In this article the geodesic motion of test particles in the spacetime of a supersymmetric AdS$_5$ black hole is studied. The equations of motion are derived and solved in terms of the Weierstrass $\wp$, $σ$ and $ζ$ functions. Effective potentials and parametric diagrams are used to analyze and characterize timelike, lightlike and spacelike particle motion and a list of possible orbit types is given. Furthermore, various plots of orbits are presented.
We present the complete analytical solution of the geodesics equations in the supersymmetric BMPV spacetime \cite{Breckenridge:1996is}. We study systematically the properties of massive and massless test particle motion. We analyze the trajectories with analytical methods based on the theory of elliptic functions. Since the nature of the effective potential depends strongly on the rotation parameter $ω$, one has to distinguish between the underrotating case, the critical case and the overrotating case, as discussed by Gibbons and Herdeiro in their pioneering study \cite{Gibbons:1999uv}. We dis…
It has been argued that supersymmetric microstate geometries are classically unstable. One argument for instability involves considering the motion of a massive particle near the ergosurface of such a spacetime. It is shown that the instability can be triggered by a particle that starts arbitrarily far from the ergosurface. Another argument for instability is related to the phenomenon of stable trapping of null geodesics in these geometries. Such trapping is studied in detail for the most symmetrical microstate geometries. It is found that there are several distinct types of trapped null geode…
A technique for generating spherically symmetric dislocation solutions of a direct Poincaré gauge theory of gravity based on homogeneous functions which makes Cartan torsion to vanish is presented.Static space supported dislocation and time dependent solutions are supplied.Photons move along geodesics in analogy to geodesics described by electrons around dislocations in solid state physics.Tachyonic sectors are also found.
In this talk we analyze the effect of recently proposed classes of sudden future singularities on causal geodesics of FLRW spacetimes. Geodesics are shown to be extendible and just the equations for geodesic deviation are singular, although tidal forces are not strong enough to produce a Big Rip.
We study the evolution of timelike geodesics for two dimensional black hole spacetimes arising in string theory and general theory of relativity by solving the Raychaudhuri equation for expansion scalar as an initial value problem. The possibility of geodesic focusing/defocusing is then examined accordingly with different settings of black hole parameters. In view of the geodesic focusing/defocusing, the critical value of expansion scalar is also calculated in each case. The effect of the charge and the cosmological constant on the evolution of expansion scalar for timelike geodesics is discus…
We investigate the geodesic motion of massless test particles in the background of a noncommutative geometry inspired Schwarzschild black hole. The behaviour of effective potential is analysed in the equatorial plane and the possible motions of massless particles (i.e. photons) for different values of impact parameter are discussed accordingly. We have also calculated the frequency shift of photons in this spacetime. Further, the mass parameter of a non-commutative inspired Schwarzschild black hole is computed in terms of the measurable redshift of photons emitted by massive particles moving a…
In a recent paper (Phys. Dark Univ. {\bf 31}, 100744 (2021)) it has been obtained new static black hole solutions with primary hairs by the Gravitational Decoupling. In this work we either study the geodesic motion of massive and massless particles around those solutions and restrict the values of the primary hairs by observational data. In particular, we obtain the effective potential, the innermost stable circular orbits, the marginally bounded orbit, and the periastron advance for time--like geodesics. In order to restrict the values taken by the primary hairs we explore their relationship …
The mass parameters of compact objects such as Boson Stars, Schwarzschild, Reissner Nordstrom and Kerr black holes are computed in terms of the measurable redshift-blueshift (zred, zblue) of photons emitted by particles moving along circular geodesics around these objects and the radius of their orbits. We found bounds for the values of (zred, zblue) that may be observed. For the case of Kerr black hole, recent observational estimates of SrgA\* mass and rotation parameter are employed to determine the corresponding values of these red-blue shifts.
We explore some of the gravitational features of a uniform ring both in the Newtonian potential theory and in General Relativity. We use a spacetime associated to a Weyl static solution of the vacuum Einstein's equations with ring like singularity. The Newtonian motion for a test particle in the gravitational field of the ring is studied and compared with the corresponding geodesic motion in the given spacetime. We have found a relativistic peculiar attraction: free falling particle geodesics are lead to the inner rim but never hit the ring.
