What are the properties required for spacetime to be a Lorentzian manifold?

[mersecske]

I know that spacetime is a Lorentzian manifold,
but what kind of properties has to be required exactly?
for example orientable, connected, Haussdorff, ...

 

[arkajad]

It is not even sure that it is a Lorentzian manifold. Different physicists try different models. Lorentzian, Finsler, dgenerate metrics, metrics changing signatures, pure affine, multi-dimensional. You need to distinguish space and time of physics from their mathematical models.
The Lorentzian model is most popular and seems to work for weak field approximations and when you do not take into account quantum effects.
It is up to you which assumptions you choose - depending on applications that you may have in your mind.

 

[Mentz114]

I know that spacetime is a Lorentzian manifold,

I would rephrase this to

Spacetime can be modeled by a Lorentzian manifold

A Lorentzian manifold is an abstraction that lives in our minds ( or in my case visits now and again), it can't be awarded the same ontological status as charge and mass, say.

 

[mersecske]

Ok, but let's see the conventional Lorentzian manifold.
What are the conventional properties?

 

[arkajad]

Ok, but let's see the conventional Lorentzian manifold.
What are the conventional properties?

You may like to assume that it admits a http://en.wikipedia.org/w/index.php?title=Sven-S._Porst&action=edit&redlink=1" .

 

[sachinism]

Relativity and the Nature of Spacetime (The Frontiers Collection)
by: Vesselin Petkov

should really be a helpful book to u

btw even these should help, worth a read

http://en.wikipedia.org/wiki/Spacetime

http://www.ws5.com/spacetime/