Innermost stable circular orbit and shadow of the 4D Einstein\u2013Gauss\u2013Bonnet black hole

Minyong Guo,Peng-Cheng Li

doi:10.1140/epjc/s10052-020-8164-7

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.

Highlights

The emergence of black hole photograph shows, the black hole shadow and the orbit of the light emitter around the black hole can be seen by the Event Horizon Telescope (EHT), and the parameters of a black hole can be identified based on the black hole model [22,23]
We studied the geodesic motions of timelike and null particles in the spacetime of the spherically symmetric 4D EGB black hole
We calculated the radius of the innermost stable circular orbit (ISCO) for the timelike particle and found that this radius is a deceasing function of the GB coupling constant

Summary

Introduction

Since the publication of the paper [7], there have appeared several works [9,10,11,12,13,14,15] debating that the procedure of taking D → 4 limit in [7] may not be consistent. The first detection of gravitational waves from a binary black hole merger by the LIGO/Virgo Collaborations [24] opened a new window to probe gravity in the strong field regime, which enables us to test gravity theories alternative to general relativity [25]. The progress in both areas may help us to distinguish Schwarzschild black hole from other black hole models, including the 4D EGB black hole, in the near future. We have set the fundamental constants c and G to unity, and we will work in the convention (−, +, +, +)

Revisit the 4 D EGB black hole solution

The innermost stable circular orbit of the 4 D EGB black hole

Photon sphere and shadow of the 4 D EGB black hole

Summary