Exact results for evaporating black holes in curvature-squared Lovelock gravity: Gauss-Bonnet greybody factors

Lovelock gravity is an important extension of general relativity that provides a promising framework to study curvature corrections to the Einstein action, while avoiding ghosts and keeping second order field equations. This paper derives the greybody factors for $D$-dimensional black holes arising in a theory with a Gauss-Bonnet curvature-squared term. These factors describe the nontrivial coupling between black holes and quantum fields during the evaporation process: they can be used both from a theoretical viewpoint to investigate the intricate space-time structure around such a black hole, and for phenomenological purposes in the framework of braneworld models with a low Planck scale. We derive exact spectra for the emission of scalar, fermion and gauge fields emitted on the brane, and for scalar fields emitted in the bulk, and demonstrate how the Gauss-Bonnet term can change the bulk-to-brane emission rates ratio in favor of the bulk channel in particular frequency regimes.

Figure 1

Gravitational potential seen by scalar particles propagating in the background of an induced Schwarzschild-Gauss-Bonnet black hole. Upper panels: The number of dimensions is fixed at 5 and the Gauss-bonnet coupling constant at $0.1M_{*}^{-2}$ on the left and at $10M_{*}^{-2}$ on the right. Lower panels: The number of dimensions is fixed at 10 and the Gauss-bonnet coupling constant at $0.1M_{*}^{-2}$ on the left and at $10M_{*}^{-2}$ on the right.

Figure 2

Absorption cross section for scalar fields on the brane for Schwarzschild-Gauss-Bonnet black holes as a function of the energy of the particle $\omega r_H$. Left panel: The Gauss-Bonnet coupling constant $\alpha$ is fixed at $0.1M_{*}^{-2}$ and the number of dimensions $D$ at $\{5,6,10\}$. Right panel: The Gauss-Bonnet coupling constant takes the values $\{0,0.1,1,10\}{M}_{*}^{-2}$ and the number of dimensions is fixed at $6$.

Figure 3

Absorption cross section for fermion fields on the brane for Schwarzschild-Gauss-Bonnet black holes as a function of the energy of the particle $\omega r_H$. Left panel: The Gauss-Bonnet coupling constant $\alpha$ is fixed at $0.1M_{*}^{-2}$ and the number of dimensions $D$ at $\{5,6,10\}$. Right panel: The Gauss-Bonnet coupling constant takes the values $\{0,0.1,1,10\}{M}_{*}^{-2}$ and $D$ is fixed at $6$.

Figure 4

Absorption cross section for gauge bosons on the brane for Schwarzschild-Gauss-Bonnet black holes as a function of the energy of the particle $\omega r_H$. Left panel: The Gauss-Bonnet coupling constant $\alpha$ is fixed at $0.1M_{*}^{-2}$ and the number of dimensions $D$ at $\{5,6,10\}$. Right panel: The Gauss-Bonnet coupling constant takes the values $\{0,0.1,1,10\}{M}_{*}^{-2}$ and $D$ is fixed at $6$.

Figure 5

Absorption cross section for scalar fields in the bulk for Schwarzschild-Gauss-Bonnet black holes as a function of the energy of the particle $\omega r_H$. Left panel: the Gauss-Bonnet coupling constant $\alpha$ is fixed at $0.1M_{*}^{-2}$ and the number of dimensions $D$ at $\{5,6,10\}$. Right panel: the Gauss-Bonnet coupling constant takes the values $\{0,0.1,1,10\}{M}_{*}^{-2}$ and the number of dimensions is fixed at $6$.

Figure 6

Flux spectrum for scalar fields emitted on the brane by a Schwarzschild-Gauss-Bonnet black hole as a function of the energy $\omega$. The Gauss-Bonnet coupling constant takes the values $\{0,0.1,1,10\}{M}_{*}^{-2}$ and the number of dimensions is fixed at $6$. The mass of the black hole is taken equal to $M_{BH}=10M_{*}$ (upper left), $M_{BH}=100M_{*}$ (upper right), $M_{BH}=1000M_{*}$ (lower left) and $M_{BH}=10000M_{*}$ (lower right).

Figure 7

Flux spectrum for fermion fields emitted on the brane by a Schwarzschild-Gauss-Bonnet black hole as a function of the energy $\omega$. The Gauss-Bonnet coupling constant takes the values $\{0,0.1,1,10\}{M}_{*}^{-2}$ and the number of dimensions is fixed at $6$. The mass of the black hole is $M_{BH}=10M_{*}$ on the left panel, and $M_{BH}=10000M_{*}$ on the right panel.

Figure 8

Flux spectrum of gauge bosons emitted on the brane by a Schwarzschild-Gauss-Bonnet black hole as a function of the energy $\omega$. The Gauss-Bonnet coupling constant takes the values $\{0,0.1,1,10\}{M}_{*}^{-2}$ and the number of dimensions is fixed at $6$. The mass of the black hole is $M_{BH}=10M_{*}$ on the left panel, and $M_{BH}=10000M_{*}$ on the right panel.

Figure 9

Flux spectrum for scalar fields emitted in the bulk by a Schwarzschild-Gauss-Bonnet black hole as a function of the energy $\omega$. The Gauss-Bonnet coupling constant takes the values $\{0,0.1,1,10\}{M}_{*}^{-2}$ and the number of dimensions is fixed at $6$. The mass of the black hole is $M_{BH}=10M_{*}$ on the left panel, and $M_{BH}=10000M_{*}$ on the right panel.

Figure 10

Bulk-to-brane relative emission rate as a function of the energy $\omega$. The Gauss-Bonnet coupling constant takes the values $\{0,0.1,1,10\}{M}_{*}^{-2}$ and the number of dimensions is fixed at $6$. The mass of the black hole is taken to be $M_{BH}=10M_{*}$ (upper left), $M_{BH}=100M_{*}$ (upper right), $M_{BH}=1000M_{*}$ (lower left) and $M_{BH}=10000M_{*}$ (lower right).

Figure 11

Bulk-to-brane relative emission rate as a function of the unidimensional parameter $\omega r_H$ for 6-dimensional black holes with a given size. Left panel: the Gauss-Bonnet coupling constant is taken at $\{0,0.1,1,10\}{M}_{*}^{-2}$ and the number of dimensions is fixed at $D=6$. Right panel: the Gauss-Bonnet coupling constant is fixed at $0.1M_{*}^{-2}$ and the number of dimensions is taken at $\{5,6,10\}$.