Black holes in modified gravity (MOG)

The field equations for scalar–tensor–vector gravity (STVG) or modified gravity (MOG) have a static, spherically symmetric black hole solution determined by the mass M with two horizons. The strength of the gravitational constant is G=GN(1+α ) where α is a parameter. A regular singularity-free MOG solution is derived using a nonlinear field dynamics for the repulsive gravitational field component and a reasonable physical energy-momentum tensor. The Kruskal–Szekeres completion of the MOG black hole solution is obtained. The Kerr-MOG black hole solution is determined by the mass M , the parameter α and the spin angular momentum $$J=Ma$$ . The equations of motion and the stability condition of a test particle orbiting the MOG black hole are derived, and the radius of the black hole photosphere and the shadows cast by the Schwarzschild-MOG and Kerr-MOG black holes are calculated. A traversable wormhole solution is constructed with a throat stabilized by the repulsive component of the gravitational field.