The Hawking temperature in the context of dark energy

Abstract

An emergent gravity metric incorporating $k-$essence scalar fields $\varphi$ 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 ${\varphi }_{emergent}$ be solutions of the emergent gravity equations of motion under cosmological boundary conditions at $\infty$, then for $r\to \infty$ the rescaled field $\frac{{\varphi }_{emergent}}{2GM-1}$ has exact correspondence with $\varphi$ with $\varphi (r,t)={\varphi }_1(r)+{\varphi }_2(t)$. The Hawking temperature of this metric is $T_{\mathrm{e}mergent}=\frac{\hslash c^3}{8\pi GM{k}_{\mathrm{B}}}(1-K{)}^2\equiv \frac{\hslash }{8\pi GM{k}_{\mathrm{B}}}(1-K{)}^2$, taking the speed of light $c=1$. Here $K={\dot{\varphi }}_2^2$ is the kinetic energy of the $k-$essence field $\varphi$ 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.

6 pages, latex, To appear in Euro Physics Letters. arXiv admin note: text overlap with arXiv:1009.4634 by other authors

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