Rotating black holes at future colliders. III. Determination of black hole evolution

TeV scale gravity scenario predicts that the black hole production dominates over all other interactions above the scale and that the Large Hadron Collider will be a black hole factory. Such higher-dimensional black holes mainly decay into the standard model fields via the Hawking radiation whose spectrum can be computed from the greybody factor. Here we complete the series of our work by showing the greybody factors and the resultant spectra for the brane-localized spinor and vector field emissions for arbitrary frequencies. Combining these results with the previous works, we determine the complete radiation spectra and the subsequent time evolution of the black hole. We find that, for a typical event, well more than half a black hole mass is emitted when the hole is still highly rotating, confirming our previous claim that it is important to take into account the angular momentum of black holes.

Figure 1

Greybody factors for spinor field ($s=1/2$) with fixed $a_{*}=0$ (left) and 1.5 (right). Each plot is for $l=m=1/2$, $3/2$, $5/2$ modes (and $7/2$ for right plot) from left to right bunches, respectively, and each bunch contains $D=5$, 7, 9, and 11 cases where the steeper curve corresponds to lower dimensions.

Figure 2

Greybody factors for vector field ($s=1$) with fixed $a_{*}=0$ (left) and 1.5 (right). Each plot is for $l=m=1$, 2, 3 modes (and 4 for right plot) from left to right bunches, respectively, and each bunch contains $D=5$, 7, 9, and 11 cases where the steeper curve corresponds to lower dimensions.

Figure 3

Superradiant amplification of brane-localized vector field amplitude scattered by a highly rotating ($a_{*}=1.5$) black hole in $D=5$ (left) and 10 (right).

Figure 4

Spinor power (upper) and angular (lower) spectra for fixed $D=5$ (left) and $D=11$ (right). In each figure, $a_{*}=0$, 0.3, …, 1.5 from lower left to upper right.

Figure 5

Vector power (upper) and angular (lower) spectra for fixed $D=5$ (left) and $D=11$ (right). In each figure, $a_{*}=0$, 0.3, …, 1.5 from lower left to upper right.

Figure 6

Spinor power (upper) and angular (lower) spectra for fixed $a_{*}=0$ (left) and 1.5 (right). In each figure, $D=5$, 7, 9, and 11 from below to above.

Figure 7

Vector power (upper) and angular (lower) spectra for fixed $a_{*}=0$ (left) and 1.5 (right). In each figure, $D=5$, 7, 9, and 11 from below to above.

Figure 8

Spinor greybody factor for $(D,a_{*})=(5,0)$, (5, 1.5), (11, 0) and (11, 1.5). The contributions from the angular modes with the same $l$ mod 10 are drawn with the same color/gray level.

Figure 9

Spinor power spectra for $(D,a_{*})=(5,0)$, (5, 1.5), (11, 0) and (11, 1.5). The contributions from the angular modes with the same $l$ mod 10 are drawn with the same color/gray level. In each figure, the uppermost enveloping black curve is the total spectrum.

Figure 10

Spinor angular spectra for $(D,a_{*})=(5,0)$, (5, 1.5), (11, 0) and (11, 1.5). The contributions from the angular modes with the same $l$ mod 10 are drawn with the same color/gray level. In each figure with $a_{*}=1.5$, the uppermost enveloping black curve is the total spectrum.

Figure 11

Vector greybody factor for $(D,a_{*})=(5,0)$, (5, 1.5), (11, 0) and (11, 1.5). The contributions from the angular modes with the same $l$ mod 10 are drawn with the same color/gray level.

Figure 12

Vector power spectra for $(D,a_{*})=(5,0)$, (5, 1.5), (11, 0) and (11, 1.5). The contributions from the angular modes with the same $l$ mod 10 are drawn with the same color/gray level. In each figure, the uppermost enveloping black curve is the total spectrum.

Figure 13

Vector angular spectra for $(D,a_{*})=(5,0)$, (5, 1.5), (11, 0) and (11, 1.5). The contributions from the angular modes with the same $l$ mod 10 are drawn with the same color/gray level. In each figure with $a_{*}=1.5$, the uppermost enveloping black curve is the total spectrum.

Figure 14

Power spectrum from a $D=10$-dimensional black hole for spinor (left) and vector (right). Left: similarly plotted as in Figs. 8, 9, 10. Right: contributions of $l=m$ modes are shown.

Figure 15

Schematic pictures for black hole life. From above to below, the production phase, the balding phase, spin-down phase, Schwarzschild phase, and Planck phase are shown.

Figure 16

Total mass loss rate $\alpha$ (left) and angular momentum loss rate $\beta$ (right) for scalar ($s$), fermion ($f$), vector ($v$), and for sum of all the standard model particles (SM) in $D=5$ (above) and 10 (below).

Figure 17

Black hole mass evolution in units of the initial mass as a function of rotation parameter $a_s$ for scalar ($s$), fermion ($f$), vector ($v$), and sum of all the standard model particles (SM) in $D=5$ (left) and $D=10$ (right).

Figure 18

Time evolution of mass and time versus rotation parameter in $D=5$.

Figure 19

Time evolution of mass and time versus rotation parameter in $D=10$.