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

[dhalilsim]

I obtained the black hole solution whose the metric function f(r) and scalar function $\varphi(r)$ are ;

$f(r)=\frac{1}{4}+\left(\frac{Z^{2}}{2r^{2}}\right)^{2}-\frac{1}{3}\Lambda r^{2}$
$\varphi(r)=\pm\left(\frac{1}{\sqrt{2}l}\right)r$
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.]

 

[bcrowell]

These look like two unrelated questions, which you should ask in two separate threads. Also, there is far too little information for anyone to be able to understand what you're actually asking about.

 

[PeterDonis]

I obtained the black hole solution

Why do you think this solution describes a black hole?

 

[PeterDonis]

These look like two unrelated questions, which you should ask in two separate threads.

Agreed, so I deleted the second one from the OP of this thread. dhalilsim, please start a separate thread if you want an answer to the other question (and it would help if you actually gave the specific equations you are asking about).

 

[PeterDonis]

whose the metric function f(r) and scalar function $\varphi(r)$

What are these supposed to mean? As bcrowell says, there is far too little information here to understand what you are talking about. Please give a reference or quite a bit more context (preferably both).

 

[pervect]

Telling us f(r) and $\varphi(r)$ does not directly gives us the line element / metric. I'm not sure what I'll be able to say about the global causal structure given the metric, but the first step is to get the metric.