Radial Geodesics Research Articles

Impact of chaplygin-like equation of state on Joule–Thomson expansion and tidal forces of AdS black holes

This study examines a recently hypothesized black hole. We study the Joule–Thomson coefficient, the inversion temperature and also the isenthalpic curves in the Ti−Pi plane. The Joule–Thomson coefficient, the inversion curves and the isenthalpic curves are discussed in AdS black holes surrounded by Chaplygin dark fluid. In T−P plane, the inversion temperature curves and isenthalpic curves are obtained with different parameters. Next, we explore the radial time-like geodesics that leads us to explore the tidal force effects for a radially in-falling particle in such black hole spacetime. We also numerically solve the geodesic deviation equation for two nearby radial geodesics for a freely falling particle. Our analysis shows that contrary to the Schwarzschild spacetime, the tidal forces do not become zero at spatial infinity due to the lack of asymptotic flatness because of the presence of a non-zero cosmological constant. The geodesic separation profile shows an oscillating trend and depends on the dynamic spacetime parameters q,B and Λ.

On geodesics in spherical Rindler space

The geodesics in various spherical Rindler frames are investigated. A display of some kinematical quantities of the spacetime is given. The constant acceleration from the metric acts as the surface gravity of the horizon [Formula: see text]. The radial geodesics are computed both for the Balasubramanian et al. form of the spherical Rindler space and for the non-diagonal metric of Huang and Sun.

New models of d-dimensional black holes without inner horizon and with an integrable singularity

Theoretically, it has been proposed that objects traveling radially along regular black holes (RBHs) would not be destroyed because of finite tidal forces and the absence of a singularity. However, the matter source allows the creation of an inner horizon linked to an unstable de Sitter core due to mass inflation instability. This inner horizon also gives rise to the appearance of a remnant, inhibiting complete evaporation. We introduce here a d-dimensional black hole model with Localized Sources of Matter (LSM), characterized by the absence of an inner horizon and featuring a central integrable singularity instead of an unstable de Sitter core. In our model, any object tracing a radial and timelike world-line would not be crushed by the singularity. This is attributed to finite tidal forces, the extendability of radial geodesics, and the weak nature of the singularity. Our LSM model enables the potential complete evaporation down to r h = 0 without forming a remnant. In higher dimensions, complete evaporation occurs through a phase transition, which could occur at Planck scales and be speculatively driven by the Generalized Uncertainty Principle (GUP). Unlike RBHs, our model satisfies the energy conditions. We demonstrate a linear correction to the conventional area law of entropy, distinct from the RBH's correction. Additionally, we investigate the stability of the solutions through the speed of sound.

Possible influence of a cosmic repulsion on large-scale jets: Geometric viewpoint

Cosmic repulsion represented by a small positive value of the cosmological constant changes significantly properties of central gravitational fields at large distances, leading to existence of a static (or turnaround) radius where gravitational attraction of a center is just balanced by cosmic repulsion. Analyzing behavior of radial timelike geodesics in the Schwarzschild–de Sitter spacetime near its static radius we show that the particles with specific energy close to unity have tendency to slow down and cluster just below the static radius, forming clumps which, subsequently, start to expand uniformly due to cosmic repulsion. For central masses of (106–1011)M⊙ and current value of the cosmological constant 1.1×10−52m−2, this phenomenon takes place at distances of tens to hundreds of kiloparsecs from the center, being comparable with distances in which huge radio-lobes from some active galaxies were observed.

Static sphere observers and geodesics in Schwarzschild-de Sitter spacetime

We analyze null- and spacelike radial geodesics in Schwarzschild-de Sitter spacetime connecting two conjugate static sphere observers, i.e. free-falling observers at a fixed radius in between the two horizons. We explicitly determine the changes in the causal structure with respect to these natural observers as a result of the inward bending of the black hole singularity, as well as the outward bending of asymptotic infinity. Notably, the inward and outward bending changes as a function of the black hole mass, first increasing towards a maximum and then decreasing to vanish in the extreme Nariai limit. For a generic mass of the black hole this implies the existence of finite size (temporal) windows for the presence of symmetric radial geodesics between the static sphere observers probing the interior region of the black hole, as well as the exterior de Sitter region. We determine the size of the interior (black hole) and exterior (de Sitter) temporal windows in 4, 5 and 6 spacetime dimensions, finding that they are equal in D = 5, and compute the proper lengths of the symmetric radial geodesics. We comment on the implications for information exchange and the potential role of the symmetric radial geodesics in a geodesic approximation of static sphere correlators in Schwarzschild-de Sitter spacetime.

