Gravitational lensing effects of Schwarzschild–de Sitter black hole

Zhao, Fan; Tang, Jianfeng

doi:10.1103/physrevd.92.083011

Cited by 16 publications

(11 citation statements)

References 28 publications

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“…Strong deflection case on the other hand, is used for another problems: for example, for investigations of so-called relativistic images. To this end, we wish to point out the strong gravitational lensing for the Schwarzschild black hole [5,6], then extended to the Reissner-Nordstr öm black hole [7,8], regular black holes [9], and wormholes [10][11][12][13], while the investigations of so-called relativistic images see also Refs. [14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Distinguishing rotating naked singularities from Kerr-like wormholes by their deflection angles of massive particles

et al. 2019

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We study the gravitational deflection of relativistic massive particles by Janis-Newman-Winicour (JNW) spacetimes (also known as a rotating source with a surface-like naked singularity), and a rotating Kerr-like wormholes. Based on the recent article [K. Jusufi, Phys.Rev. D 98, 064017 (2018)], we extend some of these results by exploring the effects of naked singularity and Kerr-like objects on the deflection of particles. We start by introducing coordinate transformation leading to an isotropic line element which gives the refraction index of light for the corresponding optical medias. On the other hand, the refraction index for massive particles is found by considering those particles as a de Broglie wave packets. To this end, we apply the Gauss-Bonnet theorem to the isotropic optical metrics to find the deflection angles. Our analysis shows that, in the case of the JNW spacetime the deflection angle is affected by the parameter 0 < γ < 1, similarly, we find that the deformation parameter λ affects the deflection angle in the case of Kerr-like wormholes. In addition to that, we presented a detailed analysis of the deflection angle by means of the Hamilton-Jacobi equation that lead to the same results. As a special case of our results the deflection angle of light is recovered. Finally, we point out that the deflection of particles by Kerr-like wormholes is stronger compared to JNW spacetime, in particular this difference can be used to shed some light from observational point of view in order to distinguish the two spacetimes.

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Section: Introductionmentioning

confidence: 99%

Distinguishing rotating naked singularities from Kerr-like wormholes by their deflection angles of massive particles

et al. 2019

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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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“…Cosmological constant and quintessence are two well-known kinds of dark energy models. Recently, the role of the cosmological constant in gravitational lensing has been the subject of focused studies [55][56][57][58][59]. The black hole shadow arises as a result of gravitational lensing in a strong gravity regime.…”

Section: Photon Sphere and Shadowmentioning

confidence: 99%

Critical behavior of charged AdS black holes surrounded by quintessence via an alternative phase space

Hendi,

Jafarzade

2020

Preprint

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Variation of the pressure of the bulk, or equivalently variation of the AdS radius (l) leads to variation of the boundary quantities: i) the number of colors N . ii) the volume of the space on which the field theory is formulated (since V ∝ l d−2 ). iii) the CFT charge Q which is related to the bulk charge Q b according to Q = lQ b . So, considering the cosmological constant as a new thermodynamical parameter may give the phase diagram an extra dimension. An alternative interpretation is suggested in [12], where the variation of the pressure in the bulk theory corresponds to vary the volume of the boundary field theory. In this approach, the number of colors is kept fixed, which requires the variation of Newton's constant to compensate the variation of the volume of the boundary field theory. This shows that one cannot employ such an approach (AdS/CFT correspondence) to investigate the extended thermodynamics of black holes.Considering the defined thermodynamic pressure and volume, one can study thermodynamics of black holes in a new framework, sometimes referred to as Black Hole Chemistry [13]. This change of perspective has led to a different concept of known processes and the discovery of a broad range of new phenomena associated with black holes such as van der Waals behavior [9,14], solid/liquid phase transitions [15], triple points [16], reentrant phase transitions [17] and heat engines [11]. Also, using black hole volume, one can study the black hole adiabatic compressibility which has attracted attention in connection with black hole stability [18]. This new perspective has also been successful in describing the thermodynamic structure of black holes in other gravitational theories such as Lovelock gravity [19], nonlinear electrodynamics [20], Einstein-Yang-Mills gravity [21], black holes with scalar hair [22], dyonic black holes [23], f(R) gravity [24], STU black holes [25], quasi topological gravity [26], conformal gravity [27] Poincare gauge gravity [28], Lifshitz gravity [29-31] and massive gravity [32].Since the thermodynamic behavior of black hole is highly affected by the variation of electric charge, an alternative approach for investigating van der Waals like phase transition is proposed [33,34] by considering the electric charge as a thermodynamic variable and fixing the cosmological constant. In this regard, a phase transition between the large and small black holes in the Q − Φ plane is seen. In addition, it is shown that [35] such a suggestion is mathematically problematic and physically unconventional and it is logical to consider the square of the electric charge, Q 2 , as a thermodynamic variable. In Ref. [35], the van der Waals like behavior of charged AdS black hole in Q 2 − Ψ plane with a fixed cosmological constant is studied. It is also obtained the critical exponents which were exactly coincident with those obtained for van der Waals liquid. As a keynote, we should emphasize that unlike the van der Waals liquid the mentioned phase transition occurred for temperature higher than criti...

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Gravitational lensing effects of Schwarzschild–de Sitter black hole

Cited by 16 publications

References 28 publications

Distinguishing rotating naked singularities from Kerr-like wormholes by their deflection angles of massive particles

Distinguishing rotating naked singularities from Kerr-like wormholes by their deflection angles of massive particles

General relativistic polytropes with a repulsive cosmological constant

Critical behavior of charged AdS black holes surrounded by quintessence via an alternative phase space

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