A Precision Test for an Extra Spatial Dimension Using Black Hole--Pulsar Binaries

We discuss the observable effects of enhanced black-hole mass loss in a black hole–neutron star (BH–NS) binary, due to the presence of a warped extra spatial dimension of curvature radius $L$ in the braneworld scenario. For some masses and orbital parameters in the expected ranges the binary components would outspiral, the opposite of the behavior due to energy loss from gravitational radiation alone. If the NS is a pulsar, observations of the rate of change of the orbital period with a precision obtained for the Binary Pulsar B1913+16 could easily detect the effect of mass loss. For $M_{BH}=7M_\odot$, $M_{NS}=1.4M_\odot$, eccentricity $e=0.1$, and $L=10\mu$m, the critical orbital period dividing systems which inspiral from systems which outspiral is P$\approx$6.5 hours, which is within the range of expected orbital periods; this value drops to P$\approx$4.2 hours for $M_{BH}=5M_\odot$. Observations of a BH–pulsar system could set considerably better limits on $L$ in these braneworld models than could be determined by torsion-balance gravity experiments in the foreseeable future.

💡 Research Summary

The paper investigates how a warped extra spatial dimension, characterized by a curvature radius L in the braneworld scenario, modifies the orbital evolution of a black‑hole–neutron‑star (BH‑NS) binary when the neutron star is a radio pulsar. In the standard general‑relativistic picture, the binary loses orbital energy through gravitational‑wave (GW) emission, causing the orbital separation a and the period P to shrink (inspiral). In the Randall‑Sundrum‑type braneworld, however, a black hole can lose mass by leaking gravitons into the fifth dimension. The mass‑loss rate scales as (\dot M_{\rm BH}\propto L^{2}M_{\rm BH}^{-1}), so for a curvature radius of order ten microns the effect can be comparable to GW radiation for astrophysical black‑hole masses.

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