Gravitational Energy: Why Negative?

[ben_jamin]

I remember that someone (maybe Hawking) said the total energy of cosmology is zero: the matter hold the positive energy and gravational field possesses the negative energy. But I can't understand it, why the gravational field's energy is negative? As far as I understood, from the view of gauge field, all the fields should possesses the positive energy with the "positive" particle. If we consider the gravational field as the gauge field or it can be quantized, how to understand the negative?

 

[Garth]

Welcome to these Forums ben jamin!

why the gravational field's energy is negative?

It depends on how you define and measure energy in GR - neither is a trivial task.

On way to look at it is to consider an extended cloud of dust collapsing down under its own gravitational field. As the cloud condenses down the process accelerates; energy has been taken out of the field to give the dust particles kinetic energy and yet the gravitational field and the particles' mutual attraction has increased. Something that gets bigger the more you take out of it is negative - like my overdraft!

Garth

 

[ben_jamin]

Usually we consider the energy in GR with the energy and momentum tensor T_\mu\nu, and we think it is positive whatever definition.(Einstein, Laudau or otherone) The different of their definition is for the conservation not for positive or negative energy.

And if you say the energy and momentum tensor T only gives the energy for the matter in the gravity not the curvature, so what's the meaning of energy of curvature? and how to calculate it. Another question: why the negative energy don't annihilate with the positive energy of matter? The related question, is the energy of graviton negative?

 

[Garth]

Usually we consider the energy in GR with the energy and momentum tensor T_\mu\nu, and we think it is positive whatever definition.(Einstein, Laudau or otherone) The different of their definition is for the conservation not for positive or negative energy.

And if you say the energy and momentum tensor T only gives the energy for the matter in the gravity not the curvature, so what's the meaning of energy of curvature? and how to calculate it. Another question: why the negative energy don't annihilate with the positive energy of matter? The related question, is the energy of graviton negative?

"And if you say" I do say! Gravitational energy is not described by the energy-momentum tensor, that describes all energy, momentum and stress apart from that which is gravitational. The gravitational energy is described by the Einsteinian tensor and in one convention of defining the Riemannian there is a negative sign connecting the two:-

R_ab - 1/2 g_ab = - 8.pi.G T_ab

Defining the energy of a gravitational system is difficult and sometimes impossible, it is only possible for a static system at 'asymptotic flatness'. There are many posts on these Forums about the subject, you can search for "energy".

Garth