We consider a traversable wormhole solution of Einstein's gravity conformally coupled to a massless scalar field, a solution derived by Barcelo and Visser based on the JNWW spacetime. We study the geodesic motion of time-, light- and space-like particles in this spacetime. We solve the equations of motion analytically in terms of the Weierstraß\ functions and discuss all possible orbit types and their parameter dependence. Interestingly, bound orbits occur for time-like geodesics only in one of the two worlds. Moreover, under no conditions there exist time-like two world bound orbits.
In this note we examine the circular time-like geodesics near a spherically symmetric dilaton black hole, described using the exact solution for a static charged black hole found by Gibbons and Maeda and, independently, by Garfinkle, Horowitz and Strominger. The existence and stability of the circular orbits are analysed using the effective potential of a free material test particle moving on time-like geodesic near this black hole. We determine the radius of the innermost stable circular orbit, the radius of the shortest circular orbit and compare our results with those obtained by other auth…
In this paper we provide a thorough classification of Friedman-Lemaître-Robertson-Walker (FLRW) cosmological models in terms of the strong or weak character of their singularities according to the usual definitions. The classification refers to a generalised Puiseux power expansion of the scale factor of the model around a singular event.
In this paper we study the timelike geodesics around a spherically symmetric charged dilaton black hole. The trajectories around the black hole are classified using the effective potential of a free test particle. This qualitative approach enables us to determine the type of the orbit described by the test particle without solving the equations of motion, if the parameters of the black hole and the particle are known. The connections between these parameters and the type of orbit described by the particle are obtained. To visualize the orbits we solve numerically the equation of motions for di…
In this paper we study geodesic motion around a distorted Schwarzschild black hole. We consider both timelike and null geodesics which are confined to the black hole's equatorial plane. Such geodesics generically exist if the distortion field has only even interior multipole moments and so the field is symmetric with respect to the equatorial plane. We specialize to the case of distortions defined by a quadrupole Weyl moment. An analysis of the effective potential for equatorial timelike geodesics shows that finite stable orbits outside the black hole are possible only for $q\in(q_{\text{min}}…
We use the Melnikov method to identify chaotic behavior in geodesic motion perturbed by the minimal length effects around a Schwarzschild black hole. Unlike the integrable unperturbed geodesic motion, our results show that the perturbed homoclinic orbit, which is a geodesic joining the unstable circular orbit to itself, becomes chaotic in the sense that Smale horseshoes chaotic structure is present in phase space.
Various observations from cosmic microwave background radiation (CMBR), type Ia supernova and baryon acoustic oscillations (BAO) are strongly suggestive of an accelerated expansion of the universe which can be explained by the presence of mysterious energy known as dark energy. The quintessential matter coupled with gravity minimally is considered one of the possible candidates to represents the presence of such dark energy in our universe. In view of this scenario, we study the geodesic of massless particles as well as massive particles around a (2+1) dimensional BTZ black hole (BH) spacetime…
We have developed a highly accurate numerical code capable of solving the coupled Einstein-Klein-Gordon system, in order to construct rotating boson stars in general relativity. Free fields and self-interacting fields, with quartic and sextic potentials, are considered. In particular, we present the first numerical solutions of rotating boson stars with rotational quantum number $k=3$ and $k=4$, as well as the first determination of the maximum mass of free-field boson stars with $k=2$. We have also investigated timelike geodesics in the spacetime generated by a rotating boson star for $k=1$, …
The inspiral of a stellar mass compact object falling into a massive Kerr black hole can be broken into three different regimes: An adiabatic inspiral phase, where the inspiral timescale is much larger than the orbital period; a late-time radial infall, which can be approximated as a plunging geodesic; and a regime where the body transitions from the inspiral to plunge. In earlier work, Ori and Thorne have outlined a method to compute the trajectory during this transition for a compact object in a circular, equatorial orbit. We generalize this technique to include inclination and eccentricity.
