Null Geodesics Research Articles

Thermodynamics under the impact of thermal fluctuations and quasi-normal modes of Euler-Heisenberg AdS BH in the framework of NLED

We study the impact of thermal fluctuations on the thermodynamics, quasi-normal modes, and phase transitions of an anti-de Sitter Euler-Heisenberg black hole (BH) with a nonlinear electrodynamic field. An anti-de Sitter Euler-Heisenberg BH with a nonlinear electrodynamic field is composed of four parameters: the mass, electric charge, cosmological constant, and Euler-Heisenberg parameter. We calculate thermodynamic variables such as Hawking temperature, entropy, volume, and specific heat, which comply with the first law of thermodynamics. First, we use this BH to determine the thermodynamics and thermal fluctuations with the Euler-Heisenberg parameter to distinguish their effect on uncorrected and corrected thermodynamical quantities. We derive the expression for corrected entropy to study the impact of thermal fluctuation with simple logarithmic corrections on unmodified thermodynamical potentials, including Helmholtz energy, pressure, Gibbs free energy, and enthalpy. The Euler-Heisenberg parameter improves BH stability at large radii. Second, we analyze the local stability of the proposed BH, and the phase shifts of the BH are also investigated using temperature and specific heat. When there is a decrease in charge and an increase in and α, the temperature shifts from an unstable region to a stable one. Similarly, increases in local stability are observed with each of these parameters. Third, we use null geodesics to deal with the effects of nonlinear electrodynamics on the quasi-normal modes of the Euler-Heisenberg anti-de Sitter BH. The null geodesics provide the angular velocity and Lyapunov exponent of the photon sphere, which are the same as the real and imaginary parts of the quasi-normal modes in the eikonal limit.

Generalized Vaidya spacetime: Horizons, conformal symmetries, surface gravity and diagonalization

In this paper, the different properties of generalized Vaidya spacetime are considered. We define the location of horizons. We show that the apparent horizon can contain the event horizon. The locations of all types of horizons are compared with the ones in the usual Vaidya spacetime. We investigate the time-like geodesics in this spacetime. New corrections to Schwarzschild and Vaidya cases appear and we give conditions when these corrections are not negligible. Also, we consider the conformal Killing vector and transform the metric to conformally static coordinates. We introduce a new constant of motion along null and time-like geodesics, which is generated by a homothetic Killing vector. The conformally static coordinates allow diagonalizing of the generalized Vaidya spacetime. The surface gravity has been calculated for the dust and stiff fluid cases.

The null geodesics of charged and non–charged black hole in mimetic gravity

The null geodesics around the charged black hole spacetimes are investigated in the mimetic gravity framework when Einstein's gravity is coupled to a nonlinear electromagnetic field. The photon paths in nonlinear electrodynamics are geodesics of the effective metric which is determined by the background metric and the particular nonlinear theory considered. The nonlinear effects are represented by a quadruple moment and appear as a correction term to Reissner Nordstrom (RN) metric and Reissner Nordstrom-anti-de Sitter (RN–(A)dS) in cylindrical metric. Remarkably, the nonlinear effects prevent the circular orbits around black holes, and the presence of the mimetic field can change the repulsive character of dS space to the attractive one. Also, the effect of the mimetic parameter manifests itself in the stronger or weaker gravity of the black hole.

Analog of a Laplace–Runge–Lenz vector for particle orbits (time-like geodesics) in Schwarzschild spacetime

In Schwarzschild spacetime, time-like geodesic equations, which define particle orbits, have a well-known formulation as a dynamical system in coordinates adapted to the time-like hypersurface containing the geodesic. For equatorial geodesics, the resulting dynamical system is shown to possess a conserved angular quantity and two conserved temporal quantities, whose properties and physical meaning are analogs of the conserved Laplace–Runge–Lenz vector, and its variant known as Hamilton’s vector, in Newtonian gravity. When a particle orbit is projected into the spatial equatorial plane, the angular quantity yields the coordinate angle at which the orbit has either a turning point (where the radial velocity is zero) or a centripetal point (where the radial acceleration is zero). This is the same property as the angle of the respective Laplace–Runge–Lenz and Hamilton vectors in the plane of motion in Newtonian gravity. The temporal quantities yield the coordinate time and the proper time at which those points are reached on the orbit. In general, for orbits that have a single turning point, the three quantities are globally constant, and for orbits that possess more than one turning point, the temporal quantities are just locally constant as they jump at every successive turning point, while the angular quantity similarly jumps only if an orbit is precessing. This is analogous to the properties of a generalized Laplace–Runge–Lenz vector and generalized Hamilton vector which are known to exist for precessing orbits in post-Newtonian gravity. The angular conserved quantity is used to define a direct analog of these vectors at spatial infinity.

