Hawking temperature for a global monopole metric in the context of k- essence and emergent gravity

Abstract

The Hawking temperature for the Barriola-Vilenkin global monopole metric is shown to be $T_{\mathrm BV}= {\hbar (1-\alpha) ^{2}\over8\pi GM k_{\mathrm B}}$, where $\alpha$ is the global monopole charge,$M$ the mass of the black hole, $k_{\mathrm B}$ is the Boltzmann constant and speed of light $c=1$. We then show that a similar metric can also be obtained for certain $k-$ essence field configurations in an emergent gravity situation. Therefore, in the context of Belgiorno {\it et al's} recent demonstration of spontaneous emission of photons in a gravitational analogue experiment, any future observation of $T_{\mathrm BV}$ need not necessarily imply the existence of global monopoles. An alternative implication might as well be a very indirect signature of dark energy in an emergent gravity scenario. This should lead to effects that may be detectable in refined and modified versions of Belgiorno {\it et al's} experiment.