Schwarzschild Black Hole Research Articles

Effective metric descriptions of quantum black holes

In a recent work (Del Piano et al. in Phys Rev D 109(2):024045, 2024), we have described spherically symmetric and static quantum black holes as deformations of the classical Schwarzschild metric that depend on the physical distance to the horizon. We have developed a framework that allows us to compute the latter in a self-consistent fashion from the deformed geometry, in the vicinity of the horizon. However, in this formalism, the distance can be replaced by other physical quantities, e.g. curvature invariants such as the Ricci- or Kretschmann scalar. Here, we, therefore, define a more general framework, which we call an effective metric description (EMD), that captures the deformed geometry based on a generic physical quantity. We develop in detail the Ricci- and Kretschmann scalar EMD, in particular demonstrating how to compute the geometry in a self-consistent manner. Moreover, we provide explicit relations that allow us to express one EMD in terms of the others, thus demonstrating their equivalence.

Dynamical implications of the Kerr multipole moments for spinning black holes

Previously the linearized stress tensor of a stationary Kerr black hole has been used to determine some of the values of gravitational couplings for a spinning black hole to linear order in the Riemann tensor in the action (worldline or quantum field theory). In particular, the couplings on operators containing derivative structures of the form (\U0001d446 ∙ ∇)\U0001d45b acting on the Riemann tensor were fixed, with \U0001d446\U0001d707 the spin vector of the black hole. In this paper we find that the Kerr solution determines all of the multipole moments in the sense of Dixon of a stationary spinning black hole and that these multipole moments determine all linear in \U0001d445 couplings. For example, additional couplings beyond the previously mentioned are fixed on operators containing derivative structures of the form \U0001d4462\U0001d45b(\U0001d45d ∙ ∇)2\U0001d45b acting on the Riemann tensor with \U0001d45d\U0001d707 the momentum vector of the black hole. These additional operators do not contribute to the three-point amplitude, and so do not contribute to the linearized stress tensor for a stationary black hole. However, we find that they do contribute to the Compton amplitude. Additionally, we derive formal expressions for the electromagnetic and gravitational Compton amplitudes of generic spinning bodies to all orders in spin in the worldline formalism and evaluated expressions for these amplitudes to \U0001d4aa(\U0001d4463) in electromagnetism and \U0001d4aa(\U0001d4465) in gravity.

Magnetic seed generation by plasma heat flux in accretion disks

Magnetic batteries are potential sources that may drive the generation of a seed magnetic field, even if this field is initially zero. These batteries can be the result of nonaligned thermodynamic gradients in plasmas, as well as of special and general-relativistic effects. So far, magnetic batteries have only been studied in ideal magnetized fluids. We studied the nonideal fluid effects introduced by the energy flux in the vortical dynamics of a magnetized plasma in curved space-time. We propose a novel mechanism for generating a heat-flux-driven magnetic seed within a simple accretion disk model around a Schwarzschild black hole. We used the 3+1 formalism for the splitting of the space-time metric into space-like and time-like components. We studied the vortical dynamics of a magnetized fluid with a heat flux in the Schwarzschild geometry in which thermodynamic and hydrodynamic quantities are only dependent on the radial coordinate. Assuming that the magnetic field is initially zero, we estimated the linear time evolution of the magnetic field due to the inclusion of nonideal fluid effects. When the thermodynamic and hydrodynamic quantities vary only radially, the effect of the coupling between the heat flux, the space-time curvature, and the fluid velocity acts as the primary driver for an initial linearly time-growing magnetic field. The plasma heat flux completely dominates the magnetic field generation at a specific distance from the black hole, where the fluid vorticity vanishes. This distance depends on the thermodynamical properties of the Keplerian plasma accretion disk. These properties control the strength of the nonideal effects in the generation of seed magnetic fields. We find that heat flux is the main driver of a seed magnetic field in black hole accretion disks if the geometry, plasma dynamics, and thermodynamics share the same axial symmetry. This suggests that nonideal fluid effects may play a major role in the magnetization of astrophysical plasmas.

