Light bending, static dark energy, and related uniqueness of Schwarzschild–de Sitter spacetime

Abstract

Since the Schwarzschild-de Sitter spacetime is static inside the cosmological event horizon, if the dark energy state parameter is sufficiently close to −1, apparently one could still expect an effectively static geometry, in the attraction dominated region inside the maximum turn around radius, RTA,max, of a cosmic structure. We take the first order metric derived recently assuming a static and ideal dark energy fluid with equation of state P (r) = αρ(r) as a source in Ref.[1], which reproduced the expression for RTA,max found earlier in the cosmological McVittie spacetime. Here we show that the equality originates from the equivalence of geodesic motion in these two backgrounds, in the nonrelativistic regime. We extend this metric up to the third order and compute the bending of light using the Rindler-Ishak method. For α = −1, a dark energy dependent term appears in the bending equation, unlike the case of the cosmological constant, α = −1. Due to this new term in particular, existing data for the light bending at galactic scales yields, (1 + α) O(10 −14 ), thereby practically ruling out any such static and inhomogeneous dark energy fluid we started with. Implication of this result pertaining the uniqueness of the Schwarzschild-de Sitter spacetime in such inhomogeneous dark energy background is discussed.

Bending of light in novel 4D Gauss-Bonnet-de Sitter black holes by the Rindler-Ishak method

“…Also the method has been applied to galactic halos, of which an excellent example is the Mannheim-Kazanas solution of conformal Weyl gravity [33][34][35]. For further insight into the use of the Rindler-Ishak method, see [36][37][38][39][40].…”

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

“…The figure demonstrates that increasing the bumblebee parameter results in a decreased probability of encountering Hawking radiations. The GFs for the second order of ã can be determined using a similar procedure by substituting Equation (60) into Equation (63). One can obtain σ (ω) (2) ≥ σ (1) (ω) + sec h 2 1 2ω(1 + )…”

“…The RIM also considers the effect of the black hole's rotation on the trajectory of light and calculates the amount of bending that occurs as a result. This method is widely used to study the properties of rotating black holes and has been applied to a variety of problems in astrophysics and cosmology [55,[57][58][59][60][61][62][63][64][65][66][67].…”

Gravitational lens on de-Sitter background

“…Many attempts have been made on the simple model in the context of the gravitational lensing e.g. [9][10][11][12][13][14][15][16][17][18][19][20][21]. Intuitively, the Minkowskian background can work as an approximation at small scale, though there can be a significant departure of the Minkowskian background from de-Sitter backgrounds especially at very large scale.…”