I obtained the black hole solution whose the metric function f(r) and scalar function ##\varphi(r)## are ;(adsbygoogle = window.adsbygoogle || []).push({});

##f(r)=\frac{1}{4}+\left(\frac{Z^{2}}{2r^{2}}\right)^{2}-\frac{1}{3}\Lambda r^{2}##

##\varphi(r)=\pm\left(\frac{1}{\sqrt{2}l}\right)r##

where ##Z##, ##\Lambda## and ##l## are just constants.

What is the global causal structure of this space-time solution described by Eqs. above?

Is the dilaton field well-behaved for r —-> infinity?

[Moderator's Note: deleted the second part of the post, needs to be posted in a separate thread.]

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# Global casual structure of space-time, well-behaved function

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