Causality Bounds on Dissipative General-Relativistic Magnetohydrodynamics

We derive necessary and sufficient conditions under which a large class of relativistic generalizations of Braginskii's magnetohydrodynamics with shear, bulk, and heat diffusion effects is causal and strongly hyperbolic in the fully nonlinear regime in curved spacetime. We find that causality severely constrains the size of nonideal effects and the onset of kinetic instabilities. Our results are crucial for assessing the regime of validity of fluid dynamical simulations of plasmas near supermassive black holes.

Charged Black-Hole-Like Electronic Structure Driven by Geometric Potential of 2D Semiconductors

One of the exotic expectations in the 2D curved spacetime is the geometric potential from the curvature of the 2D space, still possessing unsolved fundamental questions through Dirac quantization. The atomically thin 2D materials are promising for the realization of the geometric potential, but the geometric potential in 2D materials is not identified experimentally. Here, the curvature-induced ring-patterned bound states are observed in structurally deformed 2D semiconductors and formulated the modified geometric potential for the curvature effect, which demonstrates the ring-shape bound states with angular momentum. The formulated modified geometric potential is analogous to the effective potential of a rotating charged black hole. Density functional theory and tight-binding calculations are performed, which quantitatively agree well with the results of the modified geometric potential. The modified geometric potential is described by modified Gaussian and mean curvatures, corresponding to the curvature-induced changes in spin-orbit interaction and band gap, respectively. Even for complex structural deformation, the geometric potential solves the complexity, which aligns well with experimental results. The understanding of the modified geometric potential provides us with an intuitive clue for quantum transport and a key factor for new quantum applications such as valleytronics, spintronics, and straintronics in 2D semiconductors.

Geometrothermodynamics of 3D Regular Black Holes

We investigate a spherically symmetric exact solution of Einstein's gravity with cosmological constant in (2 + 1) dimensions, non-minimally coupled to a scalar field. The solution describes the gravitational field of a black hole, which is free of curvature singularities in the entire spacetime. We use the formalism of geometrothermodynamics to investigate the geometric properties of the corresponding space of equilibrium states and find their interpretation from the point of view of thermodynamics. It turns out that, as a result of the presence of thermodynamic interaction, the space of equilibrium states is curved with two possible configurations, which depend on the value of a coupling constant. In the first case, the equilibrium space is completely regular, corresponding to a stable thermodynamic system. The second case is characterized by the presence of two curvature singularities, which are shown to correspond to locations where the system undergoes two different phase transitions, one due to the breakdown of the thermodynamic stability condition and the second one due to the presence of a divergence at the level of the response functions.

The cosmological constant and scale hierarchies with emergent gauge symmetries

Motivated by the stability of the electroweak Higgs vacuum we consider the possibility that the Standard Model might work up to large scales between about [Formula: see text] GeV and close to the Planck scale. A plausible scenario is an emergent Standard Model with gauge symmetries originating in some topological-like phase transition deep in the ultraviolet. In this case, the cosmological constant scale and neutrino masses should be of similar size, suppressed by factor of the large scale of emergence. The key physics involves a subtle interplay of Poincaré invariance, mass generation and renormalization group invariance. The Higgs mass would be environmentally selected in connection with vacuum stability. Consequences for dark matter scenarios are discussed. This article is part of the theme issue 'The particle-gravity frontier'.

Cosmic ray feedback in galaxies and galaxy clusters: A pedagogical introduction and a topical review of the acceleration, transport, observables, and dynamical impact of cosmic rays

