Einsteinian Quartic Gravity: Shadows, Signals, and Stability

Abstract

Using a continued fraction ansatz we obtain an analytic approximation for a spherically symmetric black hole solution to Einsteinian Quartic Gravity (EQG), the next simplest Generalized Quasi-Topological Gravity (GQTG) after Einsteinian Cubic Gravity (ECG). This approximate solution is valid everywhere outside of the horizon and we use it to investigate the orbit of massive test bodies near a black hole, specifically computing the innermost stable circular orbit. Using Shapiro time delay we calculate the constraints on the EQG coupling parameter. Finally we compute the shadow of an EQG black hole and figure out it to be larger than its Einsteinian counterpart in general relativity for the same value of the mass. By applying our results to Sagittarius A* (Sgr A*) at the center of Milky Way we find, similar to ECG black holes, that departures from general relativity are small but distinguishable for EQG black holes.