Radiation from particles with arbitrary energy falling into higher-dimensional black holes

Abstract

We consider point particles with arbitrary energy per unit mass E that fall radially into a higherdimensional, 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.

NR/HEP: roadmap for the future

“…• That the amount of energy radiated in D = 5 head-on black hole collisions agrees well with the value obtained from (extrapolations of) linearized, point-particle calculations [63,100].…”

Gravity-dominated unequal-mass black hole collisions

“…This is the point-particle limit [8,[27][28][29][30]. Nonlinear head-on collision results agree extremely well with point-particle predictions even when the mass ratios in the simulations approach unity, at least for lowenergy encounters [13].…”

“…A new formulation of the higher-dimensional Einstein equations now allows our Lean code to compute the radiation from head-on collisions up to D = 10, so that the number of extra dimensions considered possible in higherdimensional gravity scenarios [33] falls within the range achievable by the code. The study of unequal-mass UR collisions in higher dimensions is of particular interest because perturbative calculations suggest that the percentage of kinetic energy radiated in GWs may reach a minimum as a function of D, and then increase again [30]. The perturbative calculations do not hold for D ≥ 13, since they predict a total radiation output which breaks the assumptions behind the formalism [30], and therefore our understanding of radiation in large-D spacetimes is still lacking.…”

“…The study of unequal-mass UR collisions in higher dimensions is of particular interest because perturbative calculations suggest that the percentage of kinetic energy radiated in GWs may reach a minimum as a function of D, and then increase again [30]. The perturbative calculations do not hold for D ≥ 13, since they predict a total radiation output which breaks the assumptions behind the formalism [30], and therefore our understanding of radiation in large-D spacetimes is still lacking. We plan to investigate this problem in the near future.…”

Scalar radiation from a radially infalling source into a Schwarzschild black hole in the framework of quantum field theory

“…The scientific literature about the dynamics of a test particle falling into BHs has developed significantly in the early 1970s. The existing results for the problem of radiation emission from a particle falling radially into BHs were obtained using the formalism of the Classical Field Theory (CFT) [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. The investigation of this kind of problems from the viewpoint of the Quantum Field Theory (QFT) has not been carried out.…”