Takahisa Igata

We consider the periapsis shifts of bound orbits of stars on static clouds around a black hole. The background spacetime is constructed from a Schwarzschild black hole surrounded by a static and spherically symmetric self-gravitating system of massive particles, which satisfies all the standard energy conditions and physically models the gravitational effect of dark matter distribution around a nonrotating black hole. Using nearly circular bound orbits of stars, we obtain a simple formula for the precession rate. This formula explicitly shows that the precession rate is determined by a positive contribution (i.e. a prograde shift) from the conventional general-relativistic effect and a negative contribution (i.e. a retrograde shift) from the local matter density. The four quantities for such an orbit (i.e. the orbital shift angle, the radial oscillation period, the redshift and the star position mapped onto the celestial sphere) determine the local values of the background model functions. Furthermore, we not only evaluate the precession rate of nearly circular bound orbits in several specific models but also simulate several bound orbits with large eccentricity and their periapsis shifts. The present exact model demonstrates that the retrograde precession does not mean any exotic central objects such as naked singularities or wormholes but simply the existence of significant energy density of matters on the star orbit around the black hole.

We completely classify the Friedmann–Lemaître–Robertson–Walker solutions with spatial curvature K = 0, ±1 for perfect fluids with linear equation of state p = wρ, where ρ and p are the energy density and pressure, without assuming any energy conditions. We extend our previous work to include all geodesics and parallelly propagated (p.p.) curvature singularities, showing that no non-null geodesic emanates from or terminates at the null portion of conformal infinity and that the initial singularity for K = 0, −1 and −5/3 < w < −1 is a null non-scalar polynomial curvature singularity. We thus obtain the Penrose diagrams for all possible cases and identify w = −5/3 as a critical value for both the future big-rip singularity and the past null conformal boundary.

We consider necessary and sufficient conditions for photons emitted from an arbitrary spacetime position of the extremal Kerr black hole to escape to infinity. The radial equation of motion determines necessary conditions for photons emitted from r=r∗ to escape to infinity, and the polar angle equation of motion further restricts the allowed region of photon motion. From these two conditions, we provide a method to visualize a two-dimensional photon impact parameter space that allows photons to escape to infinity, i.e., the escapable region. Finally, we completely identify the escapable region for the extremal Kerr black hole spacetime. This study has generalized our previous result [K.~Ogasawara and T.~Igata, Phys. Rev. D \textbf{103}, 044029 (2021)], which focused only on light sources near the horizon, to the classification covering light sources in the entire region.