Using the simple but robust model of a shell of dark matter (DM) around a Schwarzschild black hole (BH), represented by the mass ratio of the shell and BH $ΔM/M$, the shell extension $Δr_s$ and its inner radius $r_s$, we study the influence of DM on the spacetime structure and geodesic motion, and provide a classification of the BH+DM shell spacetimes according to the properties of the stable circular geodesics governing Keplerian disks. We focus our attention on the epicyclic motion around circular geodesics that can be related to observational phenomena in X-ray radiation from Keplerian accr…
We study bound orbits of a free particle around a singly rotating black ring. We find there exists chaotic motion of a particle which is gravitationally bound to the black ring by using the Poincare map.
In this paper, we investigate the center of mass energy of the collision for two neutral particles with different rest masses falling freely from rest at infinity in the background of a Kerr-Newman-Taub-NUT black hole. Further, we discuss the center of mass energy near the horizon(s) of an extremal and non-extremal Kerr-Newman-Taub-NUT black hole and show that an arbitrarily high center of mass energy is achievable under some restrictions. We will study the special case of the center of mass energy when the specific energy, specific angular momentum and Carter constant of both the particles ar…
We investigate the geodesic motion in the background of Kerr-Sen Black Hole arising in the heterotic string theory. The nature of effective potential is discussed in radial as well as latitudinal direction. A special class of spherical photon orbits is obtained along with the expression for the turning point for radial photons. Dependence of photon motion within this class of solution is discussed explicitly in view of the different Black Hole parameters. We have discussed the allowed regions for geodesic motion of massless test particles around Kerr- Sen Black Hole in more generalised way by …
In this paper, we consider the timelike and null geodesics around the static [GMGHS (Gibbons, Maeda, Garfinkle, Horowitz and Strominger), magnetically charged GMGHS, electrically charged GMGHS] and the rotating (Kerr-Sen dilaton-axion) dilaton black holes. The geodesic equations are solved in terms of Weierstrass elliptic functions. To classify the trajectories around the black holes, we use the analytical solution and effective potential techniques and then characterize the different types of the resulting orbits in terms of the conserved energy and angular momentum. Also, using the obtained …
In this note we take a dynamical systems approach to the equations of motion of a free test particle moving around a spherically symmetric static dilaton black hole, written in the Einstein frame. The equations of motion are obtained using the Euler-Lagrange formalism. Using the first integrals of motion, we reach the conclusion that the free test particles are moving in a plane, named \emph{plane of motion}. In it we analyze the existence and nature of the equilibrium points and compare the behavior of free test particles near the equilibrium points using the dynamics systems approach. The st…
In this article we study the geodesic motion of charged particles in the spacetime of an extremal rotating dyonic black hole in Kaluza-Klein theory. We derive the equations of motion and present their analytical solutions in terns of elliptic and hyperelliptic functions. Furthermore, we analyze the geodesic motions with the help of parametric diagrams and effective potentials.
The gravitomagnetic corrections to the Keplerian period for a circular, geodesic orbit of a test particle in a polar plane containing the proper angular momentum J of a central rotating body are considered.
We study the geodesic motions of a test particle around 2+1 dimensional charged black holes. We obtain a class of exact geodesic motions for the massless test particle when the ratio of its energy and angular momentum is given by square root of cosmological constant. The other geodesic motions for both massless and massive test particles are analyzed by use of numerical method.
We investigate the classical stability of supersymmetric, asymptotically flat, microstate geometries with five non-compact dimensions. Such geometries admit an "evanescent ergosurface": a timelike hypersurface of infinite redshift. On such a surface, there are null geodesics with zero energy relative to infinity. These geodesics are stably trapped in the potential well near the ergosurface. We present a heuristic argument indicating that this feature is likely to lead to a nonlinear instability of these solutions. We argue that the precursor of such an instability can be seen in the behaviour …
We study epicyclic oscillatory motion along circular geodesics of the Simpson--Visser meta-geometry describing in a unique way regular black-bounce black holes and reflection-symmetric wormholes by using a length parameter $l$. We give the frequencies of the orbital and epicyclic motion in a Keplerian disc with inner edge at the innermost circular geodesic located above the black hole outer horizon or on the our side of the wormhole. We use these frequencies in the epicyclic resonance version of the so-called geodesic models of high-frequency quasi-periodic oscillations (HF QPOs) observed in m…
We analyze the scalar radiation emitted by a source in geodesic circular orbits around a Schwarzschild-de Sitter black hole. We obtain the emitted power using quantum field theory in curved spacetimes framework at tree level. We compare our results with the scalar synchrotron radiation in Schwarzschild spacetime.
