Abstract
In this work, we have considered a n-dimensional Schwarzschild–Tangherlini black hole spacetime with massless minimally coupled free scalar fields in its bulk and 3-brane. The bulk scalar field equation is separable using the higher dimensional spherical harmonics on (n-2)-sphere. First, using the Hamiltonian formulation with the help of the recently introduced near-null coordinates we have obtained the expected temperature of the Hawking effect, identical for both bulk and brane localized scalar fields. Second, it is known that the spectrum of the Hawking effect as seen at asymptotic future does not correspond to a perfect black body and it is properly represented by a greybody distribution. We have calculated the bounds on this greybody factor for the scalar field in both bulk and 3-brane. Furthermore, we have reaffirmed that these bounds predict a decrease in the greybody factor as the spacetime dimensionality n increases and also reaffirmed that for a large number of extra dimensions the Hawking quanta is mostly emitted in the brane.
Highlights
It is believed that inclusion of extra spatial dimensions in a spacetime have the potential of solving the hierarchy problem [6,7,8,9,10,11], which is related to the issue concerning the huge difference between the gravitational scale and ElectroWeak scale
In this work we have considered a n-dimensional Schwarzschild–Tangherlini black hole spacetime and shown that the action corresponding to massless minimally coupled free scalar fields both in the bulk and in 3-brane can be simplified to express a (1+1) dimensional flat spacetime in the near horizon and asymptotic regions
We observed that the temperature corresponding to the Hawking effect is dependent on the spacetime dimensionality and same for both the bulk and brane-localized scalar field
Summary
It is believed that inclusion of extra spatial dimensions in a spacetime have the potential of solving the hierarchy problem [6,7,8,9,10,11], which is related to the issue concerning the huge difference between the gravitational scale and ElectroWeak scale. The greybody factor is obtained from the transmission amplitude as the field modes pass from near horizon region to an asymptotic observer through the effective potential, created due to the spacetime geometry. Estimation of this greybody factor is a very difficult job and often utilises various approximations like evaluating the greybody factors in asymptotically low or high frequency regimes [15,16,17,18,19,20,21,22,23].
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