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arXiv 1010.3874gr-qchep-phhep-th
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高达11个:来自落入高维黑洞的任意能量粒子的辐射

Up to eleven: radiation from particles with arbitrary energy falling into higher-dimensional black holes

Emanuele Berti, Vitor Cardoso, Barnabas Kipapa

摘要:

我们考虑单位质量E具有任意能量的点粒子径向落入一个高维、非旋转、渐近平坦的黑洞。我们计算在这个过程中辐射的能量和线性动量,作为E和时空维数D=n+2(n=2,.)的函数,9(在某些情况下,我们会上升到11)。我们发现,辐射的总能量增加n从静止(E=1)下降的粒子。对于固定的粒子能量1<E<=2,我们明确地证明了辐射在n的某个临界值处有一个局部极小值,然后它随n而增加。我们推测,这样的最低也存在较高的粒子能量。当n=11时,目前的点粒子计算就失败了,因为那时辐射能量变得大于粒子质量。非常有趣的是,当n=11时,我们的计算所预测的辐射能量也违反了霍金的面积限制。这暗示了n>11时引力辐射发射的质的变化。我们的结果是在非常好的协议与低能量,不等质量黑洞碰撞D=5的数值模拟(将在其他地方报道),他们是一个有用的基准未来的非线性演化的高维爱因斯坦方程。

英文摘要:

We consider point particles with arbitrary energy per unit mass E that fall radially into a higher-dimensional, nonrotating, asymptotically flat black hole. We compute the energy and linear momentum radiated in this process as functions of E and of the spacetime dimensionality D=n+2 for n=2,...,9 (in some cases we go up to 11). We find that the total energy radiated increases with n for particles falling from rest (E=1). For fixed particle energies 1<E<=2 we show explicitly that the radiation has a local minimum at some critical value of n, and then it increases with n. We conjecture that such a minimum exists also for higher particle energies. The present point-particle calculation breaks down when n=11, because then the radiated energy becomes larger than the particle mass. Quite interestingly, for n=11 the radiated energy predicted by our calculation would also violate Hawking's area bound. This hints at a qualitative change in gravitational radiation emission for n>11. Our results are in very good agreement with numerical simulations of low-energy, unequal-mass black hole collisions in D=5 (that will be reported elsewhere) and they are a useful benchmark for future nonlinear evolutions of the higher-dimensional Einstein equations.

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