Understanding the physical mechanisms that control galaxy formation is a fundamental challenge in contemporary astrophysics. Recent advances in the field of astrophysical feedback strongly suggest that cosmic rays (CRs) may be crucially important for our understanding of cosmological galaxy formation and evolution. The appealing features of CRs are their relatively long cooling times and relatively strong dynamical coupling to the gas. In galaxies, CRs can be close to equipartition with the thermal, magnetic, and turbulent energy density in the interstellar medium, and can be dynamically very important in driving large-scale galactic winds. Similarly, CRs may provide a significant contribution to the pressure in the circumgalactic medium. In galaxy clusters, CRs may play a key role in addressing the classic cooling flow problem by facilitating efficient heating of the intracluster medium and preventing excessive star formation. Overall, the underlying physics of CR interactions with plasmas exhibit broad parallels across the entire range of scales characteristic of the interstellar, circumgalactic, and intracluster media. Here we present a review of the state-of-the-art of this field and provide a pedagogical introduction to cosmic ray plasma physics, including the physics of wave-particle interactions, acceleration processes, CR spatial and spectral transport, and important cooling processes. The field is ripe for discovery and will remain the subject of intense theoretical, computational, and observational research over the next decade with profound implications for the interpretation of the observations of stellar and supermassive black hole feedback spanning the entire width of the electromagnetic spectrum and multi-messenger data.

Terahertz Twistoptics-Engineering Canalized Phonon Polaritons

The terahertz (THz) frequency range is key to studying collective excitations in many crystals and organic molecules. However, due to the large wavelength of THz radiation, the local probing of these excitations in smaller crystalline structures or few-molecule arrangements requires sophisticated methods to confine THz light down to the nanometer length scale, as well as to manipulate such a confined radiation. For this purpose, in recent years, taking advantage of hyperbolic phonon polaritons (HPhPs) in highly anisotropic van der Waals (vdW) materials has emerged as a promising approach, offering a multitude of manipulation options, such as control over the wavefront shape and propagation direction. Here, we demonstrate the THz application of twist-angle-induced HPhP manipulation, designing the propagation of confined THz radiation between 8.39 and 8.98 THz in the vdW material α-molybdenum trioxide (α-MoO3), hence extending twistoptics to this intriguing frequency range. Our images, recorded by near-field optical microscopy, show the frequency- and twist-angle-dependent changes between hyperbolic and elliptic polariton propagation, revealing a polaritonic transition at THz frequencies. As a result, we are able to allocate canalization (highly collimated propagation) of confined THz radiation by carefully adjusting these two parameters, i.e. frequency and twist angle. Specifically, we report polariton canalization in α-MoO3 at 8.67 THz for a twist angle of 50°. Our results demonstrate the precise control and manipulation of confined collective excitations at THz frequencies, particularly offering possibilities for nanophotonic applications.

From Black Hole Spectral Instability to Stable Observables

The quasinormal mode spectrum of black holes is unstable under small perturbation of the potential and has observational consequences in time signals. Such signals might be experimentally difficult to observe and probing this instability will be a technical challenge. Here, we investigate the spectral instability of time-independent data. This leads us to study the Regge poles (RPs), the counterparts to the quasinormal modes in the complex angular momentum plane. We present evidence that the RP spectrum is unstable but that not all overtones are affected equally by this instability. In addition, we reveal that behind this spectral instability lies an underlying structure. The RP spectrum is perturbed in such a way that one can still recover stable scattering quantities using the complex angular momentum approach. Overall, the study proposes a novel and complementary approach on the black hole spectral instability phenomena that allows us to reveal a surprising and unexpected mechanism at play that protects scattering quantities from the instability.

Precessing jet nozzle connecting to a spinning black hole in M87

The nearby radio galaxy M87 offers a unique opportunity to explore the connections between the central supermassive black hole and relativistic jets. Previous studies of the inner region of M87 revealed a wide opening angle for the jet originating near the black hole1-4. The Event Horizon Telescope resolved the central radio source and found an asymmetric ring structure consistent with expectations from general relativity5. With a baseline of 17 years of observations, there was a shift in the jet's transverse position, possibly arising from an 8- to 10-year quasi-periodicity3. However, the origin of this sideways shift remains unclear. Here we report an analysis of radio observations over 22 years that suggests a period of about 11 years for the variation in the position angle of the jet. We infer that we are seeing a spinning black hole that induces the Lense-Thirring precession of a misaligned accretion disk. Similar jet precession may commonly occur in other active galactic nuclei but has been challenging to detect owing to the small magnitude and long period of the variation.