Thermal fluctuations of Torus-like charged AdS Black Hole

In this article, we analyze the thermodynamics, thermal fluctuations and quasi-normal modes of a torus-like AdS black hole. The parameters of a torus-like charged AdS black hole are its mass, electric charge and cosmological constant. We used a torus-like charge in an AdS black hole to evaluate thermodynamics through thermal fluctuations and found that it significantly affected the corrected thermodynamic potentials. Black holes of larger radii are more stable and significant, as determined by our investigation of the effect of thermal fluctuation on other thermodynamic potentials such as Helmholtz free energy, Gibbs free energy, enthalpy and specific heat with constant pressure and volume, using the concept of corrected entropy. Finally, we use null geodesics to deal with quasi-normal modes. The null geodesics provide the photon sphere’s angular velocity and Lyapunov exponent, which are the real and imaginary components of the quasi-normal modes in the eikonal limit. With rising charge and photon radius, the angular velocity reaches its maximum, similar to Lyapunov’s exponent.

Lyapunov exponents and phase transitions of Born-Infeld AdS black holes

In this paper, we characterize the phase transitons of Born-Infeld AdS black holes in terms of Lyapunov exponents. We calculate the Lyapunov exponents for timelike geodesics in background metric and photon geodesics in effective metric. It is found that black hole phase transitions can be described by multiple-valued Lyapunov exponents. And its phase diagram can be characterized by Lyapunov exponents and Hawking temperature. Besides, the change of Lyapunov exponents can be considered as order parameter, and exists a critical exponent 1/2 near critical point.

Asymptotic behavior of null geodesics near future null infinity. IV. Null-access theorem for generic asymptotically flat spacetime

Asymptotic behavior of null geodesics near future null infinity. IV. Null-access theorem for generic asymptotically flat spacetime

On the visibility of singularities in general relativity and modified gravity theories

We investigate the global causal structure of the end state of a spherically symmetric marginally bound Lemaitre–Tolman–Bondi (LTB) (Lemaitre 1933 Ann. Soc. Sci. Brux. A 53 51, Tolman 1934 Proc. Natl Acad. Sci. USA 20 169–76, Bondi 1947 Mon. Not. Astron. Soc. 107 410) collapsing cloud (which is well studied in general relativity) in the framework of modified gravity having the generalized Lagrangian in the action. Here R is the Ricci scalar, and is a constant. By fixing the functional form of the metric components of the LTB spacetime, using up the available degree of freedom, we realize that the matching surface of the interior and the exterior metric are different for different values of α. This change in the matching surface can alter the causal property of the first central singularity. We depict this by showing a numerical example. Additionally, for a globally naked singularity to have physical relevance, a congruence of null geodesics should escape from such singularity to be visible to an asymptotic observer for infinite time. For this to happen, the first central singularity should be a nodal point. We here give a heuristic method to show that this singularity is a nodal point by considering the above class of theory of gravity, of which general relativity is a particular case.

An Extension of the Athena++ Code Framework for Radiation-magnetohydrodynamics in General Relativity Using a Finite-solid-angle Discretization

We extend the general-relativistic magnetohydrodynamics (GRMHD) capabilities of Athena++ to incorporate radiation. The intensity field in each finite-volume cell is discretized in angle, with explicit transport in both space and angle properly accounting for the effects of gravity on null geodesics, and with matter and radiation coupled in a locally implicit fashion. Here we describe the numerical procedure in detail, verifying its correctness with a suite of tests. Motivated in particular by black hole accretion in the high-accretion-rate, thin-disk regime, we demonstrate the application of the method to this problem. With excellent scaling on flagship computing clusters, the port of the algorithm to the GPU-enabled AthenaK code now allows the simulation of many previously intractable radiation-GRMHD systems.

