On geometric objects, the non-existence of a gravitational stress-energy tensor, and the uniqueness of the Einstein field equation
AbstractThe question of the existence of gravitational stress-energy in general relativity has exercised investigators in the field since the inception of the theory. Folklore has it that no adequate definition of a localized gravitational stress-energetic quantity can be given. Most arguments to that effect invoke one version or another of the Principle of Equivalence. I argue that not only are such arguments of necessity vague and hand-waving but, worse, are beside the point and do not address the heart of the issue. Based on a novel analysis of what it may mean for one tensor to depend in the proper way on another, which, en passant, provides a precise characterization of the idea of a "geometric object", I prove that, under certain natural conditions, there can be no tensor whose interpretation could be that it represents gravitational stress-energy in general relativity. It follows that gravitational energy, such as it is in general relativity, is necessarily non-local. Along the way, I prove a result of some interest in own right about the structure of the associated jet bundles of the bundle of Lorentz metrics over spacetime. I conclude by showing that my results also imply that, under a few natural conditions, the Einstein field equation is the unique equation relating gravitational phenomena to spatiotemporal structure, and discuss how this relates to the non-localizability of gravitational stress-energy.
Similar books and articles
Gravitational and Nongravitational Energy: The Need for Background Structures.Vincent Lam - 2011 - Philosophy of Science 78 (5):1012-1024.
Energy Localization in General Relativity: A New Hypothesis. [REVIEW]F. I. Cooperstock - 1992 - Foundations of Physics 22 (8):1011-1024.
A Strictly Geometric Interpretation of Gravitation in General Relativity.J. P. Kobus - 1973 - Foundations of Physics 3 (1):45-51.
Relativistic Theory of Gravitation.A. A. Logunov & M. A. Mestvirishvili - 1986 - Foundations of Physics 16 (1):1-26.
On General-Relativistic and Gauge Field Theories.Hans-Jürgen Treder & Wolfgang Yourgrau - 1978 - Foundations of Physics 8 (9-10):695-708.
A Class of Metric Theories of Gravitation on Minkowski Spacetime.A. Nairz - 1996 - Foundations of Physics 26 (3):369-389.
A New Approach to the Theory of Relativity. III. Problem of the Ether.L. Jánossy - 1972 - Foundations of Physics 2 (1):9-25.
A Finslerian Extension of General Relativity.G. S. Asanov - 1981 - Foundations of Physics 11 (1-2):137-154.
Vacuum Energy as the Origin of the Gravitational Constant.Durmuş A. Demir - 2009 - Foundations of Physics 39 (12):1407-1425.
The Weight of Extended Bodies in a Gravitational Field with Flat Spacetime.Ø Grøn - 1979 - Foundations of Physics 9 (7-8):501-514.
Mach’s Principle and Hidden Matter.H. -H. V. Borzeszkowski & H. -J. Treder - 1997 - Foundations of Physics 27 (4):595-603.
The Clifford Bundle and the Nature of the Gravitational Field.Waldyr A. Rodrigues & Quintino A. G. de Souza - 1993 - Foundations of Physics 23 (11):1465-1490.
Added to PP
Historical graph of downloads
Citations of this work
Two Miracles of General Relativity.James Read, Harvey R. Brown & Dennis Lehmkuhl - 2018 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 64:14-25.
A Primer on Energy Conditions.Erik Curiel - 2017 - In Dennis Lehmkuhl, Gregor Schiemann & Erhard Scholz (eds.), Towards a Theory of Spacetime Theories. Birkhäuser. pp. 43-104.
On the Existence of Spacetime Structure.Erik Curiel - 2014 - British Journal for the Philosophy of Science:axw014.
References found in this work
Topics in the Foundations of General Relativity and Newtonian Gravitation Theory.David B. Malament - 2012 - Chicago: Chicago University Press.
Gauge-Invariant Localization of Infinitely Many Gravitational Energies From All Possible Auxiliary Structures.J. Brian Pitts - unknown
Space-Time-Matter.Hermann Weyl & Henry L. Brose - 1953 - British Journal for the Philosophy of Science 3 (12):382-382.