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## Prog. Theor. Phys. Vol. 78 No. 5 (1987) pp. 1186-1201

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# Kerr Metric, de Donder Condition and Gravitational Energy Density

Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606

### Abstract:

The Kerr solution to the Einstein equation is explicitly rewritten into the one satisfying the de Donder condition. By using this result, the gravitational energy density, ht00, in Einstein's definition is calculated completely. It is positive definite if a/m \lesssim0.6, where a and m denote the angular-momentum parameter and the mass one, respectively. The validity of the conjecture proposed previously, which states that ht00 ≥0 outside black holes if calculated under the de Donder condition, is discussed by means of the gravitational-wave solution, the Reissner-Nordström solution and the Kerr solution.

DOI : 10.1143/PTP.78.1186

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### Citing Article(s) :

1. Progress of Theoretical Physics Vol. 96 No. 2 (1996) pp. 347-375 :
A New Gravitational Energy-Momentum Pseudotensor in Tetrad Form
Hideharu Hirashima