On SIR-type epidemiological models and population heterogeneity effects

In this paper we elaborate on homogeneous and heterogeneous SIR-type epidemiological models. We find an unexpected correspondence between the epidemic trajectory of a transmissible disease in a homogeneous SIR-type model and radial null geodesics in the Schwarzschild spacetime. We also discuss modeling of population heterogeneity effects by considering both a one- and two-parameter gamma-distributed function for the initial susceptibility distribution, and deriving the associated herd immunity threshold. We furthermore describe how mitigation measures can be taken into account by model fitting.

Thermal fluctuations, quasi-normal modes and phase transition of the charged AdS black hole with perfect fluid dark matter

In this paper, we study thermodynamics, thermal fluctuations, phase transitions and the charged anti-de Sitter black hole surrounded by perfect fluid dark matter. Large black holes are shown to be stable when subject to thermal fluctuations, and we begin by exploring how these fluctuations affect the uncorrected thermodynamic quantities of entropy, Helmholtz free energy, Gibbs free energy, enthalpy specific heat, and phase transition stability. We also discuss null geodesics and the radius of the photon sphere for the charged AdS BH and use the radius of a photon sphere to calculate the Lyapunov exponent and angular velocity. Exceptionally, we test the effects of various parameters of a black hole graphically by observing the existence of the correction parameter and the coupling parameter, which reveal the behavior of corrected thermodynamic quantities. Lastly, we see how the system is stable (under the effects of the dark matter parameter) by figuring out the specific heat and Hawking temperature, which are both related to entropy.

Probing the Lorentz Invariance Violation via Gravitational Lensing and Analytical Eigenmodes of Perturbed Slowly Rotating Bumblebee Black Holes

The ability of bumblebee gravity models to explain dark energy, which is the phenomenon responsible for the universe’s observed accelerated expansion, is one of their most significant applications. An effect that causes faster expansion can be linked to how much the Lorentz symmetry of our universe is violated. Moreover, since we do not know what generates dark energy, the bumblebee gravity theory seems highly plausible. By utilizing the physical changes happening around a rotating bumblebee black hole (RBBH), we aim to obtain more specific details about the bumblebee black hole’s spacetime and our universe. However, as researched in the literature, slow-spinning RBBH (SRBBH) spacetime, which has a higher accuracy, will be considered instead of general RBBH. To this end, we first employ the Rindler–Ishak method (RIM), which enables us to study how light is bent in the vicinity of a gravitational lens. We evaluate the deflection angle of null geodesics in the equatorial plane of the SRBBH spacetime. Then, we use astrophysical data to see the effect of the Lorentz symmetry breaking (LSB) parameter on the bending angle of light for numerous astrophysical stars and black holes. We also acquire the analytical greybody factors (GFs) and quasinormal modes (QNMs) of the SRBBH. Finally, we visualize and discuss the results obtained in the conclusion section.

Light rings in static and extremal black holes

In this work we establish some results concerning the existence of external light rings in extremal black hole spacetimes through the Newman-Penrose formalism. Specifically, assuming flat or (anti)--de Sitter asymptotics, staticity and the null energy condition, we show that a sufficient condition for the existence of external light rings is $R<2{K}_{G}$, where $R$, the curvature scalar of the spacetime and ${K}_{G}$, the Gaussian curvature of a spacelike two-surface, are both evaluated at the outermost event horizon, which can be endowed with spherical, hyperbolic or planar geometry. Our results are valid for any metric gravity theory where photons follow null geodesics.

On causality conditions in de Sitter spacetime

We carefully consider the Shapiro time delay due to black holes and shockwaves in de Sitter spacetime and study the implications for causality. We discuss how causality conditions of AdS and flat spacetime can be applied in de Sitter spacetime, using spatial shifts measured on the boundary to define ‘fastest null geodesics’ and taking into account the ‘stretching’ of the de Sitter Penrose diagram. We consider the propagation of a massless spin-1 field with a non-minimal coupling in a de Sitter shockwave background as an illustrative example. We also briefly discuss connections to the average null energy condition.

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.

