Unstable Circular Orbits Research Articles

Lyapunov exponents and phase transition of Hayward AdS black hole

AbstractIn this paper, we study the relationship between the phase transition and Lyapunov exponents for 4D Hayward anti-de Sitter (AdS) black hole. We consider the motion of massless and massive particles around an unstable circular orbit of the Hayward AdS black hole in the equatorial plane and calculate the corresponding Lyapunov exponents. The phase transition is found to be well described by the multivaled Lyapunov exponents. It is also found that different phases of Hayward AdS black hole coincide with different branches of the Lyapunov exponents. We also study the discontinuous change in the Lyapunov exponents and find that it can serve as an order parameter near the critical point. The critical exponent of change in Lyapunov exponent near the critical point is found to be 1/2.

Space-time structures, light trajectories and shadows for Kerr-Newman-AdS black hole with surrounding perfect fluid matter in Rastall gravity

We present the horizon structures and the shadows for Kerr-Newman-AdS black hole located in perfect fluid matter field in Rastall gravity. By considering the Hamilton-Jacobi equation and Carter constant separable method, we obtain the null geodesic equations of the black hole space-time as well as the unstable circular photon orbits in terms of the impact parameters. The horizon structures of the space-time are calculated numerically. The results show that there are four roots for a general case of the horizon equation (the Cauchy horizon r−h , the event horizon r+h , the cosmological horizon r q of Rastall gravity and the cosmological horizon r c of cosmological constant), which lead to a specific characteristic with the subregions of the space-time. The influences of the cosmological horizons r q and r c on the light trajectories around the black hole are also investigated. Furthermore, we study the effects of the parameters, including the perfect fluid matter intensity N s , the Rastall parameter k λ, the cosmological constant Λ, the black hole spin a and the black hole charge Q on black hole shadows in detail.

Particle and light motion in Lyra–Schwarzschild spacetime

Abstract In this paper we recall the static and spherically symmetric solution derived within LyST gravity. LyST stands for “Lyra Scalar-Tensor” and is a scalar-tensor proposal for the gravitational interaction modifying general relativity by adopting Lyra manifold as the spacetime substrate. Lyra manifold is characterized both by the metric tensor gµν(x) and the scale φ(x); the latter being an integral part of the definition of reference frame. In a previous work, we have launched the formal geometrical basis of LyST, we have proposed an associated action integral for the gravitational interaction, we have derived the field equations generalizing Einstein field equation, and we have solved these equation to obtain the generalized version of Schwarzschild line element in Lyra manifold. This lead us to Lyra-Schwarzschild spacetime, which is further explored in the present paper. Herein, the trajectories of test particles is thoroughly studied. This is done for both massive particles and massless particles. The geodesic equations are built and solved. The effective potential associated to the motion of these particles around the source is determined and characterized. The possible trajectories include gravitational capture, scattering, bounded orbits, stable and unstable circular orbits, near-horizon motion. The innermost circular orbit allowed for massive particles is determined and compared to the one predicted by GR. The last photon orbit is also calculated for Lyra-Schwarzschild metric. The equation for the periastron shift in the context of Lyra-Schwarzschild solution is constructed; its application to observational data could be useful to constrain the parameters typical of LyST, telling it apart from GR.

Influence of plasma on the optical appearance of spinning black hole in Kalb-Ramond gravity and its Existence around M87* and Sgr A*

The visible universe is filled with different types of plasma media in the form of stars, nebulas and other forms of excited gases. These matter fields have a high influence on the gravity and are likely to be present around the black holes due to the immense gravitational attraction. Since a plasma medium affects the speed of light, therefore we investigated the null geodesics and various optical features around the rotating black hole in Kalb-Ramond gravity immersed in plasma medium. Various plasma distributions are considered to develop a comparative study for their influence on unstable null circular orbits, shadows and evaporation rate of the black hole in the presence of a plasma medium. Moreover, the shadow results are also compared with Event Horizon Telescope data for M78* and Sgr A* in order to estimate the parametric bounds for which the rotating black hole in Kalb-Ramond gravity is considered either M87* or Sgr A* under the different values of plasma parameters. From this analysis, we also found the distribution of plasma that has a significant impact on the above mentioned features and is most likely to be present around M87* and Sgr A*.

