Malec Edward, Mars Marc, Simon Walter
Instytut Fizyki, Uniwersytet Jagielloński, Reymonta 4, P-30-059 Kraków, Poland.
Phys Rev Lett. 2002 Mar 25;88(12):121102. doi: 10.1103/PhysRevLett.88.121102. Epub 2002 Mar 6.
For asymptotically flat initial data of Einstein's equations satisfying an energy condition, we show that the Penrose inequality holds between the Arnowitt-Deser-Misner mass and the area of an outermost apparent horizon, if the data are suitably restricted. We prove this by generalizing Geroch's proof of monotonicity of the Hawking mass under a smooth inverse mean curvature flow, for data with non-negative Ricci scalar. Unlike Geroch we need not confine ourselves to minimal surfaces as horizons. Leaving smoothness issues aside, we also show that our restrictions on the data can be locally fulfilled by a suitable choice of the initial surface in a given spacetime.
对于满足能量条件的爱因斯坦方程的渐近平坦初始数据，我们证明，如果对数据进行适当限制，彭罗斯不等式在阿诺维特 - 德泽尔 - 米斯纳质量与最外层表观视界面积之间成立。我们通过推广格罗赫关于在具有非负里奇标量的数据的光滑逆平均曲率流下霍金质量单调性的证明来证明这一点。与格罗赫不同，我们不必将自己局限于作为视界的极小曲面。暂且不考虑光滑性问题，我们还表明，通过在给定时空里对初始曲面进行适当选择，我们对数据的限制可以在局部得到满足。