Distinguishing black holes with and without spontaneous scalarization in Einstein-scalar-Gauss–Bonnet theories via optical features

Spontaneous scalarization in Einstein-scalar-Gauss–Bonnet theory admits both vacuum-general relativity (GR) and scalarized hairy black holes as valid solutions, which provides a distinctive signature of new physics in strong gravity regime. In this paper, we shall examine the optical features of Gauss–Bonnet black holes with spontaneous scalarization, which is governed by the coupling parameter λ. We find that the photon sphere, critical impact parameter and innermost stable circular orbit all decrease as the increasing of λ. Using observable data from Event Horizon Telescope, we establish the upper limit for λ. Then we construct the optical appearances of the scalarized black holes illuminated by various thin accretions. Our findings reveal that the scalarized black holes consistently exhibit smaller shadow sizes and reduced brightness compared to Schwarzschild black holes. Notably, in the case of thin spherical accretion, the shadow of the scalarized black hole is smaller, but the surrounding bright ring is more pronounced. Our results highlight the observable features of the scalarized black holes, providing a distinguishable probe from their counterpart in GR in strong gravity regime.

On the gravitational hysteresis in the kinetic theory

General theory of relativity is non-linear in nature and therefore can result in hysteresis-like effects and cause systems to remember the footprint of the gravitational field. Here we have investigated this effect using the Kinetic theory in curved spacetime. It is shown that the entropy rate experiences this hysteresis behavior. The effect is then considered for some special spacetimes, including Schwarzschild black hole, Friedmann-Lemaître-Robertson-Walker cosmological solution, and the flat Minkowski spacetime perturbed by a gravitational wave pulse. It is shown that there is some hysteresis effect for the entropy rate.

Testing the non-commutative charged Schwarzschild black hole surrounded by perfect fluid dark matter for thermodynamical features and weak gravitational lensing

This paper is devoted in studying the thermodynamical properties and weak gravitational lensing in the context of a non-commutative charged Schwarzschild black hole surrounded by perfect fluid dark matter. In this context, we study the geometric mass and thermal temperature to discuss the viability of the charged black hole solution by evaluating the specific heat, the phase transition and stability of the configuration. We also study the energy emission process of the black hole. From the thermodynamical properties, we conclude that our studied black hole solution is thermally stable. Moreover, we discuss gravitational lensing in the weak plasma field by considering uniform as well as non-uniform plasma and evaluate the deflection angle where we observe that the deflection angle in the case of uniform plasma is greater than that in non-uniform plasma. We also have studied the image magnification from the source’s brightness and observed that in uniform plasma case, the source image is more magnified than the non-uniform plasma.

Schwarzschild black hole surrounded by a cloud of strings in the background of perfect fluid dark matter

Schwarzschild black hole surrounded by a cloud of strings in the background of perfect fluid dark matter

Islands far outside the horizon

Information located in an entanglement island in semiclassical gravity can be nonperturbatively reconstructed from distant radiation, implying a radical breakdown of effective field theory. We show that this occurs well outside of the black hole stretched horizon. We compute the island associated to large-angular momentum Hawking modes of a four-dimensional Schwarzschild black hole. These modes typically fall back into the black hole but can be extracted to infinity by relativistic strings or, more abstractly, by asymptotic boundary operators constructed using the timelike tube theorem. Remarkably, we find that their island can protrude a distance of order ℓprhor outside the horizon. This is parametrically larger than the Planck scale ℓp and is comparable to the Bohr radius for supermassive black holes. Therefore, in principle, a distant observer can determine experimentally whether the black hole information paradox is resolved by complementarity, or by a firewall.

Holographic thermodynamics of a charged AdS black hole with a global monopole

By regarding the Newton constant G N and cosmological constant Λ as variables, in this paper we study the thermodynamics and phase transition of the Reissner-Nordstr öm anti-de Sitter (RN-AdS) black hole with a global monopole within the framework of AdS/CFT correspondence. We find interesting critical phenomena and phase behavior in the (grand) canonical ensembles of fixed ( Q˜,V,C ), ( Φ˜,V,C ) and ( Q˜,V,μ ). When the other parameters are fixed, the free energy decreases with the global monopole increases. In the ( Q˜,V,C ) ensemble, the range of the unstable region decreases with the increase of the global monopole. In the ( Φ˜,V,C ) ensemble, when Φ˜<Φc , the free energy appears as two branches, where the upper and lower branches correspond to low and high entropy, respectively. When ( Q˜,V,μ ) is fixed, a new zero-order phase transition occurs in the high-entropy phase and the low-entropy phase at certain μ-dependent temperatures. When μ increases to a certain value, this zero-order phase transition disappears. This certain value is negatively related to the magnitude of the global monopole. Finally, we find that p−V criticality does not appear with the change of global monopole. Therefore, it is important to note that the CFT states of charged black holes with global monopoles do not correspond to van der Waals fluids. Finally, we find that charged black holes with global monopoles can better reflect thermodynamic phase transitions and critical phenomena under the AdS/CFT correspondence. By adjusting the change of the global monopole, the thermodynamic phase transition will also change.