Properties of Spherically Symmetric Black Holes in the Generalized Brans-Dicke Modified Gravitational Theory

The many problems faced by the theory of general relativity (GR) have always motivated us to explore the modified theory of GR. Considering the importance of studying the black hole (BH) entropy and its correction in gravity physics, we study the correction of thermodynamic entropy for a kind of spherically symmetric black hole under the generalized Brans-Dicke (GBD) theory of modified gravity. We derive and calculate the entropy and heat capacity. It is found that when the value of event horizon radius r+ is small, the effect of the entropy-correction term on the entropy is very obvious, while for larger values r+, the contribution of the correction term on entropy can be almost ignored. In addition, we can observe that as the radius of the event horizon increases, the heat capacity of BH in GBD theory will change from a negative value to a positive value, indicating that there is a phase transition in black holes. Given that studying the structure of geodesic lines is important for exploring the physical characteristics of a strong gravitational field, we also investigate the stability of particles' circular orbits in static spherically symmetric BHs within the framework of GBD theory. Concretely, we analyze the dependence of the innermost stable circular orbit on model parameters. In addition, the geodesic deviation equation is also applied to investigate the stable circular orbit of particles in GBD theory. The conditions for the stability of the BH solution and the limited range of radial coordinates required to achieve stable circular orbit motion are given. Finally, we show the locations of stable circular orbits, and obtain the angular velocity, specific energy, and angular momentum of the particles which move in circular orbits.

In-plane hyperbolic polariton tuners in terahertz and long-wave infrared regimes

One of the main bottlenecks in the development of terahertz (THz) and long-wave infrared (LWIR) technologies is the limited intrinsic response of traditional materials. Hyperbolic phonon polaritons (HPhPs) of van der Waals semiconductors couple strongly with THz and LWIR radiation. However, the mismatch of photon - polariton momentum makes far-field excitation of HPhPs challenging. Here, we propose an In-Plane Hyperbolic Polariton Tuner that is based on patterning van der Waals semiconductors, here α-MoO3, into ribbon arrays. We demonstrate that such tuners respond directly to far-field excitation and give rise to LWIR and THz resonances with high quality factors up to 300, which are strongly dependent on in-plane hyperbolic polariton of the patterned α-MoO3. We further show that with this tuner, intensity regulation of reflected and transmitted electromagnetic waves, as well as their wavelength and polarization selection can be achieved. Our results can help the development of THz and LWIR miniaturized devices.

A ring-like accretion structure in M87 connecting its black hole and jet

The nearby radio galaxy M87 is a prime target for studying black hole accretion and jet formation1,2. Event Horizon Telescope observations of M87 in 2017, at a wavelength of 1.3 mm, revealed a ring-like structure, which was interpreted as gravitationally lensed emission around a central black hole3. Here we report images of M87 obtained in 2018, at a wavelength of 3.5 mm, showing that the compact radio core is spatially resolved. High-resolution imaging shows a ring-like structure of [Formula: see text] Schwarzschild radii in diameter, approximately 50% larger than that seen at 1.3 mm. The outer edge at 3.5 mm is also larger than that at 1.3 mm. This larger and thicker ring indicates a substantial contribution from the accretion flow with absorption effects, in addition to the gravitationally lensed ring-like emission. The images show that the edge-brightened jet connects to the accretion flow of the black hole. Close to the black hole, the emission profile of the jet-launching region is wider than the expected profile of a black-hole-driven jet, suggesting the possible presence of a wind associated with the accretion flow.

Analogy of the interior Schwarzschild metric from transformation optics

In this paper, we make an analogy of the interior Schwarzschild metric from transformation optics (we call the method transformation cosmology). It is shown that a simple refractive index profile is sufficient to capture the behavior of the metric to bend light. There is a critical value of the ratio of the radius of the massive star to the Schwarzschild radius, which is exactly related to the condition of collapsing into a black hole. We demonstrate the light bending effect for three cases from numerical simulations as well. Especially, we find that a point source at the photon sphere will form an image inside the star approximately, and the equivalent lens is like Maxwell's fish-eye lens. This work will help us to explore the phenomena of massive stars with laboratory optical tools.