Singular space-times with bounded algebraic curvature scalars

We show that the absence of unbounded algebraic curvature invariants constructed from polynomials of the Riemann tensor cannot guarantee the absence of strong singularities. As a consequence, it is not sufficient to rely solely on the analysis of such scalars to assess the regularity of a given space-time. This conclusion follows from the analysis of incomplete geodesics within the internal region of asymmetric wormholes supported by scalar matter which arise in two distinct metric-affine gravity theories. These wormholes have bounded algebraic curvature scalars everywhere, which highlights that their finiteness does not prevent the emergence of pathologies (singularities) in the geodesic structure of space-time. By analyzing the tidal forces in the internal wormhole region, we find that the angular components are unbounded along incomplete radial time-like geodesics. The strength of the singularity is determined by the evolution of Jacobi fields along such geodesics, finding that it is of strong type, as volume elements are torn apart as the singularity is approached. Lastly, and for completeness, we consider the wormhole of the quadratic Palatini theory and present an analysis of the tidal forces in the entire space-time.

Tidal Forces in Majumdar-Papapetrou Spacetimes

Tidal disruption events occur when astrophysical objects are destroyed by black holes due to strong tidal force effects. Tidal forces have been studied in a variety of black hole spacetimes, including Reissner-Nordström and Kerr spacetimes. Despite the vast literature on the subject, tidal forces around black holes in static equilibrium have never been investigated before. The aim of this work is to fill in this gap and explore tidal forces in the Majumdar-Papapetrou spacetime describing two extremely charged binary black holes in equilibrium. We focus on tidal forces associated with radial and circular geodesics of massive neutral particles moving on the plane equidistant to the black holes. In particular, we study the behavior of the tidal forces as a function of the distance from the black holes and as a function of the energy of the geodesics. We also investigate the numerical solutions of the geodesic deviation equation for different initial conditions.

Geodesic Structure of Generalized Vaidya Spacetime through the K-Essence

This article investigates the radial and non-radial geodesic structures of the generalized K-essence Vaidya spacetime. Within the framework of K-essence geometry, it is important to note that the metric does not possess conformal equivalence to the conventional gravitational metric. This study employs a non-canonical action of the Dirac–Born–Infeld kind. In this work, we categorize the generalized K-essence Vaidya mass function into two distinct forms. Both the forms of the mass functions have been extensively utilized to analyze the radial and non-radial time-like or null geodesics in great detail inside the comoving plane. Indications of the existence of wormholes can be noted during the extreme phases of spacetime, particularly in relation to black holes and white holes, which resemble the Einstein–Rosen bridge. In addition, we have also detected a distinctive indication of the quantum tunneling phenomenon around the singularity (r→0). Furthermore, we have found that for certain types of solutions, there exist circular orbits through the event horizon as well as quasicircular orbits. Also, we have noted that there is no central singularity in our spacetime where both r and t tend towards zero. The existence of a central singularity is essential for any generalized Vaidya spacetime. This indicates that spacetime can be geodesically complete, which correlates with the findings of Kerr’s recent work (2023).

Possible Wormholes in a Friedmann Universe

We study the properties of evolving wormholes able to exist in a closed Friedmann dust-filled universe and described by a particular branch of the well-known Lemaître–Tolman–Bondi solution to the Einstein equations and its generalization with a nonzero cosmological constant and an electromagnetic field. Most of the results are obtained with pure dust solutions. It is shown, in particular, that the lifetime of wormhole throats is much shorter than that of the whole wormhole region in the universe (which coincides with the lifetime of the universe as a whole), and that the density of matter near the boundary of the wormhole region is a few times smaller than the mean density of matter in the universe. Explicit examples of wormhole solutions and the corresponding numerical estimates are presented. The traversability of the wormhole under study is shown by a numerical analysis of radial null geodesics.

