained in an inertial frame by a method that can, in principle, be applied to any electromagnetic theory. The method is based on (i) the fact that the metric near the horizon of a Schwarzschild black hole is equivalent to that of Rindler spacetime, and (ii) a theorem that guarantees that the electrostatic potential for a given nonlinear theory in a static, spherically symmetric spacetime is entirely specified by the Maxwellian electrostatic potential in the same background. Using analytical and numerical methods, the features of the radiation field and the radiation-reaction for such an accelerated particle are discussed in detail.

Schwarzschild black hole surrounded by a cavity and phase transition in the non-commutative gauge theory of gravity

In this work, we investigate the phase transition of the Schwarzschild black hole (SBH) inside an isothermal spherical cavity in the context of the non-commutative (NC) gauge theory of gravity, by using the Seiberg–Witten (SW) map and the star product. Firstly, we compute the NC correction to the Hawking temperature and derive the logarithmic correction to the entropy, then we derive the local temperature and local energy of NC SBH in isothermal cavity. Our results show that the non-commutativity removes the commutative divergence behavior of temperature, and prevents the SBH from the complete evaporation, which leads to a remnant black hole, and this geometry has predicted a minimal length in the order of Planck scale Θ∼lplanck. Therefore, the thermodynamic stability and phase transition is studied by analyzing the behavior of the local heat capacity and the Helmholtz free energy in the NC spacetime, where the results show that, the NC SBH has a two second-order phase transition and one first-order phase transition, with two Hawking–Page phase transition in the NC gauge theory.

Anisotropy Induced by Electric Charge: A Computational Analytical Approach

This paper presents a novel class of interior solutions for anisotropic stars under the imposition of a self-similar symmetry. This means proposing exact solutions to the Einstein field equations to describe charged matter distribution with radiation flow. The Einstein–Maxwell system by employing specific choices of mass function is formulated to describe the gravitational collapse of charged, anisotropic, spherically symmetric distributions using the Schwarzschild metric. Two ordinary differential equations governing the dynamics are derived by matching a straightforward solution of the symmetry equations to the charged exterior (Reissner–Nordström–Vaidya). Models with satisfactory physical behavior are constructed by extensively exploring self-similar solutions for a set of parameters and initial conditions. Finally, the paper presents the evolution of physical variables and the collapsing radius, demonstrating the inevitable collapse of the matter distribution.

Thermodynamics of the quantum Schwarzschild black hole

We discuss some thermodynamic properties as well as the stability of a quantum Schwarzschild black hole, comparing the results with those obtained within a bumblebee gravity model. In particular, the Hawking temperature, TH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{{\ ext{H}}}$$\\end{document}, the entropy, S, the heat capacity, C, and the Gibbs free energy, G, are computed for both cases. In addition to that, we compute the Brown-York quasilocal energy and compare the solution with the Schwarzschild case. We find that in both cases (quantum Schwarzschild and bumblebee gravity model) the temperature, the entropy, and the heat capacity show the same functional form, under the replacement λ2→ℓ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda ^2 \\rightarrow \\ell$$\\end{document} and vice versa. Specifically, the temperature is found to be lower compared to the classical (Schwarzschild) solution; whereas, the entropy is computed to be larger. Moreover, the heat capacity becomes more negative. Notably, a distinct contrast emerges in obtaining the Gibbs free energy between these two cases, and this distinction appears to stem from the ADM mass.

Exact massless spinor quasibound states of Schwarzschild black hole

In this work, we investigate the behavior of massless spin 12 field by working out the Dirac equation in a curved static spherically symmetric Schwarzschild space-time. Detailed derivation of novel exact massive and massless scalar quasibound state in Schwarzschild black hole background is presented in this work. After decoupling the Dirac equation, we successfully solve both of the angular and radial parts, respectively in terms of spin weighted Spherical Harmonics and Confluent Heun functions. With the exact radial wave solution in hand, applying its polynomial condition leads to the discovery of the quantized energy levels expression. We found that the massless spinor field around the Schwarzschild black hole has complex valued energy levels, in contrast to the purely imaginary for a massless boson around the same black hole. In the last section, the Hawking radiation distribution function is derived via Damour-Ruffini method and the Hawking temperature is obtained.