Photon Ring Astrometry for Superradiant Clouds

Gravitational atoms produced from the superradiant extraction of rotational energy of spinning black holes can reach energy densities significantly higher than that of dark matter, turning black holes into powerful potential detectors for ultralight bosons. These structures are formed by coherently oscillating bosons, which induce oscillating metric perturbations deflecting photon geodesics passing through their interior. The deviation of nearby geodesics can be further amplified near critical bound photon orbits. We discuss the prospect of detecting this deflection using photon ring autocorrelations with the Event Horizon Telescope and its next-generation upgrade, which can probe a large unexplored region of the cloud mass parameter space when compared with previous constraints.

Collisionless Accretion onto Black Holes: Dynamics and Flares

We study the accretion of collisionless plasma onto a rotating black hole from first principles using axisymmetric general-relativistic particle-in-cell simulations. We carry out a side-by-side comparison of these results to analogous general-relativistic magnetohydrodynamic simulations. Although there are many similarities in the overall flow dynamics, three key differences between the kinetic and fluid simulations are identified. Magnetic reconnection is more efficient, and rapidly accelerates a nonthermal particle population, in our kinetic approach. In addition, the plasma in the kinetic simulations develops significant departures from thermal equilibrium, including pressure anisotropy that excites kinetic-scale instabilities, and a large field-aligned heat flux near the horizon that approaches the free-streaming value. We discuss the implications of our results for modeling event-horizon scale observations of Sgr A* and M87 by GRAVITY and the Event Horizon Telescope.

Black holes up close

Recent developments have ushered in a new era in the field of black-hole astrophysics, providing a direct view of the remarkable environment near black-hole event horizons. These observations have enabled astronomers to confirm long-standing ideas on the physics of gas flowing into black holes with temperatures that are hundreds of times greater than at the centre of the Sun. At the same time, the observations have conclusively shown that light rays near a black hole experience large deflections that cause a dark shadow in the centre of the image, an effect predicted by Einstein's theory of general relativity. With further investment, this field is poised to deliver decades of advances in our understanding of gravity and black holes through stringent tests of general relativity, as well as insights into the role of black holes as the central engines powering a wide range of astronomical phenomena.

Exotic Compact Objects and the Fate of the Light-Ring Instability

Ultracompact objects with light rings (LRs) but without an event horizon could mimic black holes (BHs) in their strong gravity phenomenology. But are such objects dynamically viable? Stationary and axisymmetric ultracompact objects that can form from smooth, quasi-Minkowski initial data must have at least one stable LR, which has been argued to trigger a spacetime instability; but its development and fate have been unknown. Using fully nonlinear numerical evolutions of ultracompact bosonic stars free of any other known instabilities and introducing a novel adiabatic effective potential technique, we confirm the LRs triggered instability, identifying two possible fates: migration to nonultracompact configurations or collapse to BHs. In concrete examples we show that typical migration (collapse) timescales are not larger than ∼10^{3} light-crossing times, unless the stable LR potential well is very shallow. Our results show that the LR instability is effective in destroying horizonless ultracompact objects that could be plausible BH imitators.

Observational and Energetic Properties of Astrophysical and Galactic Black Holes

The work reviews the investigation of electromagnetic, optical, and energetic properties of astrophysical and galactic black holes and surrounding matter. The astrophysical applications of the theoretical models of black hole environment to the description of various observed phenomena, such as cosmic rays of the ultra-high-energy, black hole shadow, gravitational lensing, quasinormal modes, jets showing relativistic effects such as the Doppler beaming, thermal radiation from the accretion discs, quasiperiodic oscillations are discussed. It has been demonstrated that the observational data strongly depends on the structure and evolution of the accretion disk surrounding the central black hole. It has been shown that the simulated images of supermassive black holes obtained are in agreement with the observational images obtained by event horizon telescope collaboration. High energetic activity from supermassive black holes due to the magnetic Penrose process discussed in the work is in agreement with the highly energetic cosmic rays observed. The astronomical observation of black holes provides rich fundamental physics laboratories for experimental tests and verification of various models of black hole accretion and different theories of gravity in the regime of strong gravity.

