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 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.[1]
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.[2]
^Geroch, Robert (1968), "Spinor Structure of Space-Times in General Relativity. I", Journal of Mathematical Physics, 9 (11): 1739–1743, Bibcode:1968JMP.....9.1739G, doi:10.1063/1.1664507
^Section 6.2 in Szabados, László B. (2009), "Quasi-Local Energy-Momentum and Angular Momentum in GR", Living Rev. Relativ., 12 (1): 4, doi:10.12942/lrr-2009-4, PMC 5256466, PMID 28179826
The Gerochenergy or Geroch mass is one of the possible definitions of mass in general relativity. It can be derived from the Hawking energy, itself a...
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variety of proposed definitions such as the Hawking energy, the Gerochenergy or Penrose's quasi-local energy–momentum based on twistor methods, the field is...
Institute 2001 Summer School, David Hoffman (Ed.), pp. 113–136. Geroch, Robert (1973). "Energy Extraction". Annals of the New York Academy of Sciences. 224:...
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1995. Robert Geroch. Energy extraction. Ann. New York Acad. Sci. 224 (1973), 108–117. Pong Soo Jang and Robert M. Wald. The positive energy conjecture and...
Enrico Fermi, Nobel laureate in physics Riazuddin, nuclear physicist Robert Geroch, general relativist James Hartle, general relativist Craig Hogan, astronomer...
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)\left[r_{i}r_{j}-{\frac {1}{3}}r^{2}\delta _{ij}\right]d^{3}r,} The total energy (luminosity) carried away by gravitational waves is d E d t = ∑ i j G 5...
metric should give the stress-energy contribution due to the field.) Finally, when all the contributions to the stress–energy tensor are added up, the result...
Lectures on Physics. Vol. I. Addison Wesley Longman. ISBN 978-0-201-02115-8. Geroch, Robert (1981). General Relativity from A to B. University of Chicago Press...
frame of reference. Correspondingly the kinetic energy of an object, and even the change in this energy due to a change in velocity, depends on the inertial...
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