Peeling for tensorial wave equations on Schwarzschild spacetime

In this paper, we establish the asymptotic behavior along outgoing and incoming radial geodesics, i.e. the peeling property for the tensorial Fackerell–Ipser and spin [Formula: see text] Teukolsky equations on Schwarzschild spacetime. Our method combines a conformal compactification with vector field techniques to prove the two-side estimates of the energies of tensorial fields through the future and past null infinity [Formula: see text] and the initial Cauchy hypersurface [Formula: see text] in a neighborhood of spacelike infinity [Formula: see text] far away from the horizon and future timelike infinity. Our results obtain the optimal initial data which guarantees the peeling at all orders.

Analytical study of particle geodesics around a scale-dependent de Sitter black hole

We give a fully analytical description of radial and angular geodesics for massive particles that travel in the spacetime provided by a (3+1)-dimensional scale-dependent black hole in the cosmological background, for which, the quantum corrections are assumed to be small. We show that the equations of motion for radial orbits can be solved by means of Lauricella hypergeometric functions with different numbers of variables. We then classify the angular geodesics and argue that no planetary bound orbits are available. We calculate the epicyclic frequencies of circular orbits at the potential’s maximum and the deflection angle of scattered particles is also calculated. Finally, we resolve the raised Jacobi inversion problem for the angular motion by means of a genus-2 Riemannian theta function, and the possible orbits are derived and discussed.

Geodesic incompleteness of some popular regular black holes

Throughout the study of the geodesics of some popular spherically symmetric regular black holes, we hereby prove that the analytically extended Hayward black hole is geodetically incomplete. The simplest extension of the Culetu-Simpson-Visser's non-analytic smooth black hole is also geodetically incomplete, with the exception of the antipodal continuation of the radial geodesics. However, the huge ambiguity in the extension of non analytic spacetimes is tantamount of geodesic incompleteness and such spacetimes do not solve the singularity issue unless at least all the extensions turn out to be complete. Hence, we provide several mere modifications of such spacetimes in order to make them geodetically complete in all possible extensions beyond r=0.

Deriving the physical phenomena of real TOUGMA's solution

In this paper, we derive the physical phenomena that implies the real TOUGMA's metric. We fristly found radial light geodesics and orbits of material bodies and finish by studied theirs physical charactericties. Due to astrophysical applications, the interest of studing the TOUGMA metric right now is to implement using a metric concrete the new physical concepts that implies this metric.

Tidal properties of D-dimensional Tangherlini black holes

This paper investigates tidal forces in multidimensional spherically symmetric spacetimes. We consider geodesic deviation equation in Schwarzschild-Tangherlini metric and its electrically charged analog. It was shown that for radial geodesics these equations can be solved explicitly as quadratures in spaces of any dimension. In the case of five, six and seven dimensional spaces, these solutions can be represented in terms of elliptic integrals. For spacetimes of higher dimension, we find the asymptotics of the solution. It was found that in the physical singularity vicinity tidal stretch along the radial direction is the stronger the greater the dimension of space. Whereas the tidal compression in transverse to radial directions, starting from a certain dimension, does not change in the main order. Also in the case of non-radial geodesics, the presence of black hole electric charge does not affect the force of transverse compression in the leading order. For non-radial geodesics with non-zero angular momentum, the local properties of solutions of geodesic deviation equations in the vicinity of a singularity are studied.

Trouble with geodesics in black-to-white hole bouncing scenarios

By utilizing the thin shell approximation, we investigate the behavior of radial timelike geodesics in a black hole to white hole bouncing scenario with a mass (de-)amplification relation. We show that those geodesics lose energy after crossing the transition surface if the white hole mass is less than the black hole mass and vice versa. That is, the bounded timelike radial geodesics become closer to the event horizon in the mass decreasing direction. We then show that by tracing a finite amount of bouncing cycles along the mass decreasing direction, all bounded radial geodesics can be squeezed into the range of the stretched horizon while the black hole and white hole are still massive. Those highly squeezed geodesics are problematic since there exists a Planck-scale blueshift between them and the regular infalling trajectories. We also discuss the possible implication and rescues.

Geodesic deviation on symmetry axis in Taub–NUT metric

An important aspect of general relativity is to study properties of geodesics. A useful tool for describing geodesic behavior is the geodesic deviation equation. It allows to describe the tidal properties of gravitating objects through the curvature of spacetime. This paper focuses on the study of the axially symmetric Taub–NUT metric. We study tidal effects in this metric using the geodesic deviation equation. Radial geodesics along the symmetry axis of spacetime are considered. We show that all spatial components of tidal forces always change sign under the event horizon. We find a solution of the geodesic deviation equation for all geodesic deviation vector components. It allows us to quantify the effect of the NUT-charge on the tidal properties of Taub–NUT metric. Another important feature that we found is the regular behavior of all tidal force components at all points of spacetime.