Dynamical Instability of Self-Gravitating Membranes

We show that a generic relativistic membrane with in-plane pressure and surface density having the same sign is unstable with respect to a series of warping mode instabilities with high wave numbers. We also examine the criteria of instability for commonly studied exotic compact objects with membranes, such as gravastars, anti-de Sitter bubbles, and thin-shell wormholes. For example, a gravastar which satisfies the weak energy condition turns out to be dynamically unstable. A thin-layer black hole mimicker is stable only if it has positive pressure and negative surface density (such as a wormhole), or vice versa.

Black String Bounce to Traversable Wormhole

In this work, a regular black string solution is presented from the method used by Simpson–Visser to regularize the Schwarzschild solution. As in the Simpson–Visser work, in this new black string solution, it is possible to represent both a regular black hole and a wormhole simply by changing the value of a parameter “a” used in its metric. Tensors and curvature invariants are analyzed to verify the regularity of the solution as well as the energy conditions of the system. It is found that the null energy condition is always violated for the entire space. An additional analysis of the thermodynamic properties of the regular black string is carried out, in which the modifications generated about the original solution of the black string are evaluated, specifically, the Hawking temperature, entropy, its thermal capacity, and the Helmholtz free energy. Finally, we investigate the possible stable or unstable circular orbits for photons and massive particles. The results are compared with those for the non-regular black string, seeking to make a parallel with the Simpson–Visser work.

Synthetic Images of Magnetospheric Reconnection-Powered Radiation around Supermassive Black Holes

Accreting supermassive black holes can now be observed at the event-horizon scale at millimeter wavelengths. Current predictions for the image rely on hypotheses (fluid modeling, thermal electrons) which might not always hold in the vicinity of the black hole, so that a full kinetic treatment is in order. In this Letter, we describe the first 3D global general-relativistic particle-in-cell simulation of a black-hole magnetosphere. The system displays a persistent equatorial current sheet. Synthetic radio images are computed by ray-tracing synchrotron emission from nonthermal particles accelerated in this current sheet by magnetic reconnection. We identify several time-dependent features of the image at moderate viewing angles: a variable radius of the ring, and hot spots moving along it. In this regime, our model predicts that most of the flux of the image lies inside the critical curve. These results could help promote understanding of future observations of black-hole magnetospheres at improved temporal and spatial resolution.

Black Hole Solutions as Topological Thermodynamic Defects

In this Letter, employing the generalized off-shell free energy, we treat black hole solutions as defects in the thermodynamic parameter space. The results show that the positive and negative winding numbers corresponding to the defects indicate the local thermodynamical stable and unstable black hole solutions, respectively. The topological number defined as the sum of the winding numbers for all the black hole branches at an arbitrary given temperature is found to be a universal number independent of the black hole parameters. Moreover, this topological number only depends on the thermodynamic asymptotic behaviors of the black hole temperature at small and large black hole limits. Different black hole systems are characterized by three classes via this topological number. This number could help us in better understanding the black hole thermodynamics and, further, shed new light on the fundamental nature of quantum gravity.

Constraining extra dimensions using observations of black hole quasi-normal modes

The presence of extra dimensions generically modify the spacetime geometry of a rotating black hole, by adding an additional hair, besides the mass M and the angular momentum J, known as the 'tidal charge' parameter, β . In a braneworld scenario with one extra spatial dimension, the extra dimension is expected to manifest itself through - (a) negative values of β , and (b) modified gravitational perturbations. This in turn would affect the quasi-normal modes of rotating black holes. We numerically solve the perturbed gravitational field equations using the continued fractions method and determine the quasi-normal mode spectra for the braneworld black hole. We find that increasingly negative values of β correspond to a diminishing imaginary part of the quasi-normal mode, or equivalently, an increasing damping time. Using the publicly available data of the properties of the remnant black hole in the gravitational wave signal GW150914, we check for consistency between the predicted values (for a given β ) of the frequency and damping time of the least-damped ℓ = 2 , m = 2 quasi-normal mode and measurements of these quantities using other independent techniques. We find that it is highly unlikely for the tidal charge, β ≲ - 0.05 , providing a conservative limit on the tidal charge parameter. Implications and future directions are discussed.

