Constraining the Rate of Primordial Black-Hole Explosions and Extra Dimension Scale using a Low-Frequency Radio Antenna Array

An exploding primordial black-hole (PBH) may produce a single pulse of electromagnetic radiation detectable at the low-frequency end of the radio spectrum. Furthermore, a radio transient from an exploding PBH could be a signature of an extra spatial dimension. We describe here an approach for searching for PBH explosions using a low-frequency radio antenna array, and as a practical example, the results of a such a search using the Eight-meter-wavelength Transient Array (ETA). No compelling astrophysical signal was detected in $\approx 4$ hours of data implying an observational upper limit on the rate of exploding PBHs is $4.2 \times 10^{-7} \,\rm{pc}^{-3}\,\rm{yr}^{-1}$ for an exploding PBH with a fireball Lorentz factor of $10^{4.5}$ for the standard scenario of Page and Hawking. This rate limit is the strongest constraint yet set for PBH explosions with this fireball Lorentz factor. Observations ($\sim300$ hours) using the Arecibo Observatory were used to set a stronger constraint on the rate of PBH explosions for a fireball Lorentz factor of $10^{4.6}$ but the limit set by those observations for the fireball Lorentz factor considered here are less stringent by more than an order of magnitude. The limits considered here are applicable to exploding PBHs in the halo of the Galaxy. These observations also imply an upper limit of $2.0 \times 10^{-4} \,\rm{pc}^{-3}\,\rm{yr}^{-1}$ on the rate of PBH explosions in the context of certain extra dimension models as described by Kavic et al. This rate limit is for a fireball Lorentz factor of $10^{4.3}$ which corresponds to an extra dimension compactification scale of $3.0 \times 10^{-18}$m.