Gravity/conservation of energy?

[navonoD]

If gravity is warped space time, and potential/kenetic energy can be derived from gravities effect on mass, apparently without exhausting any energy, how can conservation of energy hold true?
I'm not arguing in any sense, i just really don't get it... NEone?

 

[Chris Hillman]

This is a FAQ, asked on average every week here.

Localization of gravitational field energy, and "gravitational potential energy", are very tricky concepts in gtr, for mathematical reasons. See the discussion in MTW, Gravitation or other good textbooks.

 

[pervect]

The usual FAQ oriented towards the layperson is at http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html

Here's a very short quote from the introduction:

Is Energy Conserved in General Relativity?

In special cases, yes. In general -- it depends on what you mean by "energy", and what you mean by "conserved".

In flat spacetime (the backdrop for special relativity) you can phrase energy conservation in two ways: as a differential equation, or as an equation involving integrals (gory details below). The two formulations are mathematically equivalent. But when you try to generalize this to curved spacetimes (the arena for general relativity) this equivalence breaks down. The differential form extends with nary a hiccup; not so the integral form.

I'll encourage interested people to read the original in its entirety (due to copyright and other reasons, it's not appropriate to repost it, but to rerfer people to the original).