Avoidance of Strong Coupling in General Relativity Solutions with a Timelike Scalar Profile in a Class of Ghost-Free Scalar-Tensor Theories

Modified gravity theories can accommodate exact solutions, for which the metric has the same form as the one in general relativity, i.e., stealth solutions. One problem with these stealth solutions is that perturbations around them exhibit strong coupling when the solutions are realized in degenerate higher-order scalar-tensor theories. We show that the strong coupling problem can be circumvented in the framework of the so-called U-DHOST theories, in which the degeneracy is partially broken in such a way that higher-derivative terms are degenerate only in the unitary gauge. In this sense, the scordatura effect is built-in in U-DHOST theories in general. There is an apparent Ostrogradsky mode in U-DHOST theories, but it does not propagate as it satisfies a three-dimensional elliptic differential equation on a spacelike hypersurface. We also clarify how this nonpropagating mode, i.e., the "shadowy" mode shows up at the nonlinear level.

Chaos in a Magnetized Brane-World Spacetime Using Explicit Symplectic Integrators

A brane-world metric with an external magnetic field is a modified theory of gravity. It is suitable for the description of compact sources on the brane such as stars and black holes. We design a class of explicit symplectic integrators for this spacetime and use one of the integrators to investigate how variations of the parameters affect the motion of test particles. When the magnetic field does not vanish, the integrability of the system is destroyed. Thus, the onset of chaos can be allowed under some circumstances. Chaos easily occurs when the electromagnetic parameter becomes large enough. Dark matter acts as a gravitational force, so that chaotic motion can become more obvious as dark matter increases. The gravity of the black hole is weakened with an increasing positive cosmological parameter; therefore, the extent of chaos can be also strengthened. The proposed symplectic integrator is applied to a ray-tracing method and the study of such chaotic dynamics will be a possible reference for future studies of brane-world black hole shadows with chaotic patterns of self-similar fractal structures based on the Event Horizon Telescope data for M87* and Sagittarius A*.

Near-Horizon Thermodynamics of Hairy Black Holes from Gravitational Decoupling

The horizon structure and thermodynamics of hairy spherically symmetric black holes generated by the gravitational decoupling method are carefully investigated. The temperature and heat capacity of the black hole is determined, as well as how the hairy parameters affect the thermodynamics. This allows for an analysis of thermal stability and the possible existence of a remanent black hole. We also calculate the Hawking radiation corrected by the generalized uncertainty principle. We consider the emission of fermions and apply the tunneling method to the generalized Dirac equation. This shows that, despite the horizon location being the same as the Schwarzschild one for a suitable choice of parameters, the physical phenomena that occur near the horizon of both black holes are qualitatively different.

From Galactic Bars to the Hubble Tension: Weighing Up the Astrophysical Evidence for Milgromian Gravity

Astronomical observations reveal a major deficiency in our understanding of physics—the detectable mass is insufficient to explain the observed motions in a huge variety of systems given our current understanding of gravity, Einstein’s General theory of Relativity (GR). This missing gravity problem may indicate a breakdown of GR at low accelerations, as postulated by Milgromian dynamics (MOND). We review the MOND theory and its consequences, including in a cosmological context where we advocate a hybrid approach involving light sterile neutrinos to address MOND’s cluster-scale issues. We then test the novel predictions of MOND using evidence from galaxies, galaxy groups, galaxy clusters, and the large-scale structure of the universe. We also consider whether the standard cosmological paradigm (LCDM) can explain the observations and review several previously published highly significant falsifications of it. Our overall assessment considers both the extent to which the data agree with each theory and how much flexibility each has when accommodating the data, with the gold standard being a clear a priori prediction not informed by the data in question. Our conclusion is that MOND is favoured by a wealth of data across a huge range of astrophysical scales, ranging from the kpc scales of galactic bars to the Gpc scale of the local supervoid and the Hubble tension, which is alleviated in MOND through enhanced cosmic variance. We also consider several future tests, mostly at scales much smaller than galaxies.

