TY - JOUR

T1 - Internal time formalism for spacetimes with two Killing vectors

AU - Romano, Joseph D.

AU - Torre, Charles G.

PY - 1996

Y1 - 1996

N2 - The Hamiltonian structure of spacetimes with two commuting Killing vector fields is analyzed for the purpose of addressing the various problems of time that arise in canonical gravity. Two specific models are considered: (i) cylindrically symmetric spacetimes and (ii) toroidally symmetric spacetimes, which respectively involve open and closed universe boundary conditions. For each model, canonical variables which can be used to identify points of space and instants of time, i.e., internally defined spacetime coordinates, are identified. To do this it is necessary to extend the usual ADM phase space by a finite number of degrees of freedom. Canonical transformations are exhibited that identify each of these models with harmonic maps in the parametrized field theory formalism. The identifications made between the gravitational models and harmonic map field theories are completely gauge invariant; that is, no coordinate conditions are needed. The degree to which the problems of time are resolved in these models is discussed.

AB - The Hamiltonian structure of spacetimes with two commuting Killing vector fields is analyzed for the purpose of addressing the various problems of time that arise in canonical gravity. Two specific models are considered: (i) cylindrically symmetric spacetimes and (ii) toroidally symmetric spacetimes, which respectively involve open and closed universe boundary conditions. For each model, canonical variables which can be used to identify points of space and instants of time, i.e., internally defined spacetime coordinates, are identified. To do this it is necessary to extend the usual ADM phase space by a finite number of degrees of freedom. Canonical transformations are exhibited that identify each of these models with harmonic maps in the parametrized field theory formalism. The identifications made between the gravitational models and harmonic map field theories are completely gauge invariant; that is, no coordinate conditions are needed. The degree to which the problems of time are resolved in these models is discussed.

UR - http://www.scopus.com/inward/record.url?scp=0001154961&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.53.5634

DO - 10.1103/PhysRevD.53.5634

M3 - Article

AN - SCOPUS:0001154961

SN - 0556-2821

VL - 53

SP - 5634

EP - 5650

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

IS - 10

ER -