Guido Magnano and Leszek M Sokolowski 2002 Class. Quantum Grav. 19 223 doi:10.1088/0264-9381/19/2/304
Guido Magnano1 and Leszek M Sokolowski2
Show affiliationsWe derive a generic identity which holds for the metric (i.e. variational) energy–momentum tensor under any field transformation in any generally covariant classical Lagrangian field theory. The identity determines the conditions under which a symmetry of the Lagrangian is also a symmetry of the energy–momentum tensor. It turns out that the stress tensor acquires the symmetry if the Lagrangian has the symmetry in a generic curved spacetime. In this sense, a field theory in flat spacetime is not self-contained. When the identity is applied to the gauge invariant spin-2 field in Minkowski space, we obtain an alternative and direct derivation of a known no-go theorem: a linear gauge invariant spin-2 field, which is dynamically equivalent to linearized general relativity, cannot have a gauge invariant metric energy–momentum tensor. This implies that attempts to define the notion of gravitational energy density in terms of the metric energy–momentum tensor in a field-theoretical formulation of gravity must fail.
03.50.-z Classical field theories
04.40.-b Self-gravitating systems; continuous media and classical fields in curved spacetime
04.20.Fy Canonical formalism, Lagrangians, and variational principles
70S05 Lagrangian formalism and Hamiltonian formalism
83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
Issue 2 (21 January 2002)
Received 12 July 2001, in final form 11 October 2001
Published 2 January 2002
Guido Magnano and Leszek M Sokolowski 2002 Class. Quantum Grav. 19 223
J G Pereira et al 2001 Class. Quantum Grav. 18 833
Eiichi Hanamura et al 2003 J. Phys.: Condens. Matter 15 L103
Jacob Noel-Storr et al. 2007 ApJ 663 71
Roxana M Vlad et al 2005 Phys. Med. Biol. 50 197
H J Jung 1986 Metrologia 23 19
T Smith 1930 Trans. Opt. Soc. 32 85
Ya'akov Achiam 1980 J. Phys. A: Math. Gen. 13 1825
Yung-Jin Hu and Corwin H Booth 2009 J. Phys.: Conf. Ser. 190 012029
Arkadiusz Blaut and Jerzy Kowalski Glikman 1996 Class. Quantum Grav. 13 39