Lectures on General Relativity

Hamilton's formalism for systems with constraints

“…Thus we expect that gauge theories are singular systems. Actually this follows from the generalized Bianchi identity [46,44] which we derive next.…”

A Note on Lagrangians and Lovelock-Rund’s Identities

“…In the case of general relativity theory, L given by (9), and a complete study of (13) when r ξ is a vectorial field, leads to results of Komar (1959) andDu Plessis (1969), and if r ξ is a Killing vector, then it is also possible to deduce the relations of Trautman (1964) and Moss (1972). On the other hand, (16) allows to construct the energy-momentum pseudo-tensors of Landau and Lifshitz (1955), Caltenco et al (2005), Misner et al (1973), Synge (1976), Anderson (1967), Möller (1958), Goldberg (1958) and Stachel (1977).…”

“…Here we shall employ the property (2) to obtain (in general relativity) in natural manner the energymomentum pseudo-tensors of Einstein (1916), (also see Trautman (1962), Adler et al (1965), Davis (1974), Dirac (1975), Persides (1979), Palmer (1980, Landau and Lifshitz (1955), Anderson (1967), Misner et al (1973), Synge (1976), Caltenco et al (2005), Möller (1958, Laurent (1959), Florides (1962), Shah (1967), Goldberg (1958) and Stachel (1977) ); and also the continuity equations of Komar (1959), Trautman (1964), Du Plessis (1969, and Moss (1972).…”

Geometrization Versus Transcendent Matter: A Systematic Historiography of Theories of Matter Following Weyl

“…(Of course, a mathematician might argue that the 30 I use Mielke as an example here although the mathematical inventory of his geometrization approach goes already back to, amongst others (Trautman [1973]; Wu and Yang [1975]; Drechsler and Mayer [1977]; Hehl and Š ijački [1980]). See also (Trautman [1980]) for an overview.…”