We consider the escape probability of a photon emitted from the innermost stable circular orbit (ISCO) around a rapidly rotating black hole. As an isotropically emitting light source on a circular orbit reduces its orbital radius, the escape probability of a photon emitted from it decreases monotonically. The escape probability evaluated at the ISCO decreases monotonically as the black hole spin increases. When the dimensionless Kerr parameter a is the Thorne limit a = 0.998, the escape probability at the ISCO is 58.8%.In the extremal case a = 1, even if the orbital radius of the light source is arbitrarily close to the ISCO radius, which coincides with the horizon radius, the escape probability remains at 54.6%. We also show that such photons that have escaped from the vicinity of the horizon reach infinity with sufficient energy because Doppler blueshift due to the proper motion of a source can overcome the gravitational redshift. Our findings indicate that if the M87 galactic center is a rapidly rotating black hole, signs of the near-horizon physics will be detectable on the edge of the black hole shadow. * Electronic address: igata@rikkyo.ac.jp † Electronic address: nakashi@rikkyo.ac.jp
We investigate the positions of stable circular massive particle orbits in the Majumdar-Papapetrou dihole spacetime with equal mass. In terms of qualitative differences of their sequences, we classify the dihole separation into five ranges and find four critical values as the boundaries. When the separation is relatively large, the sequence on the symmetric plane bifurcates, and furthermore, they extend to each innermost stable circular orbit in the vicinity of each black hole. In a certain separation range, the sequence on the symmetric plane separates into two parts. On the basis of this phenomenon, we discuss the formation of double accretion disks with a common center. Finally, we clarify the dependence of the radii of marginally stable circular orbits and innermost stable circular orbits on the separation parameter. We find a discontinuous transition of the innermost stable circular orbit radius. We also find the separation range at which the radius of the innermost stable circular orbit can be smaller than that of the stable circular photon orbit. * Electronic address: nakashi@rikkyo.ac.jp † Electronic address: igata@rikkyo.ac.jp
We study the null geodesics in a static circularly symmetric (SCS) black hole spacetime which is a solution in the (2 + 1)-dimensional massive gravity proposed by Bergshoeff, Hohm and Townsend (BHT massive gravity). We obtain analytic solutions for the null geodesic equation in the SCS black hole background and find the explicit form of deflection angles. We see that for various values of the impact parameter, the deflection angle can be positive, negative or even zero in this black hole spacetime. The negative deflection angle indicates the repulsive behavior of the gravity which comes from the gravitational hair parameter that is the most characteristic quantity of the BHT massive gravity.
We investigate how stable circular orbits around a main compact object appear depending on the presence of a second one by using the Majumudar-Papapetrou dihole spacetime, which consists of the two extremal Reissner-Nordström black holes with different masses. While the parameter range of the separation of the two objects is divided due to the appearance of stable circular orbits, this division depends on its mass ratio. We show that the mass ratio range separates into four parts, and we find three critical values as the boundaries. I. INTRODUCTIONRecent progress in the observation of gravitational waves supports the existence of binary black hole systems. The LIGO Scientific and Virgo collaborations have already detected gravitational waves ten times from binary black hole mergers and once from a binary neutron star merger so far [1][2][3][4]. Furthermore, since they have started the third observation run, the number of detections will increase in the future. These results imply that binary black hole systems are a quite common phenomenon in our Universe.A pure binary black hole system is a highly idealized model, around which a third object or matter distribution usually exists in realistic situations. Therefore, one of the next issues is clarifying perturbative interactions with a third body around them. As traditional problems in Newtonian gravity, there are Poincaré's three-body problem and the Kozai mechanism. In recent years, some problems related to these topics have been considered in the framework of the relativistic three body problem [5,6], in the context of resonance in a compound extreme mass ratio inspiral/massive black hole binary [7], and in gravitational wave emission induced by a third body [8][9][10][11]. If a third body itself is the target of observation, we can view it as a test body in a fixed background. As a traditional problem in Newtonian gravity, there is Euler's three-body problem, test particle motion in two fixed centers. The corresponding relativistic system is the main topic of this paper.The study of test body motion is significant for the predictions of astrophysical phenomena around a gravitational system such as a binary. In particular, the circular orbit of a test body plays some essential roles in both theory and observations. In the black hole spacetime, for instance, the bending of light due to strong gravity makes a photon orbit circular near the horizon. If the circular photon orbit is unstable, it relates to the formation of the black hole shadow. On the other hand, the sequence of stable circular massive particle orbits is relevant to accretion disks and a binary system. The innermost stable circular orbit (ISCO) radius is a distinctive one because it is identified as the inner edge of a standard accretion disk model and a compact binary switches the stage of the evolution from the inspiraling phase to the merging phase there [12,13].Actual binary black hole systems exist as highly dynamical systems so that one needs to use the numerical method to analyze the phenomen...
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