Shadow of novel rotating black hole in GR coupled to nonlinear electrodynamics and constraints from EHT results

We study the optical properties of spacetime around a novel black hole in general relativity coupled to nonlinear electrodynamics, which is asymptotically flat. First, we study the angular velocity and Lyapunov exponent in unstable photon circular orbits in the novel spherically symmetric black hole spacetime. Later, we obtain the rotating black hole solution using the Newman–Janis algorithm and determine the event horizon properties of the black hole. We analyze the effective potential for the circular motion of photons in the spacetime of the novel rotating black hole. Also, we analyze the photon sphere around the novel black hole and its shadow using celestial coordinates. We obtain that an increase of the black hole spin and charge as well as nonlinear electrodynamics field nonlinearity parameters causes an increase in the distortion parameter of the black hole shadow, while, the area of the shadow and its oblateness decrease. Moreover, we also obtain the constraint values for the black hole charge and the nonlinearity parameters using Event Horizon Telescope data from shadow sizes of supermassive black holes Sgr A* and M87*. Finally, the emission rate of black hole evaporation through Hawking radiation is also studied.

Stability, quasinormal modes in a charged black hole in perfect fluid dark matter

In this work, we study time-like and null geodesics in a charged black hole background immersed in perfect fluid dark matter (PFDM). Using the condition for circular geodesics, we evaluate the energy and angular momentum in terms of the radius (r 0) of the timelike circular orbits. The existence and finiteness of energy and angular momentum constrain the possible range of PFDM parameter (χ) and r 0. In case of null geodesics, we calculate the radius rp of the unstable circular photon orbits. We then use the Lyapunov exponent to study the stability of the geodesics. Then we analyze the critical exponent useful for determining the possibility of detection of gravitational wave signals. After that, we study the perturbation due to a massless scalar field in such a background and calculate the quasinormal mode (QNM) frequencies and their dependence on χ and black hole charge Q. Also, we compare the obtained QNM frequencies both in the exact case and in the eikonal limit. We also calculate the quality factor of the oscillating system and study its dependence on χ and Q. Finally, we evaluate the black hole shadow radius Rs and graphically observe the effect of χ and Q on it.

Geodesic analysis and steady accretion on a traversable wormhole

In this work, we analyze the behavior of light and matter as they pass near and through a traversable wormhole throat. In particular, we study the trajectories of massive and massless particles and the dust accretion around a traversable wormhole previously reported in Rueda et al. (2022). For massive particles, we integrate the trajectory equation for ingoing and outgoing geodesics and classify the orbits of particles scattered by the wormhole in accordance with their asymptotic behavior far from the throat. We represent all the time-like trajectories in an embedding surface where it is shown explicitly the trajectories of (i) particles that deviate from the throat and remain in the same universe, (ii) particles that traverse the wormhole to another universe, and (iii) particles that get trapped in the wormhole in unstable circular orbits. For the massless particles, we numerically integrate the trajectory equation to show the ray-tracing around the wormhole specifying the particles that traverse the wormhole and those that are only deviated by the throat. For the study of accretion, we consider the steady and spherically symmetric accretion of dust. Our results show that the wormhole parameters can significantly affect the behavior of light and matter near the wormhole. Some comparisons with the behavior of matter around black holes are made.

