Can I use normal grease for a car on the surface of carbon bike?
From Sheldon Brown:

Grease lubrication is commonly used on all ball bearings. Good mechanics also use grease (or oil) on the threads of most threaded fittings and fasteners, and also inside the steerer (to keep the stem from becoming stuck) and the seat tube (to keep the seatpost from becoming stuck.)
There are a great many different greases on the market with different special features, mainly for automotive applications. For bicycle use, almost any grease is adequate, since the loads and temperatures are generally low.

Seems to me like the answer is yes, although to be safe why don't you invest in some Finish Line Teflon Grease - one tube will last you for years. From the Finish Line website:

Q. Are Finish Line products safe for use on Carbon Fiber Frames and Parts?
A. Yes. All of our products are safe to use on carbon fiber bike parts; our three degreasers, four lubes, our polish, grease, etc are all safe to use on and around carbon fiber bike parts. The exception is our DOT Brake Fluid – you don’t want to get DOT fluid on any painted or finished surface because it’ll attack the paint / finish.