Shadow and Weak Deflection Angle of a Black Hole in Nonlocal Gravity

Black hole shadow and gravitational lensing play important roles in testing gravitational theories in the strong field regime. As the first-order modifications from quantum gravity, the nonlocality can be manifested by black hole shadow and gravitational lensing. For example, the nonlocal parameter introduced by nonlocality will affect the shape and size of the black hole shadow, and also affect the deflection angle of light rays. In this paper, we mainly investigate the effects of the nonlocality on the black hole shadow and the gravitational lensing for two types of rotating black holes in nonlocal gravity. It is found that the size of the black hole shadow decreases with the nonlocal parameter since the nonlocality weakens the gravitational constant, and the shape of the shadow becomes more deformed with the increase in the nonlocal parameter. However, if the rotation parameter is small, the shape of the shadow is almost a circle even though the nonlocal parameter approaches its maximum. The energy emission rate in both models is also studied. The results show that there is a peak for each curve and the peak decreases and shifts to the low frequency with the increase in the nonlocal parameter. In addition, we also explore the shadow of both types of black holes surrounded by a nonmagnetized pressureless plasma which satisfies the separability condition. It is found that the plasma has a frequency-dependent dispersive effect on the size and shape of the black hole shadow. For the gravitational lensing, we find that the nonlocal parameter of model A makes a positive contribution to the deflection angle, which can be compared with the contribution of the rotation parameter, while the nonlocal parameter of model B makes a negative contribution which can be ignored. These results may be helpful for probing nonlocal gravity in future observations.

Chaos in a Magnetized Modified Gravity Schwarzschild Spacetime

Based on the scalar–tensor–vector modified gravitational theory, a modified gravity Schwarzschild black hole solution has been given in the existing literature. Such a black hole spacetime is obtained through the inclusion of a modified gravity coupling parameter, which corresponds to the modified gravitational constant and the black hole charge. In this sense, the modified gravity parameter acts as not only an enhanced gravitational effect but also a gravitational repulsive force contribution to a test particle moving around the black hole. Because the modified Schwarzschild spacetime is static spherical symmetric, it is integrable. However, the spherical symmetry and the integrability are destroyed when the black hole is immersed in an external asymptotic uniform magnetic field and the particle is charged. Although the magnetized modified Schwarzschild spacetime is nonintegrable and inseparable, it allows for the application of explicit symplectic integrators when its Hamiltonian is split into five explicitly integrable parts. Taking one of the proposed explicit symplectic integrators and the techniques of Poincaré sections and fast Lyapunov indicators as numerical tools, we show that the charged particle can have chaotic motions under some circumstances. Chaos is strengthened with an increase of the modified gravity parameter from the global phase space structures. There are similar results when the magnetic field parameter and the particle energy increase. However, an increase of the particle angular momentum weakens the strength of chaos.

Hyperelliptic Functions and Motion in General Relativity

Analysis of black hole spacetimes requires study of the motion of particles and light in these spacetimes. Here exact solutions of the geodesic equations are the means of choice. Numerous interesting black hole spacetimes have been analyzed in terms of elliptic functions. However, the presence of a cosmological constant, higher dimensions or alternative gravity theories often necessitate an analysis in terms of hyperelliptic functions. Here we review the method and current status for solving the geodesic equations for the general hyperelliptic case, illustrating it with a set of examples of genus g=2: higher dimensional Schwarzschild black holes, rotating dyonic U(1)2 black holes, and black rings.

Quasinormal modes and shadow of noncommutative black hole

In this paper we investigate quasinormal modes (QNM) for a scalar field around a noncommutative Schwarzschild black hole. We verify the effect of noncommutativity on quasinormal frequencies by applying two procedures widely used in the literature. The first is the Wentzel-Kramers-Brillouin (WKB) approximation up to sixth order. In the second case we use the continuous fraction method developed by Leaver. Besides, we also show that due to noncommutativity, the shadow radius is reduced when we increase the noncommutative parameter. In addition, we find that the shadow radius is nonzero even at the zero mass limit for finite noncommutative parameter.

Extended Gravity Constraints at Different Scales

We review a set of the possible ways to constrain extended gravity models at Galaxy clusters scales (the regime of dark energy explanations and comparison with ΛCDM), for black hole shadows, gravitational wave astronomy, binary pulsars, the Solar system and a Large Hadron Collider (consequences for high-energy physics at TeV scale). The key idea is that modern experimental and observational precise data provide us with the chance to go beyond general relativity.