Gravitational probe of ꝗuantum spacetime

A quest for phenomenological footprints of quantum gravity is among the central scientific tasks in the rising era of gravitational wave astronomy. We study gravitational wave dynamics within the noncommutative geometry framework, based on a Drinfeld twist and newly proposed noncommutative Einstein equation, and obtain the leading quantum correction to Regge-Wheeler potential up to first order in the noncommutativity parameter. By calculating the quasinormal mode frequencies we show that the noncommutative Schwarzschild black hole remains stable under axial gravitational perturbations.

Anisotropic generalized polytropic spheres: Regular 3D black holes

We model gravitating relativistic 3D spheres composed of an anisotropic fluid in which the radial and transverse components of the pressure correspond to the vacuum energy and a generalized polytropic equation-of-state, respectively. By using the generalized Tolman–Oppenheimer–Volkoff (TOV) equation, and solving the complete system of equations for these anisotropic generalized polytropic spheres, for a given range of model parameters, we find three novel classes of asymptotically AdS black hole solutions with regular core. We show the regularity of the solutions using curvature scalars and the formalism of geodesic completeness. Then, using the eigenvalues of the Riemann curvature tensor, we consider the effects of repulsive gravity in the three static 3D regular black holes, concluding that their regular behavior can be explained as due to the presence of repulsive gravity near the center of the objects. Finally, we study the stability of the regular black holes under the flow of the energy through the Cauchy horizon.

Dark dimension, the swampland, and the dark matter fraction composed of primordial near-extremal black holes

In a recent publication we studied the decay rate of primordial black holes perceiving the dark dimension, an innovative five-dimensional (5D) scenario that has a compact space with characteristic length scale in the micron range. We demonstrated that the rate of Hawking radiation of 5D black holes slows down compared to 4D black holes of the same mass. Armed with our findings we showed that for a species scale of O(1010 GeV), an all-dark-matter interpretation in terms of primordial black holes should be feasible for black hole masses in the range 1014≲M/g≲1021. As a natural outgrowth of our recent study, herein we calculate the Hawking evaporation of near-extremal 5D black holes. Using generic entropy arguments we demonstrate that Hawking evaporation of higher-dimensional near-extremal black holes proceeds at a slower rate than the corresponding Schwarzschild black holes of the same mass. Assisted by this result we show that if there were 5D primordial near-extremal black holes in nature, then a primordial black hole all-dark-matter interpretation would be possible in the mass range 105β≲M/g≲1021, where β is a parameter that controls the difference between mass and charge of the associated near-extremal black hole. Published by the American Physical Society 2024

Vanishing of nonlinear tidal Love numbers of Schwarzschild black holes

It is well known that asymptotically flat Schwarzschild black holes in general relativity in four spacetime dimensions have vanishing induced linear tidal response. We extend this result beyond linear order for the polar sector, by solving the static nonlinear Einstein equations for the perturbations of the Schwarzschild metric and computing the quadratic corrections to the electric-type tidal Love numbers. After explicitly performing the matching with the point-particle effective theory at leading order in the derivative expansion, we show that the Love number couplings remain zero at higher order in perturbation theory.

Particles with magnetic dipole moment orbiting magnetized Schwarzschild black holes: Applications to orbits of hot-spots around Sgr A*

We study the circular motion of particles with magnetic dipole moment around Schwarzschild black holes immersed in external asymptotically uniform and dipolar magnetic field configurations and calculate the orbital velocity of the particles. We assume that the flares observed around supermassive black hole Sagittarius (Sgr) A* detected by the GRAVITY ESO collaboration (on May 27, July 22, and July 28, 2018) are magnetized compact objects, in particular, neutron stars (NSs) and white dwarfs (WDs). Also, we apply orbital and luminosity data from (three) flares to explore the possible role of magnetic interaction on hot spots’ dynamics. First, we found the mass range of SgrA* using the orbital data in the absence of external magnetic fields as M=(3−6.3)M⊙. It is also found that, for magnetized particles that can be in the hot spot’s orbits, the magnetic coupling parameter β has to take values less than 0.13 and 0.25 in the cases of external dipolar and uniform magnetic fields, respectively. The critical values for the surface magnetic fields, mass, and radius of magnetized NSs and WDs are found to be candidates for the hot-spot objects. Finally, we found upper and lower limits for the surface magnetic field, radius, and rotating period of the NSs and WDs, using the luminosity data of the hot spots.