Towards a unitary formulation of quantum field theory in curved space-time: the case of Schwarzschild black hole

Abstract We argue that the origin of unitarity violation and information loss paradox in our understanding of black holes (BHs) lies in the standard way of doing quantum field theory in curved spacetime (QFTCS), which is heavily biased on intuition borrowed from classical General Relativity. In this paper, with the quantum first approach, we formulate a so-called direct-sum QFT (DQFT) in BH spacetime based on a novel formulation of discrete spacetime transformations in gravity that potentially restores unitarity. By invoking the quantum effects associated with the gravitational backreaction, we show that the Hawking quanta emerging outside of the Schwarzschild radius (rS = 2GM) cannot be independent of the quanta that continue to be inside rS. This enables the information to be carried by Hawking quanta, but in the BH DQFT formalism, we do not get any firewalls. Furthermore, DQFT leads to the BH evaporation involving only pure states. This means the quantum mechanical effects at the BH horizon produce two components of a maximally entangled pure state in geometric superselection sector Hilbert spaces. This construction enables pure states to evolve into pure states, restoring unitarity and observer complementarity. Finally, we discuss how our framework leaves important clues for formulating a scattering matrix and probing the nature of quantum gravity.

The shadow and gamma-ray bursts of a Schwarzschild black hole in asymptotic safety

The effects and rules of the dimensionless parameter ξ on neutrino annihilation ν+ν¯→e−+e+ dominated gamma-ray bursts are analysed and investigated within the context of black holes in asymptotic safety. We also computationally model photon orbits around black holes, as photons and neutrinos have the same geodesic equations near black holes. We show that the black hole shadow radius decreases with increasing ξ. Calculations are made to determine the temperature of the accretion disk surrounding the black hole and the ratio Q̇/Q̇Newt of energy deposition per unit time and compared to that of the Newtonian scenario. The accretion disk temperature peaks at a higher temperature due to quantum gravity corrections, which increases the probability of neutrino emission from the black hole. It is interesting to note that larger quantum gravity effects cause the ratio value to significantly decline. In the neutrino–antineutrino annihilation process, the energy deposition rate is sufficient even while the energy conversion is inhibited because of quantum corrections. Gamma-ray bursts might originate from the corrected annihilation process. Additionally, we examine the derivative dQ̇/dr about the star radius r. The findings demonstrate that the ratio is lowered by the black hole’s quantum influence. The neutrino pair annihilation grows weaker the more prominent the influence of quantum gravity.

Maxwell equations in Schwarzschild black hole with topological defects and the gravitational magnetoelectric effect

Maxwell equations in Schwarzschild black hole with topological defects and the gravitational magnetoelectric effect

Extended black hole solutions in Rastall theory of gravity

We utilize the gravitational decoupling via the extended geometric deformation to extend the Schwarzschild vacuum solution to new black holes in Rastall theory. By employing linear transformations that deform both the temporal and radial coefficients of the metric, the field equations with a dual matter source are successfully decoupled into two sets. The first of these sets is described by the metric for the vacuum Schwarzschild spacetime, while the second set corresponds to the added extra source. Three extended solutions are obtained using two restrictions on the metric potentials and extra source, respectively. For selected values of the Rastall and decoupling parameters, we study the impact of the fluctuation of these parameters on the obtained models. We also investigate the asymptotic flatness of the resulting spacetimes by analysis of the metric coefficients. Finally, the nature of the additional source is explored for each model, via analysis of the energy conditions. It is found among other results that none of the obtained models satisfy the energy conditions, while only the model corresponding to the barotropic equation of state mimics an asymptotically flat spacetime.

