The quantum emission spectra of rapidly-rotating Kerr black holes: discrete or continuous?. (arXiv:1909.04057v1 [gr-qc])

<a href="http://arxiv.org/find/gr-qc/1/au:+Hod_S/0/1/0/all/0/1">Shahar Hod</a>

Bekenstein and Mukhanov (BM) have suggested that, in a quantum theory of

gravity, black holes may have discrete emission spectra. Using the time-energy

uncertainty principle they have also shown that, for a (non-rotating)

Schwarzschild black hole, the natural broadening $deltaomega$ of the

black-hole emission lines is expected to be small on the scale set by the

characteristic frequency spacing $Deltaomega$ of the spectral lines:

$zeta^{text{Sch}}equivdeltaomega/Deltaomegall1$. BM have therefore

concluded that the expected discrete emission lines of the quantized

Schwarzschild black hole are unlikely to overlap. In this paper we calculate

the characteristic dimensionless ratio $zeta(bar

a)equivdeltaomega/Deltaomega$ for the predicted BM emission spectra of

rapidly-rotating Kerr black holes (here $bar aequiv J/M^2$ is the

dimensionless angular momentum of the black hole). It is shown that $zeta(bar

a)$ is an increasing function of the black-hole angular momentum. In

particular, we find that the quantum emission lines of Kerr black holes in the

regime $bar agtrsim 0.9$ are characterized by the dimensionless ratio

$zeta(bar a)gtrsim1$ and are therefore effectively blended together. Our

results thus suggest that, even if the underlying mass (energy) spectrum of

these rapidly-rotating Kerr black holes is fundamentally discrete as suggested

by Bekenstein and Mukhanov, the natural broadening phenomenon (associated with

the time-energy uncertainty principle) is expected to smear the black-hole

radiation spectrum into a continuum.

Bekenstein and Mukhanov (BM) have suggested that, in a quantum theory of

gravity, black holes may have discrete emission spectra. Using the time-energy

uncertainty principle they have also shown that, for a (non-rotating)

Schwarzschild black hole, the natural broadening $deltaomega$ of the

black-hole emission lines is expected to be small on the scale set by the

characteristic frequency spacing $Deltaomega$ of the spectral lines:

$zeta^{text{Sch}}equivdeltaomega/Deltaomegall1$. BM have therefore

concluded that the expected discrete emission lines of the quantized

Schwarzschild black hole are unlikely to overlap. In this paper we calculate

the characteristic dimensionless ratio $zeta(bar

a)equivdeltaomega/Deltaomega$ for the predicted BM emission spectra of

rapidly-rotating Kerr black holes (here $bar aequiv J/M^2$ is the

dimensionless angular momentum of the black hole). It is shown that $zeta(bar

a)$ is an increasing function of the black-hole angular momentum. In

particular, we find that the quantum emission lines of Kerr black holes in the

regime $bar agtrsim 0.9$ are characterized by the dimensionless ratio

$zeta(bar a)gtrsim1$ and are therefore effectively blended together. Our

results thus suggest that, even if the underlying mass (energy) spectrum of

these rapidly-rotating Kerr black holes is fundamentally discrete as suggested

by Bekenstein and Mukhanov, the natural broadening phenomenon (associated with

the time-energy uncertainty principle) is expected to smear the black-hole

radiation spectrum into a continuum.

http://arxiv.org/icons/sfx.gif