## About the effect of higher-curvature gravity on the shadow of a black hole

##### Summary

In this thesis I will explore the effect on the shadow of a black hole of adding higher order curvature terms to the Einstein-Hilbert action. I will do this by using an approach similar to that used in Newtonian mechanics to calculate orbits. I develop this further to describe the geodesics of general relativity and finally apply this to a new theory called ’Einstein-scalar- Gauss-Bonnet’ gravity in which we calculate the photon trajectories near black holes. An interesting feature in this new theory is that black holes in EsGB gravity are scalarized, also called scalar hair. In this gravity theory I use the frame of the ’observer’s sky’ to plot the shadow of a black hole and discover the radius of the shadow shrinks compared to general relativity for any value of the new parameters of the theory within the validity of my approximation. I also give an analytical approximation for expressing the radius of the shadow and compare it to the numerically found values. This analytical expression is dependent on the black hole mass and parameters of Einstein-scalar-Gauss-Bonnet theory and agrees remarkably well for in the small coupling regime.