Innermost stable circular orbit and shadow of the 4D Einstein–Gauss–Bonnet black hole

Abstract

Recently, a novel 4D Einstein-Gauss-Bonnet gravity was formulated by Glavan and Lin (Phys Rev Lett 124(8):081301, 2020). Although whether the theory is well defined is currently debatable, the spherically symmetric black hole solution is still meaningful and worthy of study. In this paper, we study the geodesic motions in the spacetime of the spherically symmetric black hole solution. First of all, we find that a negative GB coupling constant is allowable, as in which case the singular behavior of the black hole can be hidden inside the event horizon. Then we calculate the innermost stable circular orbits for massive particles, which turn out to be monotonic decreasing functions of the GB coupling constant. Furthermore, we study the unstable photon sphere and shadow of the black hole. It is interesting to find that the proposed universal bounds on black hole size in Lu and Lyu (Phys Rev D 101(4):044059, 2020) recently can be broken when the GB coupling constant takes a negative value.

Shadows and photon spheres with spherical accretions in the four-dimensional Gauss–Bonnet black hole

“…In this paper, we have investigated the shadows and photon spheres cast by the four-dimensional Gauss-Bonnet black hole with spherical accretions. We first obtain the radius of the photon sphere and critical impact parameter for different Gauss-Bonnet constants, and find that the larger the Gauss-Bonnet constant is, the smaller the radius of the photon sphere and critical impact parameter will be, which is consistent with the previous results [50,51]. It should be noted that a simple approximation of the radius of the shadow was derived in Section 5 of [32], in which the authors mainly studied the quasinormal modes and stability of the four-dimensional spherical Gauss-Bonnet black hole.…”

“…In particular, gravitational lensing by black holes in ordinary medium and homogeneous plasma in four-dimensional Gauss-Bonnet gravity have been studied in [48,49]. The shadows cast by the spherically symmetric [32,50] and rotating [51] four-dimensional Gauss-Bonnet black hole have also been studied. It will be more interesting to investigate the corresponding light intensity of the shadow, which comprises the main issue of this paper.…”

Greybody factor and power spectra of the Hawking radiation in the 4D Einstein–Gauss–Bonnet de-Sitter gravity

“…where r 0 is the root when the quadratic radical of the metric function f (r ) is vanishing and we have taken into account the condition m > 0 for the inequalities. By using these conditions in combination and following the similar analysis in [58], we conclude f (1) = 0 and f (1) > 0 give the necessary and sufficient condition that this spacetime always contains a dS black hole, that is, both the event horizon and the cosmological horizon exist. Thus, we find the allowed region and show it in Fig.…”

“…For the first time it was discovered from the gravity with a conformal anomaly [52] and then it was recovered in the gravity with quantum corrections [53,54]. This 4D EGB gravity has aroused great interest since its publication [55][56][57][58][59][60][61][62][63][64][65][66][67][68][69]. Particularly, as many works have pointed out the procedure of taking D → 4 limit in [51] may not be consistent [70][71][72][73][74][75][76].…”

On causal structure of 4D-Einstein–Gauss–Bonnet black hole

“…Firstly this way of taking limit is rather contentious and most importantly, there is no corresponding 4D-action for the equation. Not withstanding all this, it has instantly caught up like a wild fire as is evidenced by the runaway activity [7][8][9][10][11][12][13] which is still going stronger by the day as there continues to be a steady flow of papers on the arxiv.…”