An emergent gravity metric incorporating $k-$essence scalar fields $\phi$ having a Born-Infeld type lagrangian is mapped into a metric whose structure is similar to that of a blackhole of large mass $M$ that has swallowed a global monopole. However, here the field is not that of a monopole but rather that of a $k-$essence scalar field. If $\phi_{ emergent}$ be solutions of the emergent gravity equations of motion under cosmological boundary conditions at $\infty$, then for $r\rightarrow\infty$ the rescaled field $\frac { \phi_{ emergent}}{ 2GM-1}$ has exact correspondence with $\phi$ with $\phi(r,t)=\phi_{ 1}(r)+\phi_{ 2}(t)$. The Hawking temperature of this metric is $T_{ \mathrm emergent}= \frac{ \hbar c^{ 3}}{ 8\pi GM k_{ \mathrm B}}(1-K)^{ 2}\equiv \frac{ \hbar}{ 8\pi GM k_{ \mathrm B}}(1-K)^{ 2}$, taking the speed of light $c=1$. Here $K=\dot\phi_{ 2}^{ 2}$ is the kinetic energy of the $k-$essence field $\phi$ and $K$ is always less than unity, $k_{ \mathrm B}$ is the Boltzmann constant. This is phenomenologically interesting in the context of Belgiorno { \it et al's} gravitational analogue experiment.
Categories: physics.gen-ph