${\partial_t}$, and it is thus located at a specific radius ${\bar r}_h$ satisfying $$h \big|_{{\bar r}={\bar r}_h}=0\,. \label{standardhorizon}$$

In terms of the new metric form , we may similarly employ the vector field ${\partial_u}$ which coincides with ${\partial_t}$ everywhere. Its norm is given by $\Omega^2\, \H$. Since the conformal factor $\Omega$ is nonvanishing throughout the spacetime, the Killing horizon is uniquely located at a specific radius $r_h$ satisfying the condition $$\H \big|_{r=r_h}=0\,. \label{horizon}$$ Interestingly, via the relations this automatically implies ${h({\bar r_h})=0=f({\bar r_h})}$.

It is also important to recall that there is a *time-scaling freedom* of the metric tt/, \[scaling-t\] where ${\sigma \ne 0}$ is any constant, which implies ${h\to h\,\sigma^2}$. This freedom can be used to adjust an appropriate value of $h$ at a chosen radius ${\bar r}$. Or, in an asymptotically flat spacetime such as (\[SchwarzschildBH\]) it could be used to achieve ${h \to 1}$ as ${{\bar r}\to \infty}$, thus enabling us to determine the mass of a black hole.

The Kundt seed of the Schwarzschild solution {#Kundt seed of the Schwarzschild}
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It is also important to explicitly identify the Kundt seed geometry (\[Kundt seed\]) which, via the conformal relation (\[confrelation\]), generates the well-known vacuum *Schwarzschild solution*. 