Maximal extension of Schwarzschild-like spacetimes in Lorentz gauge theory

Abstract

We study the maximal analytic extension of the Schwarzschild-like black hole solution in Lorentz gauge theory. The lapse function is $f(r)=A_0^{-2}-2\m/r$, so the horizon is located at $r_+=2\m A_0^2$ and the non-affinity coefficient of the horizon generator is $κ=1/(4\m A_0^4)$. We first analyze the radial null curves in the Schwarzschild-Droste (SD) and ingoing Eddington-Finkelstein (IEF) charts, and then construct the Kruskal-Szekeres (KS) chart adapted to the LGT geometry. The KS extension contains two exterior regions, a black-hole region and a white-hole region. We also present the standard and regular Carter-Penrose (CP) compactifications. The conformal skeleton is Schwarzschild-like, but the physical scale of the horizon, the surface gravity and the constant-radius curves remain controlled by $A_0$. Hence the solution has the same causal topology as Schwarzschild, while it is geometrically inequivalent to it when $A_0\neq1$.