Thermal stability and phase transitions of static magnetic charged black holes in the background of perfect fluid-type dark matter: Analysis of crucial thermodynamic parameters and P–V criticality along with higher-order entropy corrections

This work focuses on the analysis of P–V criticality for several entropy corrections of uncorrected zeroth entropy of the static magnetic charged black hole embedded in perfect fluid-type dark matter. During the study of P–V criticality, critical points up to several orders are found out. However, the critical points for distinct orders are found to occur at distinct values of the radius of the event horizon. We have resolved the physical significance of those critical points. Further, we have observed that P–V curve wise characteristics do not follow Boyle’s law for some corrections of entropy but it pursues Boyle’s law if we modify the zeroth entropy in some different ways. Physical significance of this phenomenon is also discussed. Again, the heat capacity of the charged black hole for corrected entropies is calculated. Significantly, several phase transitions are observed after plotting those data. We have also investigated how these phase transitions affect the structure of the black hole. Besides, study of free energy and Hawking temperature gives different important cuspidal nodes. The physical significance of these cusps is also discussed. Finally, we obtained an explicit scenario of the phase evolution and stability of the concerned investigated black hole embedded in dark matter.

Black Hole Solutions in Non-Minimally Coupled Weyl Connection Gravity

Schwarzschild and Reissner–Nordstrøm black hole solutions are found in the context of a non-minimal matter–curvature coupling with Weyl connection both in vacuum and in the presence of a cosmological constant-like matter content. This model has the advantage of an extra force term which can mimic dark matter and dark energy, and simultaneously following Weyl’s idea of unifying gravity and electromagnetism. In fact, vacuum Schwarzschild solutions differ from the ones in a constant curvature scenario in f(R) theories, with the appearance of a coefficient in the term that is linear in r and a corrected “cosmological constant”. Non-vacuum Schwarzschild solutions formally have the same solutions as in the previous case, with the exception being the physical interpretation of a cosmological constant as the source of the matter Lagrangian and not a simple reparameterization of the f(R) description. Reissner–Nordstrøm solutions cannot be found in a vacuum, only in the presence of matter fields, with the result that the solutions also differ from the constant curvature scenario in f(R) theories by the term being linear in r, the corrected/dressed charge, and the cosmological constant. These results have bearings on future numerical simulations for black holes and gravitational waves in next-generation wavelet templates.

Расчет отклонения лазерных импульсов при локации искусственных спутников Земли с учетом ее гравитационного поля

Accurate laser location of artificial Earth satellites (AES) makes it possible to obtain valuable information on the dynamic parameters of the Earth, its gravitational fields, and to clarify the global coordinates of the system. The effect of laser pulses deviation at the ranging AES is studied. The angle of deviation is formed between directions of emitted and returned signals at the point of the laser station’s location. The main contribution into the value of the angle is conditioned by relativity theory effects connected with non-inertiality of the station frame on the rotating Earth surface. In this article, the value of the deviation angle is calculated considering the Earth’s gravitational field that was not considered in previous works. Exactness of necessary approximations enables modelling a motion of AES by Keplerian orbits. The gravitational field of the Earth is described by the Schwarzschild solution, in the framework of which equations for the laser pulse trajectories are presented. All the calculations are made in the coordinates of the proper frame of the station. The obtained variation of the main deviation angle value is less for three orders with respect to the one that can be detected by the modern devices. Therefore, we can state that it should not be taken into account. Such a conclusion is very important for developments in this field because simpler methods, including analytical ones, are permissible. The efficiency of the numerical calculations of the effect for concrete AES remains high as well

Superradiance scattering of electromagnetic and gravitational fields and thin accretion disk around non-commutating Kerr black hole

We consider the non-commutative (NC) Kerr black hole where the mass of the central object is smeared over a region of linear size b\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{b}$$\\end{document}, b is the strength of the NC character of spacetime. For the spacetime under consideration, we calculate the amplification factor for electromagnetic and gravitational fields and study various properties of a thin accretion disk. The expression for the amplification factor is obtained with the help of the asymptotic matching technique. The amplification factor is then plotted against frequency for various values of the spin a and the NC parameter b. Though the amplification factor increases with a but decreases with b, the cut-off frequency up to which we have amplification increases with a and b. We then study the effect of the spin and the NC nature of spacetime on the energy flux, temperature distribution, emission spectrum, energy conversion efficiency, and the radius of the innermost stable circular orbit of a thin accretion disk around the black hole with the help of the steady-state Novikov–Thorne model. Our study reveals that these quantities increase with the spin and the NC parameter. We also find that the disk around the NC Kerr black is hotter and more luminous than that around the Kerr black hole and the NC Schwarzschild black hole. We can conclusively infer from our investigation that the NC nature of spacetime has a significant impact on the superradiance phenomenon as well as on various properties of thin accretion disks.

