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.

We study the influence of the cosmic expansion on the size of the shadow of a spinning black hole observed by a comoving observer. We first consider that the expansion is driven by a cosmological constant only and build the connection between the Kerr-de Sitter metric and the FLRW metric. We then calculate the angular size of the shadow for an observer comoving with the cosmic expansion. Furthermore, by adopting the approximate method proposed in [48] we extend the study to the general multi-component universe case. It is interesting to find that the oblateness of the black hole shadow, namely the ratio of the horizontal and vertical angular radii, becomes significant in the case that the black hole is at a high redshift.

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We study the black string solutions in the Einstein-Gauss-Bonnet(EGB) theory at large D. By using the 1/D expansion in the near horizon region we derive the effective equations that describe the dynamics of the EGB black strings. The uniform and nonuniform black strings are obtained as the static solutions of the effective equations. From the perturbation analysis of the effective equations, we find that thin EGB black strings suffer from the Gregory-Laflamme instablity and the GB term weakens the instability when the GB coefficient is small, however, when the GB coefficient is large the GB term enhances the instability. Furthermore, we numerically solve the effective equations to study the non-linear instability. It turns out that the thin black strings are unstable to developing inhomogeneities along their length, and at late times they asymptote to the stable nonuniform black strings. The behavior is qualitatively similar to the case in the Einstein gravity. Compared with the black string instability in the Einstein gravity at large D, when the GB coefficient is small the time needed to reach to final state increases, but when the GB coefficient is large the time to reach to final state decreases. Starting from the point of view in which the effective equations can be interpreted as the equations for the dynamical fluid, we evaluate the transport coefficients and find that the ratio of the shear viscosity and the entropy density agrees with that obtained previously in the membrane paradigm after taking the large D limit.

Abstract:We study the charged slowly rotating black holes in the Einstein-Maxwell theory in the large dimensions (D). By using the 1/D expansion in the near regions of the black holes we obtain the effective equations for the charged slowly rotating black holes. The effective equations capture the dynamics of various stationary solutions, including the charged black ring, the charged slowly rotating Myers-Perry black hole and the charged slowly boosted black string. Via different embeddings we construct these stationary solutions explicitly. For the charged black ring at large D, we find that the charge lowers the angular momentum due to the regularity condition on the solution. By performing the perturbation analysis of the effective equations, we obtain the quasinormal modes of the charge perturbation and the gravitational perturbation analytically. Like the neutral case the charged thin black ring suffers from the Gregory-Laflamme-like instability under the non-axisymmetric perturbations, but the charge weakens the instability. Besides, we find that the large D analysis always respects the cosmic censorship.