Internal structure and its connection with thermodynamics and dynamics in black holes

In general, a finite metric function at the center of a black hole describes a non-singular spacetime but an infinite metric at the center gives a singular spacetime, where the former is associated with convergent Ricci and Kretschmann scalars together with complete radial geodesics, while the latter is related to divergent Ricci and Kretschmann scalars together with incomplete radial geodesics. For the charged black hole in the four-dimensional Einstein-Gauss-Bonnet theory, we find that its metric function is finite at its center in one region of parameters but complex in the other region of parameters. The finite case describes a strange spacetime which presents the Ricci and Kretschmann scalars of a singular spacetime and the radial geodesics of a non-singular spacetime, while the complex case gives rise to the similar situation. We verify that the cosmic censorship conjecture is maintained for the black hole model. Further, we investigate the second-order phase transition, quasinormal modes of perturbation of a test scalar field in the eikonal limit, and shadow radius for the black hole and find that the thermodynamic and dynamic properties depend on the metrics. In this way, we connect the internal structure with the thermodynamics and dynamics for this black hole. Moreover, we compare such a black hole of modified gravity with the Reissner-Nordström black hole of Einstein's general relativity in these thermodynamic and dynamic properties.

A closed universe: de Sitter cosmic gate

A new cosmological object in analogy with the concept of a wormhole in general relativity is introduced. As wormholes connect two distant points through a tunnel in spacetime, this new object connects two spacetime through a large mouth which is referred to as a “Cosmic Gate”. In this context, two identical copies of the regular part of the de Sitter spacetime are cut through a timelike hyperplane. Then, they are glued at their identical boundaries (the only boundary) to form a complete spacetime. The stability of the cosmic gate against a linear radial perturbation is studied as well. Finally, the radial geodesics of the spacetime for a timelike and a null particle are presented.

Timelike orbits around accelerating black holes

We study the geodesics of massive particles around an accelerating Schwarzschild black hole. We show that the radius of the innermost stable circular orbit and the angular momentum of a particle at this orbit decrease by increasing the acceleration. Apart from quantitative influence, the acceleration qualitatively changes the physics. We show that in accelerating black hole spacetime there exists an outermost stable circular orbit in flat, de Sitter, and anti--de Sitter backgrounds. Investigations of radial geodesics show that the acceleration acts like a repulsive force in the sense that test particles around accelerating black holes can move radially outward, unless there exists a large negative value of cosmological constant in the background to compensate the repulsive force. We also investigate the precession of perihelion of orbits around accelerating black holes. The precession would be larger compared to the nonaccelerating case. It is also shown that the precession in anti--de Sitter background could be opposite to the particle motion.

A time-dependent spacetime in f(R,T) gravity: Gravitational collapse

In this note, a time-dependent spacetime is explored in the background of [Formula: see text] gravity via the gravitational collapse of a massive star. The star is modeled by the Vaidya spacetime which is time-dependent in nature. The coupling of matter with curvature is the key feature of [Formula: see text] theory and here we have investigated its effects on a collapsing scenario. Two different types of models, one involving minimal and the other involving nonminimal coupling between matter and curvature are considered for our study. Power law and exponential functionalities are considered as examples to check the outcome of the gravitational collapse. A detailed analysis on the appearance of horizons in Vaidya spacetime is performed and its astrophysical implications are explored. Our prime objective is to explore the nature of singularities (black hole or naked singularity) that form as an end state of the collapse. Existence of outgoing radial null geodesics from the central singularity was probed and such existence implied the formation of naked singularities thus defying the cosmic censorship hypothesis. The absence of such outgoing null geodesics would imply the formation of an event horizon and the singularity formed becomes a black hole. Conditions under which such possibilities occur are derived for all the models and sub-models. Gravitational strength of the singularity is also investigated and the conditions under which we can get a strong or a weak singularity is derived. The results obtained are very interesting and may be attributed to the coupling between curvature and matter. It is seen that for nonminimal coupling there is a possibility of a globally naked singularity, whereas for a minimal coupling scenario local nakedness is the only option. It is also found that the singularity formed can be sufficiently weak in nature, which is cosmologically desirable.