Dark photon–dark energy stationary axisymmetric black holes

Dark photon–dark energy stationary axisymmetric black holes

Relativistic massive and massless scalar fields bound to the Bumblebee gravity's black hole

In this letter, we examine massive and massless scalar quasibound states bound in the static spherically symmetric black hole solution of the Einstein-Bumblebee space-time. We start with constructing the governing relativistic fields' dynamical equation, i.e. the Klein-Gordon equation, component by component. With the help of the ansatz of separation of variables, we find the exact solution of the angular part in terms of Spherical Harmonics while the radial exact solution is discovered in terms of the Confluent Heun function. The quantization of the quasibound state is done by applying the polynomial condition of the Confluent Heun function that reveals a complex-valued energy levels expression for the case of massive scalar, where the real part is the scalar particle's energy and the imaginary part represents the quasibound state's decay. And for a massless scalar, a pure imaginary energy levels is obtained. The quasibound states, thus, describe decaying relativistic states bound in the black hole's gravitational potential well. At the end, we investigate the Hawking radiation of the static Bumblebee black hole's horizon by deriving and investigating the radiation distribution function.

TWO-STAGE ‘slingshot amplifier’ can detect subtle gravitational deviations

The possibility of setting up a space experiment aimed at detecting ultra-small deviations of the law of gravity of the central star of the planetary system from the Newton and Schwarzschild formats is demonstrated. The experiment comprises a ballistic flight of a space-probe along a trajectory composed of three treks divided by two gravity assist (GA) maneuvers at different planets, each GA acting as a powerful amplifier of the probe deflections caused by small deviations of the gravitational law. It is shown that the proposed (different) analytical and numerical computations of the probe's flight in a model of a planetary system simulating the Sun, Earth, and Venus, give similar results confirming a certain possibility to distinguish the forces of gravity described by the Schwarzschild and Eddington-Robertson metrics.

Greybody factors, quasi-normal modes and thermal fluctuations of quantum-corrected Schwarzschild black hole surrounded by quintessence

In this study, we examine the effects of a quintessence field-enclosed Schwarzschild black hole that has undergone quantum corrections on a number of different physical phenomena. The effective potential and its graphical features across different values of the quantum correction and quintessence field as well as relevant physical parameters are analyzed by deriving the radial equation from the Klein–Gordon equation and converting it into a Schrodinger wave equation using the tortoise coordinate. Both the event and cosmic horizons are found in the solutions to the radial equation. We provide a detailed analysis of the greybody component and its behavior by merging these solutions in the intermediate regime. By analyzing the black hole metric function, effective potential, and absorption probabilities, the study uncovers the complex relationship between black hole characteristics, quantum corrections, and the surrounding quintessence field. Investigating the BH’s quasinormal modes and thermal fluctuations provides insights into its stability as well as thermodynamic properties. The findings offer a comprehensive understanding of how the black hole interacts with its environment and responds to environmental changes, shedding light on the rich dynamics of black hole systems in the presence of quantum corrections and quintessence fields.

Quasinormal modes in noncommutative Schwarzschild black holes

We investigate the quasinormal modes of a massless scalar field in a Schwarzschild black hole, which is deformed due to noncommutative corrections. We introduce the deformed Schwarzschild black hole solution, which depends on the noncommutative parameter Θ. We then extract the master equation as a Schrödinger-like equation, giving the explicit expression of the effective potential which is modified due to the noncommutative corrections. After that, we solve the master equation numerically. The significance of these results is twofold. Firstly, our results can be related to the detection of gravitational waves by the near future gravitational wave detectors, such as LISA, which will have a significantly increased accuracy. In particular, these observed gravitational waves produced by binary strong gravitational systems have oscillating modes which can provide valuable information. Secondly, our results can serve as an additional tool to test the predictions of GR, as well as to examine the possible detection of this kind of gravitational corrections.

Echoes of massless scalar field induced from hairy Schwarzschild black hole

A hairy Schwarzschild black hole describes the deformation of Schwarzschild black hole with an exponent correction due to the introducing of additional sources. Inspired by the novel feature that the hairy Schwarzschild black hole can have double photon spheres for certain parameters space, in this paper we study the echo signals of a massless scalar field from this hairy Schwarzschild black hole by calculating its time evolution. We mainly analyze how the hairy parameters and scalar field's angular momentum affect the echo waveform of the perturbing scalar field. Additionally, we roughly evaluate the time delay of echoes. We find that the hairy parameters have significant influences on the echo signals.