Topological defects in solids, usually described by complicated boundary conditions in elastic theory, may be described more simply as sources of a gravity- like deformation field in the geometric approach of Katanaev and Volovich. This way, the deformation field is described by non-Euclidean metric that incorporates the boundary imposed by the defects. A possible way of gaining some insight into the motion of particles in a medium with topological defects (e.g., electrons in a dislocated metal) is to look at the geodesics of the medium around the defect. In this work, we find the exact soluti…
Oscillatons are spherically symmetric solutions to the Einstein Klein Gordon (EKG) equations for soliton stars made of real time dependent scalar fields. These equations are non singular and satisfy flatness conditions asymptotically with periodic time dependency. In this paper, we investigate the geodesic motion of particles moving around an oscillaton related to a time dependent scalar field. Bound orbital is found for these particles under the condition of particular values of angular momentum L and initial radial position. We discuss this topic for an exponential scalar field potential whi…
There are circular planar null geodesics at $r=3M$ around a Schwarzschild black hole of mass $M$. These geodesics form a photon sphere. Null geodesics of the Schwarzschild space-time which do not form the photon sphere are either escape to null infinity or get captured by the black hole. Thus, from the dynamical point of view, the photon sphere represents a smooth basin boundary that separates the basins of escape and capture of the dynamical system governing the null geodesics. Here we consider a Schwarzschild black hole distorted by an external, static, and axisymmetric quadrupolar gravitati…
Mallett has exhibited a cylindrically symmetric spacetime containing closed timelike curves produced by a light beam circulating around a line singularity. I analyze the static version of this spacetime obtained by setting the intensity of the light to zero. Some null geodesics can escape to infinity, but all timelike geodesics in this spacetime originate and terminate at the singularity. Freely falling matter originally at rest quickly attains relativistic velocity inward and is destroyed at the singularity.
We present a novel method to study interacting orbits in a fixed mean gravitational field associated with a solution of the Einstein field equations. The idea is to consider the Newton gravity among the orbiting particles in a geometry given by the main source. We apply the technique in the of study two and three self-gravitating particles moving around a black hole, i.e., in a Schwarzschild geometry. We also compare with the equivalent Newtonian problem and noted differences in the structural stability, e.g., binary systems were found only in the general relativistic approach.
We study collision of two general geodesic particles around the Kerr-Newman (KN) black hole and get the center-of-mass (CM) energy of the non-marginally and marginally bound critical particles in the direct collision and LSO collision scenarios. We find the constraint conditions that arbitrarily high CM energy can be obtained for the near-horizon collision of two general geodesic particles in the extremal KN black hole, and note that the charge decreases the value of the latitude in which arbitrarily high CM energy can occurs. We also interpret why the high-velocity collision belt centers to t…
We examine the dynamics of a neutral particle around a Kerr-Newman black hole, and in particular focus on the effects of the charge of the spinning black hole on the motion of the particle. We first consider the innermost stable circular orbits (ISCO) on the equatorial plane. It is found that the presence of the charge of the black hole leads to the effective potential of the particle with stronger repulsive effects as compared with the Kerr black hole. As a result, the radius of ISCO decreases as charge $Q$ of the black hole increases for a fixed value of black hole's angular momentum $a$. We…
A charge-free, point particle of infinitesimal mass orbiting a Kerr black hole is known to move along a geodesic. When the particle has a finite mass or charge, it emits radiation which carries away orbital energy and angular momentum, and the orbit deviates from a geodesic. In this paper we assume that the deviation is small and show that the half-advanced minus half-retarded field surprisingly provides the correct radiation reaction force, in a time-averaged sense, and determines the orbit of the particle.
