Why isn't there an event horizon in the negative mass Schwarzschild metric?

Question

The negative mass Schwarzschild metric has no event horizon.

Why isnt there a particular radius in which spactime flows outwards at the speed of light? This would imply a region of the solution for which exterior particles could not cross.

Answer 1

With negative $\rm M$ in Schwarzschild spacetime the lightlike geodesics in static coordinates are in natural units $\rm dr/dt=\pm (r+2)/r$.

In the $\rm \{t,r\}$ spacetime diagram below are the in- (blue) and outgoing (red) photon geodesics for a negative mass singularity at $\rm r=0$ (for the calculation click on the image):

As you can see they can escape from and travel toward $\rm r=0$, and due to the inversed gravitational time dilation they do so with $\rm |dr/dt|>c$ (with positive mass the shapirodelayed coordinate velocity would be slower than $\rm c$, while relative to local observers the photons always have $\rm v=c$).

Answer 2

Bc Goo = 1+2Gm/(c^2*r) is never zero. No negative mass is known; anti matter behaves like regular matter in gravity.