Thermodynamics of spacetime and fibre bundle models of gauge theories

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In a nice paper by Jacobson it is shown that Einstein's field equations follow from thermodynamics and 0264-9381/13/11/023/img1 if the entropy is related to the area of the local Rindler causal horizons. We extend this to a fibre bundle describing electromagnetism (easily generalized to any gauge theory) coupled to gravity and to source fields. We show that the field equations of the gauge theory coupled to general relativity can now be written rather suggestively in terms of entropy alone as 0264-9381/13/11/023/img2. The field equations of the gauge theory now come in geometrically just like gravitation and are also `equations of state' in the sense used by Jacobson. If source fields, such as a charged scalar field, are included they contribute to 0264-9381/13/11/023/img3.

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