An investigation of the Newman-Penrose constants for massless free fields of arbitrary spin

Thesis/Dissertation · Mon Jan 01 04:00:00 EST 1990

OSTI ID:6313397

Kerrick, D M

The origin and significance of the Newman-Penrose absolutely conserved quantities for a spin s massless free fields including, and in particular, the gravitational field in general relativity is investigated. It is found that the NP conservation law for these fields can be generated by suitable (asymptotic) integration of a covariant wave equation satisfied by the fields at null infinity in an asymptotically flat spacetime resulting in a set of 2s + 1 complex constants of the motion, identified as the NP constants. The key to this derivation of the Newman-Penrose constants is the reduction of the above-mentioned wave equation to an intrinsic divergence on the null hypersurface, representing infinity in Penrose's treatment of asymptotic flat spacetimes. This result is refined and elaborated by considering the NP constants at a quasi-local level. In particular, a quasi-local NP conservation law for (linear) massless fields, valid on both Minkowski and Schwarzschild spacetime, is presented, corresponding to an integral formulation of the decoupled wave equations for a type D background given by Teukolsky in 1973. For a Minkowski background one obtains an exact quasi-local conservation law formally identical to the original, asymptotic version. In a Schwarzschild background, however, an exact conservation law is not possible due to the presence of the single non-vanishing component of the Weyl curvature characteristic of type D spacetimes. Invoking a recent theorem of Carminati and McLenaghan, it is argued that the non-exact nature of the quasi-local law on a Schwarzschild background is due to the non-Huygens character of (linear) massless fields propagating on a type D background. Conversely, it is conjectured that an exact quasi-local NP conservation law is possible only in those regions of spacetime in which the field propagates free of dispersion. Implications for the gravitational field are discussed.

• Research Organization: Temple Univ., Philadelphia, PA (USA)
• OSTI ID: 6313397
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR MOMENTUM
CONSERVATION LAWS
DATA
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD THEORIES
GENERAL RELATIVITY THEORY
GRAVITATIONAL FIELDS
INFORMATION
METRICS
NUMERICAL DATA
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE PROPERTIES
RELATIVITY THEORY
SCHWARZSCHILD METRIC
SPACE-TIME
SPIN
THEORETICAL DATA
WAVE EQUATIONS