Gravitational lensing effects of a Reissner–Nordstrom–de Sitter black hole

Zhao, Fan; Tang, Jianfeng; He, Feng

doi:10.1103/physrevd.93.123017

Cited by 19 publications

(12 citation statements)

References 28 publications

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“…and a 1 is a function of x defined in Eq. (45). Further expanding v around 1, one should easily find the apparent angle θ to the order of O(1 − v).…”

Section: Velocity Correctionsmentioning

confidence: 98%

Gravitational lensing of massive particles in Reissner–Nordström black hole spacetime

Pang¹,

Jia²

2019

Class. Quantum Grav.

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In this work we study the deflection angle ∆ϕ and gravitational lensing of both lightlike and timelike neutral rays in Reissner-Nordström (RN) spacetimes. The exact deflection angle is found as an elliptical function of the impact parameter b and velocity v of the ray, and the charge Q of the spacetime. In obtaining this angle, we found the critical impact parameter bc and radius of particle sphere rc that are also dependent on v and Q. In general, both the increase of velocity and charge reduces the bc as well as rc. To study the effect of v and Q on the deflection angle ∆ϕ, its weak and strong deflection limits, relativistic and non-relativistic limits, and small charge and extremal RN limits are analyzed carefully. It is found that both the increase of velocity and charge reduces the deflection angle. For weak deflection, the velocity and charge corrections appear respectively in the O(1/b) and O(1/b 2 ) orders. For strong deflections, these two corrections appear in the same order. The apparent angles and magnifications of weak and strong regular lensing, and retro-lensing are studied for both lightlike and timelike rays. In general, in all cases the increase of velocity or charge will decrease the apparent angle of any order. We show that velocity correction is much larger than that of charge in the weak lensing case, while their effects in the strong regular lensing and retrolensing are comparable. It is further shown that the apparent angle and magnification in strong regular lensing and retro-lensing can be effectively unified. These observables at different orders in these two kinds of lensing are staggered: the apparent angles can be ordered in a staggered way and the magnifications forms two staggered geometric series. Finally, we argue that the correction of v and Q on the apparent angle can be correlated to mass or mass hierarchy of timelike particles with certain energy. In addition, the effects of v and Q on shadow size of black holes are discussed.

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“…and a 1 is a function of x defined in Eq. (45). Further expanding v around 1, one should easily find the apparent angle θ to the order of O(1 − v).…”

Section: Velocity Correctionsmentioning

confidence: 98%

Gravitational lensing of massive particles in Reissner–Nordström black hole spacetime

Pang¹,

Jia²

2019

Class. Quantum Grav.

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“…In axially symmetric, rotating case, the vacuum spacetime is determined by the Kerr-de Sitter (KdS) geometry [34]. In the spacetimes with the repulsive cosmological term (and the related solutions of the f(R) gravity), motion of photons is treated in a series of papers [35][36][37][38][39][40][41][42][43][44][45], while motion of test particles was studied in [15,31,. Oscillatory motion of current carrying string loops in SdS and KdS spacetimes was treated in [69][70][71][72][73][74][75].…”

Section: Introductionmentioning

confidence: 99%

General relativistic polytropes with a repulsive cosmological constant

2016

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Spherically symmetric equilibrium configurations of perfect fluid obeying a polytropic equation of state are studied in spacetimes with a repulsive cosmological constant. The configurations are specified in terms of three parameters-the polytropic index n, the ratio of central pressure and central energy density of matter σ, and the ratio of energy density of vacuum and central density of matter λ. The static equilibrium configurations are determined by two coupled first-order nonlinear differential equations that are solved by numerical methods with the exception of polytropes with n = 0 corresponding to the configurations with uniform distribution of energy density, when the solution is given in terms of elementary functions. The geometry of the polytropes is conveniently represented by embedding diagrams of both the ordinary space geometry and the optical reference geometry reflecting some dynamical properties of the geodesic motion. The polytropes are represented by radial profiles of energy density, pressure, mass, and metric coefficients. For all tested values of n > 0, the static equilibrium configurations with fixed parameters n, σ, are allowed only up to a critical value of the cosmological parameter λc = λc(n, σ). In the case of n > 3, the critical value λc tends to zero for special values of σ. The gravitational potential energy and the binding energy of the polytropes are determined and studied by numerical methods. We discuss in detail the polytropes with extension comparable to those of the dark matter halos related to galaxies, i.e., with extension ℓ > 100 kpc and mass M > 10 12 M⊙. For such largely extended polytropes the cosmological parameter relating the vacuum energy to the central density has to be larger than λ = ρvac/ρc ∼ 10 −9 . We demonstrate that extension of the static general relativistic polytropic configurations cannot exceed the so called static radius related to their external spacetime, supporting the idea that the static radius represents a natural limit on extension of gravitationally bound configurations in an expanding universe dominated by the vacuum energy.PACS numbers: 98.80. Es,

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“…The study of gravitational lensing is not only limited to the Schwarzschild black hole. Lensing by other black holes such as Reissner-Nordström [15][16][17][18], Kerr [19][20][21], Kiselev [22,23], global monopole [24][25][26], Einstein-Born-Infeld [27], Eddington-Born-Infeld [28][29][30], scalar-tensor [31,32], braneworld [33][34][35][36], dilaton [37][38][39][40], phantom [41,42], regular [43][44][45][46], Kaluza-Klein [47][48][49][50], Horava-Lifshitz [51], Myers-Perry [52] and Galileon [53] black holes, have been studied. Gravitational lensing by naked singularities has been analyzed to see whether one can distinguish between a black hole and a naked singularity [54][55][56][57][58].…”

Section: Introductionmentioning

confidence: 99%

Gravitational lensing by scalar-tensor wormholes and the energy conditions

Shaikh

Kar

2017

Phys. Rev. D

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We study gravitational lensing by a class of zero Ricci scalar wormholes which arise as solutions in a scalar-tensor theory of gravity. An attempt is made to find a possible link between lensing features, stable/unstable photon orbits and the energy conditions on the matter required to support these spacetimes. Our analysis shows (for this class of wormholes) that light rays always exhibit a positive deflection if the energy conditions are satisfied (nonexotic matter content). In contrast, if the energy conditions are violated (exotic matter), the net deflection of a light ray may be positive, negative or even zero, depending on values of the metric and impact parameters. This prompts us to introduce a surface defined by a turning point value at which the net deflection of a light ray is equal to zero, even though we have a curved spacetime geometry. We argue that the existence of such a surface may be linked to exotic/energy condition violating matter. Wormholes in modified gravity with matter satisfying the energy conditions do not seem to have such a zero deflection surface. Finally, we study strong gravitational lensing briefly and also look into the formation of Einstein and relativistic Einstein rings. We conclude with some estimates on the wormhole mass, throat-radius and the detectability of the Einstein rings. * rajibulshaikh@cts.iitkgp.ernet.in; Present address:

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Gravitational lensing effects of a Reissner–Nordstrom–de Sitter black hole

Cited by 19 publications

References 28 publications

Gravitational lensing of massive particles in Reissner–Nordström black hole spacetime

Gravitational lensing of massive particles in Reissner–Nordström black hole spacetime

General relativistic polytropes with a repulsive cosmological constant

Gravitational lensing by scalar-tensor wormholes and the energy conditions

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