Rotating black hole in Kalb–Ramond gravity: Constraining parameters by comparison with EHT observations of Sgr A* and M87*

This article deals with the study of some properties of the static and rotating black holes in Kalb–Ramond gravity in four dimensional spacetime. First, we discuss the action of the corresponding theory and the static black hole metric. Then we investigate the light sphere for the static black hole by using the Hamiltonian formalism and the corresponding linear radius of the shadow, angular velocity and Lyapunov exponent. For the rotating black hole, we discuss the horizon structure. Moreover, we study the effective potential to discuss the structure of null sphere and unstable circular null orbits around the rotating black hole. The properties such as energy emission rate and distortion are calculated and analyzed by using the numerical data for the shadows calculated by appropriately chosen parametric values for two different angular locations of the observer off the equatorial plane. We also obtain the constraints on the black hole parameters by comparing the shadow sizes of the black hole in Kalb–Ramond gravity and the supermassive black holes M87* and Sgr A*. Finally, we investigate the effect of mass, energy, angular momentum and the black hole parameters on the center of mass energy of two colliding particles that are accelerated in the vicinity of the black hole.

Distinct topological configurations of equatorial timelike circular orbit for spherically symmetric (hairy) black holes

Topology is a promising approach toward to the light ring in a generic black hole background, and equatorial timelike circular orbit in a stationary black hole background. In this paper, we consider the distinct topological configurations of the timelike circular orbits in static, spherically symmetric, and asymptotic flat black holes. By making use of the equation of motion of the massive particles, we construct a vector with its zero points exactly relating with the timelike circular orbits. Since each zero point of the vector can be endowed with a winding number, the topology of the timelike circular orbits is well established. Stable and unstable timelike circular orbits respectively have winding number +1 and -1. In particular, for given angular momentum, the topological number of the timelike circular orbits also vanishes whether they are rotating or not. Moreover, we apply the study to the Schwarzschild, scalarized Einstein-Maxwell, and dyonic black holes, which have three distinct topological configurations, representations of the radius and angular momentum relationship, with one or two pairs timelike circular orbits at most. It is shown that although the existence of scalar hair and quasi-topological term leads to richer topological configurations of the timelike circular orbits, they have no influence on the total topological number. These results indicate that the topological approach indeed provides us a novel way to understand the timelike circular orbits. Significantly, different topological configurations can share the same topology number, and hence belong to the same topological class. More information is expected to be disclosed when other different topological configurations are present.

Particle dynamics around a static spherically symmetric black hole in the presence of quintessence

This paper studies the orbital dynamics of timelike and lightlike particles in a static spherically symmetric black hole spacetime in the presence of quintessence. More precisely, using the effective potential to analyze the particle orbits between the black hole horizon and the cosmological horizon, it is found that there are attracting orbits, escape orbits, bound orbits, and stable and unstable circular orbits. The effects of angular momentum and normalization factors on the effective potential and the structure of timelike and null geodesics are also analyzed. In addition, the horizontal properties of various parameters are discussed, with the case of ωq=−2/3 being the most interesting.

Particle motions around regular black holes

We investigate the bound orbits of massive/massless, neutral particles and photons moving around regular black holes of Fan and Wang. For massive particles, we show the existence of stable/unstable circular orbits and the charge dependence of the radius of the innermost stable circular orbit. Remarkably, we find an unstable circular orbit of photons inside the event horizon. For massless particles and photons, we show that both stable and unstable circular orbits can exist in a regular and horizonless spacetime with a slight overcharge. Then, we also discuss the periapsis shift of massive neutral particles orbiting around the black hole, and show that the charge gives a negative correction to the shift for black holes with small nonlinearity of electrodynamics.

Can two ultrarelativistic objects lose almost all their energy to gravitational radiation?

In 2007, Pretorius and Khurana [Black hole mergers and unstable circular orbits, Classical Quantum Gravity 24, S83 (2007).] did ``speculate that at threshold [at a critical impact parameter], all of the kinetic energy of the system [two ultrarelativistic black holes] is converted to gravitational waves, which can be an arbitrarily large fraction of the total energy.'' However, in 2012, Sperhake et al. [Universality, Maximum Radiation and Absorption in High-Energy Collisions of Black Holes with Spin, Phys. Rev. Lett. 111, 041101 (2013).] performed numerical calculations that led them to the contrary conclusion: ``An extrapolation of our results to the limit $\ensuremath{\gamma}\ensuremath{\rightarrow}\ensuremath{\infty}$ suggests that about half of the center-of-mass energy of the system can be emitted in gravitational radiation, while the rest must be converted into rest-mass and spin energy.'' Here I present arguments against this latter conclusion and in support of the earlier speculation that for sufficiently large $\ensuremath{\gamma}$, all but an arbitrarily small fraction of the total energy can be radiated away as gravitational waves.

