Shadow of a naked singularity without photon sphere

Precession of timelike bound orbits in Kerr spacetime

“…: V,-vol the Schwarzschild mass M of the black hole. In [47,48], we show that the bound orbits of a freely falling particle in Schwarzschild spacetime always precess in the positive direction. In positive precession, the angular distance travelled by a particle between two successive perihelion points is greater than 2π .…”

“…From the expression of m in Eq. (27), one can verify that in Schwarzschild spacetime, m is always less than one which implies positive precession of timelike bound orbits [47,48]. If we consider L >> M, we can write down an approximate expression of m for the Schwarzschild spacetime,…”

“…From the above expression of m, we can get the following positive perihelion shift of timelike bound orbits in Schwarzschild spacetime [47,48],…”

“…are studied [3][4][5][6][7][8]. It has been shown that compact objects, like naked singularities can cast similar type of shadow which is expected to be cast by a black hole [3,7,8]. Recently, GRAVITY collaboration has shown the possibility of the existence of general relativistic precession of the orbit of S2 star, where they consider Schwarzschild black hole at the center [9].…”

“…can cause or allow for a negative precession of the stars. In [47,48], we study the bound orbits of a test particle in Schwarzschild, Joshi-Malafarina-Narayan (JMN), and Janis-Newman-Winicour (JNW) spacetimes. Both the JMN and JNW spacetimes are naked singularity spacetimes which have spherically symmetric matter distributions [49][50][51][52].…”