Decay of solutions to the Maxwell equation on the Schwarzschild background

• A new Morawetz or integrated local energy decay estimate for Maxwell test fields on the exterior of a Schwarzschild black hole spacetime is proved. The proof makes use of a new superenergy tensor H-ab defined in terms of the Maxwell field and its first derivatives. The superenergy tensor, although not conserved, yields a conserved higher order energy current H-ab (partial derivative(t))(b). The tensor Hab vanishes for the static Coulomb field, and the Morawetz estimate proved here therefore yields integrated decay for the Maxwell field to the Coulomb solution on the Schwarzschild exterior.

Ämnesord

NATURVETENSKAP  -- Fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences (hsv//eng)

Nyckelord

Maxwell equation

Schwarzschild

energy estimate

Morawetz estimate

rotating black hole

kerr spacetime

wave-equation

energy

field

spin

perturbations

manifolds

geometry

tensors

spin

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ref (ämneskategori)

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