Topology of equatorial timelike circular orbits around stationary black holes

A topological approach has been successfully used to study the properties of the light ring and the null circular orbit, in a generic black hole background. However, for the equatorial timelike circular orbit, quite different from the light ring case, its radius is closely dependent of the energy and angular momentum of a test particle. This fact seems to restrict the extension of the topological treatment to the timelike circular orbit. In this paper, we confirm that the angular momentum does not affect the asymptotic behavior of the constructed vector with its zero points denoting the equatorial timelike circular orbits. As a result, a well-behaved topology to characterize the equatorial timelike circular orbits can be constructed. Our study shows that the total topological number of the timelike circular orbits vanishes for a generic black hole, which is dependent of the energy of the particle. Significantly, it reveals that if there the timelike circular orbits exist, they always come in pairs for fixed angular momentum. Meanwhile, the stable and unstable timelike circular orbits have positive or negative winding number. Of particular interest is that the marginally stable circular orbit corresponds to the bifurcation point of the zero point of the constructed vector. Moreover, we also examine the case when the particle energy acts as the control parameter. It is shown that there will be topological phase transition when the value of the particle energy is one. Below this value, the timelike circular orbits always come in pairs for fixed energy. Otherwise, we will have one more unstable timelike circular orbit. We further apply the treatment to the Kerr black hole. All the results given in a generic black hole background are exactly reproduced. These strongly indicate that our topological approach can be generalized to the equatorial timelike circular orbits.

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.

Quantum contribution to luminosity of quasars

The accretion of galactic gas is regarded as the source of the giant luminosity of quasars. The gravitational energy converts itself into radiation close to the Schwarzschild horizon of the central supermassive black hole with efficiency of ca. 30% mass to radiation energy conversion rate. Particularities of such an extremely effective mechanism of mass to energy conversion are, however, still obscure. We propose to take into account quantum statistics properties of fermions, which could emit in close outer vicinity of the Schwarzschild zone a giant energy accumulated in the Fermi spheres of electrons and protons in degenerate quantum collective state created in this region by the gravitational compression of plasma. The release of photons is possible due to the local revoking of Pauli exclusion principle constraint induced by the rapid change of the homotopy of multiparticle trajectories beneath the innermost unstable circular orbit of the black hole, which causes the collapse of Fermi spheres of electrons and protons.

Equatorial orbits of spinning test particles in rotating boson stars

In this paper, we study circular orbits of spinning test particles in the background of a rotating boson star. Using the pole-dipole approximation and neglecting the back-reaction of the spinning test particle on the spacetime, the equation of motion of the spinning test particle is described by the Mathisson–Papapetrou–Dixon equation. We solve this equation under the Tulczyjew spin-supplementary condition and obtain the four-momentum and four-velocity of the spinning test particle. Quite different from the spinless particle, the effective potential of the spinning particle with zero orbital angular momentum goes to infinite at the center of the rotating boson star. This will lead to the fact that the spinning particle can not pass through the center of the boson star. However, when the spin angular momentum and orbital angular momentum satisfy 2{bar{s}}+{bar{l}}=0, the effective potential is not divergent anymore and the spinning particle can pass through the center of the rotating boson star. We still investigate how the spin affects the structure of the circular orbits and we find that the spin will induce the larger or smaller regions of no circular orbits, unstable circular orbits, and stable circular orbits. Moreover, the radius and energy of the circular orbit will be decreased or increased by the particle spin. These results will have an important application in testing the gravitational waves in the boson star background.

