Dragging of inertial frames in the composed black-hole-particle system and the weak cosmic censorship conjecture
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Regular Article - Theoretical Physics
Dragging of inertial frames in the composed black-hole-particle system and the weak cosmic censorship conjecture Shahar Hod1,2,a 1 2
The Ruppin Academic Center, 40250 Emeq Hefer, Israel The Hadassah Academic College, 91010 Jerusalem, Israel
Received: 10 May 2020 / Accepted: 25 July 2020 © The Author(s) 2020
Abstract We analyze a gedanken experiment in which a spinning particle that also possesses an extrinsic orbital angular momentum is captured by a spinning Kerr black hole. The gravitational spin-orbit interaction decreases the energy of the particle, thus allowing one to test the validity of the Penrose weak cosmic censorship conjecture in extreme situations that have not been analyzed thus far. It is explicitly shown that, to leading order in the black-hole-particle interactions, the linearized test particle can over-spin the black hole, thus exposing its inner spacetime singularity to external observers. However, we prove that the general relativistic effect of dragging of inertial frames by the orbiting particle contributes to the energy budget of the system a non-linear black-hole-particle interaction term that ultimately ensures the validity of the Penrose cosmic censorship conjecture in this type of gedanken experiments.
1 Introduction Singularities in curved spacetimes represent extreme physical situations in which general relativity, Einstein’s theory of gravity, loses its predictive power. In order to preserve the deterministic nature of classical general relativity in the presence of spacetime singularities, Penrose [1] has suggested that spacetime singularities that arise in gravitational collapse are always hidden inside of black holes. This intriguing idea, known as the weak cosmic censorship conjecture, has attracted the attention of physicists and mathematicians over the last five decades (see e.g., [2–14] and references therein). The elegant singularity theorems of Hawking and Penrose [15,16] have revealed the physically interesting fact that generic solutions of the Einstein field equations may contain curvature singularities which, according to the cosmic censorship conjecture [1], should be hidden inside of black
holes, invisible to distant (external) observers. Physical processes that threat to remove the shieling horizon of a black hole and to expose its inner spacetime singularity to external observers are therefore forbidden by the Penrose weak cosmic censorship conjecture [1]. For the advocates of the cosmic censorship conjecture, the mathematically challenging (and physically interesting) task is to find out how such ‘dangerous’ physical processes, which threat to violate the weak cosmic censorship conjecture, eventually fail to remove the black-hole horizon [2–14]. One may try to transform a near-extremal spinning Kerr black hole of mass M and angular momentum per unit mass a, which is characterized by the relation [17]1 M 2 − a2 ≥ 0 ,
(1)
into a naked (horizonless) singularity by sending into the black hole particles that carry large amount
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