Cosmology

Twilight for the energy conditions?

Carlos Barcelo (Portsmouth, UK), Matt Visser (Washington University in Saint Louis)

(Submitted on 16 May 2002)

The tension, if not outright inconsistency, between quantum physics and general relativity is one of the great problems facing physics at the turn of the millennium. Most often, the problems arising in merging Einstein gravity and quantum physics are viewed as Planck scale issues (10^{19} GeV, 10^{-34} m, 10^{-45} s), and so safely beyond the reach of experiment. However, over the last few years it has become increasingly obvious that the difficulties are more widespread. There are already serious problems of fundamental principles at the semi-classical level, and worse, certain classical systems (inspired by quantum physics, but in no sense quantum themselves). One manifestation of these problems is in the so-called “energy conditions” of general relativity. Patching things up in the gravity sector opens gaping holes elsewhere and some “fixes” are more radically problematic than the problems they are supposed to cure.

How can one show from General Relativity that gravity is an attractive force. Under which conditions does it become repulsive. Also why does positive vacuum energy drive repulsive gravity?

The Einstein field equations actually don’t say anything at all about the nature of matter. Their structure is that they relate a certain measure of space-time curvature G to the stress-energy tensor T. The stress-energy tensor describes any matter that is present; it’s zero in a vacuum. Trivially, you can write down any equations you like describing an arbitrary space-time that you’ve made up. Then by calculating G you can find the T that is required in order to allow the existence of that space-time.

We need a clear operational meaning about what it means for gravity to be “repulsive”.

In the context of General Relativity, small test particles move on geodesics.

In general relativity, gravity can be regarded as not a force but a consequence of a curved space-time geometry where the source of curvature is the stress–energy tensor (representing matter, for instance). Thus, for example, the path of a planet orbiting around a star is the projection of a geodesic of the curved space-time geometry around the star.

Albert Einstein believed that the geodesic equation of motion can be derived from the field equations for empty space.

He wrote:

“It has been shown that this law of motion — generalized to the case of arbitrarily large gravitating masses — can be derived from the field equations of empty space alone. According to this derivation the law of motion is implied by the condition that the field be singular nowhere outside its generating mass points.”

Both physicists and philosophers have often repeated the assertion that the geodesic equation can be obtained from the field equations to describe the motion of a gravitational singularity, but this claim remains disputed.

Edited: 2017/7/20