Tripartite measurement uncertainty in Schwarzschild space-time

The effect of Hawking radiation on tripartite measurement uncertainty in a Schwarzschild black hole background is analyzed in this study. Two scenarios are examined. In the first, quantum memory particles approach a Schwarzschild black hole and are positioned near the event horizon, while the particle being measured remains in the asymptotically flat region. In the second scenario, the measured particle moves toward the black hole, and the quantum memories stay in the asymptotically flat region. This study considers two initial quantum states, namely GHZ and W states. Our findings reveal that in both cases, measurement uncertainty increases steadily with rising Hawking temperature. When comparing the GHZ and W states, the GHZ state initially exhibits lower measurement uncertainty at low Hawking temperatures than the W state, indicating greater resilience to Hawking radiation. Additionally, when the quantum memories remain in the asymptotically flat region while the measured particle falls toward the black hole, the uncertainties for GHZ and W states do not align at high temperatures. The GHZ state consistently demonstrates lower measurement uncertainty, showcasing its superior robustness against Hawking radiation.

Perturbations of Gibbons-Maeda black holes in Einstein-Maxwell-dilaton theories

The study of perturbations around black hole backgrounds in general relativity and Einstein-Maxwell theory has a long history, going back to the work of Regge and Wheeler in the 1950s. As part of a broader investigation of perturbations around black holes in supergravity, we describe here our results for the perturbations around the Gibbons-Maeda static charged black holes in a class of Einstein-Maxwell-Dilaton theories. Our analysis follows the general strategy developed by Chandrasekhar and Xanthopoulos for the perturbations of the Reissner-Nordström black hole. Here, the analysis is considerably more involved, because of the presence of the dilaton field, which couples to the other polar modes. We nonetheless find that the problem is completely solvable, in the sense that one can separate variables and eventually describe all the perturbations in terms of diagonalised second-order radial equations. We are able to prove the mode stability of all the Gibbons-Maeda black hole solutions. Published by the American Physical Society 2024

ExaGRyPE: Numerical general relativity solvers based upon the hyperbolic PDEs solver engine ExaHyPE

ExaGRyPE describes a suite of solvers and solver ingredients for numerical relativity that are based upon ExaHyPE 2, the second generation of our Exascale Hyperbolic PDE Engine. Numerical relativity simulations are crucial in resolving astrophysical phenomena in strong gravitational fields and are fundamental in analyzing and understanding gravitational wave emissions. The presented generation of ExaGRyPE solves the Einstein field equations in the standard CCZ4 formulation under a 3+1 foliation and focuses on black hole space-times. It employs a block-structured Cartesian grid carrying a higher-order Finite Difference scheme with full support of adaptive mesh refinement (AMR), it facilitates massive parallelism combining message passing, domain decomposition and task parallelism, and it supports the injection of particles into the grid as static data probes or as moving tracers. We introduce the ExaGRyPE-specific building blocks within ExaHyPE 2, and discuss its software architecture and compute-n-feel.For this, we formalize the creation of any specific astrophysical simulation with ExaGRyPE as a sequence of lowering operations, where a few abstract logical tasks are successively broken down into finer and finer tasks until we obtain an abstraction level which can directly be mapped onto a C++ executable. The overall program logic is fully specified via a domain-specific Python interface, we automatically map this logic onto a more detailed set of numerical tasks, subsequently lower this representation onto technical tasks that the underlying ExaHyPE engine uses to parallelize the application, before eventually the technical tasks in turn are mapped onto small task graphs including the actual astrophysical PDE term evaluations, initial conditions, boundary conditions, and so forth. These can be injected manually by the user, or users might instruct the solver on the most abstract user interface level to use out-of-the-box ExaGRyPE implementations. We end up with a rigorous separation of concerns which shields ExaGRyPE users from technical details and hence simplifies the development of novel physical models. We present the simulations and data for the gauge wave, static single black holes and rotating binary black hole systems, demonstrating that the code base is mature and usable. However, we also uncover domain-specific numerical challenges that need further study by the community in future work.