Thermodynamic phase transition rate for the third-order Lovelock black hole in diverse dimensions

The phase transition has always been a major focus in the study of black hole thermodynamics. This study employs the Kramer escape rate from stochastic processes to investigate the first-order phase transition strength between the large and small black hole states. The results indicate that the phase transition of the third-order Lovelock black holes exhibits significant asymmetric characteristics in diverse dimensions both in the hyperbolic and spherical topology, with an overall trend of the transition from large black holes to small black holes. Especially for the spherical topology, when the dimension is higher than seven, there exists a certain temperature beyond which a dynamic equilibrium is established for the phase transition. This study provides valuable insights into the first-order phase transition rate of black holes and enriches the understanding of black hole phase transitions.

Resolving the vicinity of supermassive black holes with gravitational microlensing

ABSTRACT Upcoming wide-field surveys will discover thousands of new strongly lensed quasars which will be monitored with unprecedented cadence by the Legacy Survey of Space and Time (LSST). Many of these quasars will undergo caustic-crossing events over the 10-yr LSST survey, during which the quasar’s inner accretion disc crosses a caustic feature produced by an ensemble of microlenses. Such caustic-crossing events offer the unique opportunity to probe the vicinity of the central supermassive black hole, especially when combined with high cadence, multi-instrument follow-up triggered by LSST monitoring. To simulate the high-cadence optical monitoring of caustic-crossing events, we use relativistic accretion disc models which leads to strong asymmetric features. We develop analysis methods to measure the innermost stable circular orbit (ISCO) crossing time of isolated caustic-crossing events and benchmark their performance on our simulations. We also use our simulations to train a convolutional neural network (CNN) to infer the black hole mass, inclination angle, and impact angle directly from these light curves. As a pilot application of our methods, we used archival caustic-crossings of QSO 2237+0305 to estimate the black hole mass and inclination angle. From these data, two of these methods called the second derivative and wavelet methods measure an ISCO crossing time of 48.5 and 49.5 d, corresponding to a Kerr black hole mass of MBH = (1.5 ± 1.2) × 109 and (1.5 ± 1.3) × 109 M⊙, respectively. The CNN inferred log10(MBH/M⊙) = 8.35 ± 0.30 when trained on Schwarzschild black hole simulations, and a moderate inclination of i = 45 ± 23°. These measurements are found to be consistent with previous estimates.

The quantum corrected Schwarzschild black hole with a linear-quadratic GUP: a comprehensive evaluation

In this manuscript, we delve into an analytic and numerical probe of shadow with different accretion models, quasinormal modes, Hawking radiation, and gravitational lensing to study observational impacts of quantum effect introduced through linear-quadratic GUP(LQG). Our investigation reveals that the shadows of LQG-modified black holes are smaller and brighter than Schwarzschild black holes. To examine the impact of the quantum correction on the quasinormal mode, linear-quadratic GUP-modified black holes are explored under scalar andelectromagnetic field perturbation. Here, linear-quadratic GUP isused to capture quantum corrections. It is observed that theincorporation of quantum correction by linear-quadratic GUP altersthe singularity structure of the black hole. To compute thequasinormal modes of this linear-quadratic GUP-inspiredquantum-corrected black holes, we compute the effective potentialgenerated under the perturbation of scalar and electromagneticfield, and then we use the sixth-order WKB approach in conjunctionwith the appropriate numerical analysis. We find that the greybody factor decreases with the GUP parameter α implying that the probability of transmission decreases with the GUP parameter. The total power emitted by LQG modified black hole is found to be greater than that emitted by Schwarzschild black hole. Finally, we study weak gravitational lensing and make a comparison with quadratic GUP and linear GUP-modified black holes.

Notes on emergent conformal symmetry for black holes

We examine the motion of the massless scalar field and nearly bound null geodesics in the near-ring region of a black hole, which may possess either acceleration or a gravitomagnetic mass. Around such black holes, the photon ring deviates from the equatorial plane. In the large angular momentum limit, we demonstrate that the massless scalar field exhibits an emergent conformal symmetry in this near-ring region. Additionally, in the nearly bound limit, we observe the emergence of a conformal symmetry for the null geodesics that constitute the photon ring in the black hole image. These findings suggest that the hidden conformal symmetry, associated with the Lie algebra 𝔰𝔩(2, ℝ), persists even for black holes lacking north-south reflection symmetry, thereby broadening the foundation of photon ring holography. Finally, we show that the conformal symmetry also emerges for nearly bound timelike geodesics and scalar fields in proximity to the particle ring, and with specific mass around a Schwarzschild black hole.