Long-term Evolution of Tightly Packed Stellar Black Holes in AGN Disks: Formation of Merging Black Hole Binaries via Close Encounters

We study the long-term evolution of two or more stellar black holes (BHs) on initially separated but unstable circular orbits around a supermassive BH (SMBH). Such a close-packed orbital configuration can naturally arise from BH migrations in the AGN disk. Dynamical instability of the orbits leads to recurring close encounters between two BHs, during which the BH separation r p becomes less than the Hill radius R H. In rare very close encounters, a tight merging BH binary can form with the help of gravitational wave emission. We use N-body simulations to study the time evolution of close encounters of various degrees of closeness. For a typical “SMBH+2BH” system, the averaged cumulative number of close encounters (with r p ≲ R H) scales approximately as ∝ t 0.5. The minimum encounter separation r p follows a cumulative distribution P(<r p) ∝ r p for r p ≪ R H. We obtain a semi-analytical expression for the averaged rate of binary captures that lead to BH mergers. Our results suggest that close-packed BHs in AGN disks may take a long time (≳107 orbits around the SMBH) to experience a sufficiently close encounter and form a bound binary. This time can be shorter if the initial BH orbits are highly aligned. The BH binary mergers produced in this scenario have high eccentricities when entering the LIGO band and broad distribution of orbital inclinations relative to the original AGN disk. We explore the effects of the gas disk and find that simple gas drags on the BHs do not necessarily lead to an enhanced BH binary capture rate.

Geometric approach to circular photon orbits and black hole shadows

Circular photon orbits and black hole shadows are significantly important issues in physics and astronomy, and a number of breakthroughs have been witnessed in recent years. Conventionally, the stable and unstable circular photon orbits are obtained using the effective potential of test particles moving in black hole spacetime. In this work, a pure geometric approach is developed to calculate these circular photon orbits and black hole shadow radius. Furthermore, it can be proved that our geometric approach is completely equivalent to the conventional approach based on effective potentials of test particles.

Null geodesics and shadow of hairy black holes in Einstein-Maxwell-dilaton gravity

The timelike and null-like geodesics around compact objects are some of the best tools to classify and understand the structure of a space-time. We study the null geodesics around charged static dilaton black holes in Einstein-Maxwell-dilaton gravity. The physical parameters for nonradial geodesics, including the effective potential, effective force, radius of the photon sphere, and impact parameter, are obtained, and effects of the charge parameter and dilaton coupling constant on these quantities are studied. Possible photon motions for different values of the impact parameter are analyzed, and unstable circular orbits and unbounded orbits are plotted. These results are compared to that of Schwarzschild, Reissner-Nordstr\"om, and Gibbons-Maeda-Garfinkle-Horowitz-Strominger black holes. Also, we study the shadow cast by a dilaton black hole and investigate how the dilaton coupling affects the size of the black hole shadow. Finally, as an application of null geodesics, we calculate the deflection of light and investigate the effects of the model parameters on the bending angle.

Null geodesics and shadow of 4D Einstein–Gauss–Bonnet black holes surrounded by quintessence

We study the properties of the null geodesics of four-dimensional Einstein–Gauss–Bonnet (4D EGB) black holes surrounded by quintessence matter, recently derived by Shah et al. [Phys. Lett. B 818 (2021) 136383]. Due to the quintessence correction, we discuss the radial and nonradial geodesics. For the case of nonradial geodesics we obtain the effective potential, photon sphere and impact parameter associated to the null geodesics in detail. We analyze the different possible orbits of massless particles (i.e. photons) such as unstable circular orbits and unbounded orbits and investigate the role of the Gauss–Bonnet coupling [Formula: see text] and the quintessence parameter q on the null geodesic trajectories. Moreover, we study the effects of the model parameters on the shadow cast by such black holes. The results are compared to that of Schwarzschild black hole with and without quintessence matter and 4D EGB black holes without quintessence. As a physical application of null geodesics, the deflection angle is calculated and the effect of the quintessence matter on it is investigated.