The existence of chaotic behavior for the geodesics of the test particles orbiting compact objects is a subject of much current research. Some years ago, Guéron and Letelier [Phys. Rev. E \textbf{66}, 046611 (2002)] reported the existence of chaotic behavior for the geodesics of the test particles orbiting compact objects like black holes induced by specific values of the quadrupolar deformation of the source using as models the Erez--Rosen solution and the Kerr black hole deformed by an internal multipole term. In this work, we are interesting in the study of the dynamic behavior of geodesics…
In higher-dimensional Schwarzschild black hole spacetimes, there are no stable bound orbits of particles. In contrast to this, it is shown that there are stable bound orbits in a five-dimensional black lens spacetime.
We investigate the occurrence chaos in the escape of test particles moving in the field of a Schwarzschild black hole surrounded by an external halo. The motion of both material particles and zero rest mass particles is considered. The chaos is characterized by the fractal dimension of boundary between the basins of the different escapes, which is a topologically invariant characterization. We find chaos in the motion of both material particles and null geodesics.
We study the self force acting on a scalar charge in uniform circular motion around a Schwarzschild black hole. The analysis is based on a direct calculation of the self force via mode decomposition, and on a regularization procedure based on Ori's mode-sum regularization prescription. We find the four self-force at arbitrary radii and angular velocities (both geodesic and non-geodesic), in particular near the black hole, where general-relativistic effects are strongest, and for fast motion. We find the radial component of the self force to be repulsive or attractive, depending on the orbit.
I calculate the self-force acting on a particle with electric charge q moving on a generic geodesic around a Schwarzschild black hole. Using methods similar to those developed for the scalar field case discussed in a previous paper, I investigate the relative sizes of the conservative (half-advanced plus half-retarded) and dissipative (half-advanced minus half-retarded) pieces of the self-force. I also display the regularization parameters used in the mode-sum regularization scheme.
This paper is devoted to study the geodesic structure of regular Hayward black hole. The timelike and null geodesic have been studied explicitly for radial and non-radial motion. For timelike and null geodesic in radial motion there exists analytical solution, while for non-radial motion the effective potential has been plotted, which investigates the position and turning points of the particle. It has been found that massive particle moving along timelike geodesics path are dragged towards the BH and continues move around BH in particular orbits.
Null and timelike geodesics around a 2+1 black hole are determined. Complete geodesics of both types exist in the rotating black-hole background, but not in the spinless case. Upper and lower bounds for the radial size of the orbits are given in all cases and the possibility of passing from one black hole exterior spacetime to another is discussed using the Penrose diagrams. An analysis of particle motions by means of effective potentials and orbit graphs are also included.
Recent observations of the orbits of star clusters around Sgr $A^\star$, imaging of black holes and gravitational waveforms of merging compact objects require a detailed understanding of the general relativistic geodesic motion. We came up with a method to provide all the possible geodesics in an axially symmetric space-time. The Kerr metric is explicitly worked out, recovering the Schwarzschild geodesics in the static limit. We also found the most general Killing tensor and its associated constant of motion for an axisymmetric space-time. The relevance of these results is crucial to understan…
The geodesics of the rotating extreme black hole in five spacetime dimensions found by Breckenridge, Myers, Peet and Vafa are Liouville integrable and may be integrated by additively separating the Hamilton-Jacobi equation. This allows us to obtain the Stäckel-Killing tensor. We use these facts to give the maximal analytic extension of the spacetime and discuss some aspects of its causal structure. In particular, we exhibit a `repulson'-like behaviour occuring when there are naked closed timelike curves. In this case we find that the spacetime is geodesically complete (with respect to causal g…
In this comment we explain the discrepancies mentioned by the authors between their results and ours about the influence of the gravitational quadrupole moment in the perturbative calculation of corrections to the precession of the periastron of quasielliptical Keplerian equatorial orbits around a point mass. The discrepancy appears to be consequence of two different calculations of the angular momentum of the orbits.
The geodesic equation in the five-dimensional singly rotating black ring is non-integrable unlike the case of the Myers-Perry black hole. In the Newtonian limit of the black ring, its geodesic equation agrees with the equation of motion of a particle in the Newtonian potential due to a homogeneous ring gravitational source. In this paper, we show that the Newtonian equation of motion allows the separation of variables in the spheroidal coordinates, providing an non-trivial constant of motion quadratic in momenta. This shows that the Newtonian limit of a black ring recovers the symmetry of its …
