Hi;(adsbygoogle = window.adsbygoogle || []).push({});

I am trying to find the geometry of a near-extremal D3 brane. I have been told that this geometry is the same as the 5D analog to the Schwarzschild metric with a negative cosmological constant. Trying to mimic Schutz (Ch 10) I tried plugging the metric

[tex]ds^2=e^{2\eta}dq^2-e^{2\zeta}dt^2+e^{2\xi}dr^2+r^{2}d\Omega^2[/tex]

into the Einstein field equations with [tex]T_{a b}=0[/tex], to solve for the functions [tex]\eta,\zeta,\xi[/tex], which I am assuming are functions of r only. The coordinate q is for the extra dimension. The system of DEs I get from this are terrible.

Anyway, I'm not expecting anyone to solve this problem for me. I am almost certain that this calculation has been done before, so I am wondering if anyone knows of any references that might help me out, or if someone could maybe tell me if I am going about this problem the right way. Please keep in mind that my main goal is to get a handle on the near-extremal D3 brane geometry.

Note: I don't really know anything about string theory, so please try not to use to much of its language, or else please define any string theory jargon that you may use. Also, I have to go shovel some snow, so I may not be online to reply for an hour or so.

Thank you.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Schwarzschild in 5D

**Physics Forums | Science Articles, Homework Help, Discussion**