Black hole pulsar

In anticipation of a LIGO detection of a black hole/neutron star merger, we expand on the intriguing possibility of an electromagnetic counterpart. Black hole/Neutron star mergers could be disappointingly dark since most black holes will be large enough to swallow a neutron star whole, without tidal disruption and without the subsequent fireworks. Encouragingly, we previously found a promising source of luminosity since the black hole and the highly magnetized neutron star establish an electronic circuit—a black hole battery. In this paper, arguing against common lore, we consider the electric charge of the black hole as an overlooked source of electromagnetic radiation. Relying on the well known Wald mechanism by which a spinning black hole immersed in an external magnetic field acquires a stable net charge, we show that a strongly magnetized neutron star in such a binary system will give rise to a large enough charge in the black hole to allow for potentially observable effects. Although the maximum charge is stable, we show there is a continuous flux of charges contributing to the luminosity. Most interestingly, the spinning charged black hole then creates its own magnetic dipole to power a black hole pulsar.

Figure 1

Shaded contours of $E·B/B_o^2$ for the specified BH charge. Yellow shading is where $E·B>0$ and blue shading represents where $E·B<0$. Magnetic field vectors, as seen by ZAMOs, are drawn as blue triangles while ZAMO electric field vectors are drawn as red triangles. Each panel, from left to right, top to bottom is drawn for an increasing value of the BH charge Q, in units of the Wald charge, $Q_W$. The black sphere sphere represents the BH horizon.

Figure 2

Examples of orbits of charged particles around the spinning BH in the Wald field, with at-rest initial conditions ($r_i=10M$, ${\theta }_i=\pi /6$). Red triangles are electric field vectors and blue lines represent the uniform immersing magnetic field, aligned with the BH spin axis. The left column is for negatively charged test charges and the right column is for positively charged test charges. The initial position of the charge is marked by a blue dot and the final position is marked by a red dot.

Figure 3

The same as Fig. 2 but for a plunging orbit.

Figure 4

The horizon charge flux (left column) and the final cylindrical radius of a test charge (right column) as a function of BH charge in units of the Wald charge, for the labeled initial theta coordinate, ${\theta }_i$, of the test charge. When a charge reaches spherical radius $250M$ we plot the final radius at this maximum value to show that it has been expelled.

Figure 5

The horizon charge flux (left column) and the final cylindrical radius of a test charge (right column) as a function of ${\theta }_i$ for a BH with the labeled charge in units of the Wald charge. When a charge reaches spherical radius $250M$ we plot the final radius at this maximum value to show that it has been expelled.

Figure 6

Electric charge $Q$ enclosed within a sphere of radius $R$, plotted as a function of $R/M$ and normalized by $C{a}^3/M^3$. The dashed horizontal line corresponds to the value $-1/128$ that the curve approaches to at infinity. The inset is a detail of the same plot showing the minimum of $Q$ at $R\simeq 10M$.