The Geroch energy or Geroch mass is one of the possible definitions of
mass in
general relativity. It can be derived from the
Hawking energy, itself a measure of the bending of ingoing and outgoing rays of
light that are
orthogonal
In mathematics, orthogonality is the generalization of the geometric notion of ''perpendicularity''.
By extension, orthogonality is also used to refer to the separation of specific features of a system. The term also has specialized meanings in ...
to a 2-
sphere surrounding the region of space whose mass is to be defined, by leaving out certain (positive) terms related to the sphere's external and internal
curvature
In mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane.
For curves, the canonic ...
.
The equation for the mass of a 2-sphere is based on the equation for the ingoing and outgoing ray of light corresponding to an electron on its surface, expressed as: γ = 2 γ. The inverse of this equation represents the value of the Hawking energy , and the result is the mass of an entangled pair of photons: the two photons can not be entangled if only they are located at the same location on the surface. But in this case, both photons must be propagating simultaneously. So the two photons, or their antiparticles, must be travelling through a field that is 3-dimensional, and the field can be regarded as containing the mass of another point.
[Section 6.2 in ]
See also
*
Mass in general relativity
*
Robert Geroch
Robert Geroch (born 1 June 1942 in Akron, Ohio) is an American theoretical physicist and professor at the University of Chicago. He has worked prominently on general relativity and mathematical physics and has promoted the use of category theo ...
References
General relativity
Mass
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