Gravitational lensing by Morris-Thorne–type wormhole space-time with cosmic strings

In this paper, we study the deflection angle of photon light in Morris-Thorne–type wormhole space-time with a cosmic string. It is shown that the angle of deflection of photon light as well as the effective potential (time-like or light-like geodesics) of the system is influenced by the cosmic string and is higher compared to the known result.

Possible relationship between initial conditions for inflation and past geodesic incompleteness of the inflationary spacetime

According to the Borde-Guth-Vilenkin (BGV) theorem an expanding region of spacetime cannot be extended to the past beyond some boundary ℬ. Therefore, the inflationary universe must have had some kind of beginning. However, the BGW theorem says nothing about the boundary conditions on ℬ, or even about its location. Here we present a single-scalar field model of the Two-Measure Theory, where the non-Riemannian volume element Υ d 4 x is present in the action. As a result of the model dynamics, an upper bound φ 0 of admissible values of the scalar field φ appears, which sets the position of ℬ in the form of a spacelike hypersurface Υ(x) = 0 with a boundary condition: Υ → 0+ as φ → φ 0 -. A detailed study has established that if the initial kinetic energy density ρ kin (in) prevails over initial gradient energy density ρ grad (in) then there is an interval of initial values φ in (min) ≤ φ in < φ 0, where ρ kin (in) and ρ grad (in) cannot exceed the potential energy density and hence the initial conditions necessary for the onset of inflation are satisfied. It is shown that under almost all possible left-handed boundary conditions on ℬ, that is where Υ → 0-, the metric tensor in the Einstein frame has a jump discontinuity on ℬ, so the Christoffel connection coefficients are not defined on the spacelike hypersurface Υ = 0. Thus, if φ in (min) ≤ φ in < φ 0 and ρ kin (in) > ρ grad (in), then there was an inflationary stage in the history of our Universe and the congruence of timelike geodesics cannot be extended to the past beyond the hypersurface Υ = 0.

Lense–Thirring effect and precession of timelike geodesics in slowly rotating black hole and naked singularity spacetimes

In this paper, we investigate the properties of the Lense-Thirring precession frequency and periastron precession of the relativistic bound orbits in slowly rotating naked singularity spacetimes. We show that the precession frequencies of a stationary test gyroscope are quite unique in slowly rotating naked singularity spacetimes, and therefore, one can easily distinguish them from the slowly rotating Kerr black hole spacetime. On the other hand, we also show that in slowly rotating Joshi-Malafarina-Narayan (JMN1) naked singularity spacetime, negative precession of the timelike bound orbits is allowed which is not possible in Kerr and slowly rotating null naked singularity spacetimes.

Probing a non-linear electrodynamics black hole with thin accretion disk, shadow, and deflection angle with M87* and Sgr A* from EHT

Non-linear interaction between the electromagnetic fields (EMF) occurs when vacuum polarization in quantum electrodynamics (QED) happens. The field of non-linear electrodynamics, which may result from this interaction, could have important effects on black hole physics. This paper considers the asymptotically flat black hole solution in Einstein-nonlinear electrodynamics (NLE) fields. We study the effect of the NLE parameters on the black hole deflection angle using the Gauss-Bonnet theorem in weak field limits, shadow cast using the null geodesics method, and thin accretion disk using the Novikov-Thorne model. In particular, we studied the time-averaged energy flux, the disk temperature, the differential luminosity, the different emission profiles, and infalling spherical accretion. Then we show how the physical quantities depend on $\beta$ and $C$ parameters of NLE and provide some constraints on the NLE parameters using the observations of M87* and Sgr A* from EHT.

The existence of null circular geodesics outside extremal spherically symmetric asymptotically flat hairy black holes

The existence of null circular geodesics in the background of non-extremal spherically symmetric asymptotically flat black holes has been proved in previous works. An interesting question that remains, however, is whether extremal black holes possess null circular geodesics outside horizons. In the present paper, we focus on the extremal spherically symmetric asymptotically flat hairy black holes. We show the existence of the fastest circular trajectory around an extremal black hole. As the fastest trajectory corresponds to the position of null circular geodesics, we prove that null circular geodesics exist outside extremal spherically symmetric asymptotically flat hairy black holes.