J Jezierski 1989 Class. Quantum Grav. 6 1535 doi:10.1088/0264-9381/6/11/008
J Jezierski
Show affiliationsAssuming the existence of a solution of the 3-harmonic equation Del i( mod Del rho mod 3 Del i rho )=0 on a spacelike 3-manifold Sigma with boundary K(assume that the solution has no critical points and fulfils certain asymptotic conditions), the author constructs an integral identity. The boundary term (at infinity) of this integrand is ADM mass at infinity. The global integrand, in the case when Sigma is a maximal surface with spacetime curvature satisfying the weak energy condition, is manifestly positive. The boundary term on K gives some number (when integrated over K) related to the area of the horizon but in general differs from it. This gives a proof of a following theorem (which is similar to the Penrose inequality for a time symmetric surface Sigma ).
04.20.Ex Initial value problem, existence and uniqueness of solutions
04.20.Gz Spacetime topology, causal structure, spinor structure
14J80 Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants)
83C30 Asymptotic procedures (radiation, news functions, H-spaces, etc.)
Issue 11 (November 1989)
J Jezierski 1989 Class. Quantum Grav. 6 1535
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