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INTERPLAY BETWEEN LINEARITY AND NONLINEARITY IN GENERAL RELATIVITY: SCALAR FIELDS, PERFECT FLUIDS AND EINSTEIN SPACES

1989
14 pages
Published in:
  • Class.Quant.Grav. 6 (1989) 1613-1626
DOI:
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Abstract: (IOP)
The authors investigate when the linearised equations and the fully non-linear Einstein equations with sources are equivalent in the cases where gravity is coupled to (i) a massless scalar field, and (ii) a perfect fluid. The metrics are subject to generalised Kerr-Schild-type transformations. Simple algebraic conditions are determined on the matter fields such that the linear superposition of the (exact) background solution and the (approximate) linearised solution is, surprisingly, a new solution. For the case of a massless scalar field two subcases are obtained, for which the superposition holds. For the perfect fluids the conditions required are quite restrictive, leading to a superposition theorem for Einstein spaces.
  • general relativity
  • Einstein equation
  • FIELD EQUATIONS: SOLUTION
  • Einstein-Maxwell equation
  • FIELD EQUATIONS: LINEAR
  • TENSOR: ENERGY-MOMENTUM
  • FIELD THEORY: SCALAR
  • FIELD THEORY: MASSLESS
  • MASSLESS: FIELD THEORY
  • MODEL: FLUID
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