Overcharging a multi-black-hole system and cosmic censorship

Abstract

We study the generalization of the gadenken experiment of overcharging an extremal black hole proposed by Wald in the context of a multi black hole solution. In particular, we attempt to overcharge a system of two extremal black holes via test particle absorption to produce a system involving a black hole and a naked singularity. If such a process is possible, then this would be a potential violation of the cosmic censorship hypothesis. However, we find that, analogous to Wald's result for a single charged black hole, such a test particle which can expose the singularity, would not be able to enter the horizon. This provides an interesting and non-trivial example that supports the validity of the cosmic censorship hypothesisin four dimensional general relativity. * akash.mishra@iitgn.ac.in † sudiptas@iitgn.ac.in

Overcharging problem and thermodynamics in extended phase spaces

“…He found that the black hole could not be overspun by throwing a particle with energy and large enough angular momentum into the hole. This result is in consistence with that gotten in the new version Gedanken experiment [45,46,47,48,49,50]. In the extremal and near-extremal cases, the entropies decreased.…”

Six-dimensional Myers-Perry rotating black hole cannot be overspun

“…Recently, CCC has also been conisdered for a rotating anti-de Sitter black hole [41,42]. Non-extremalization of black hole was also considered [43][44][45] in the context of black hole dynamics [46]. It is worth noting that the gedanken experiment [14] was also extended to an extremal magnetized black hole case [47].…”

Overcharging higher curvature black holes

“…Interestingly, the physics of general relativity prohibits such a process, the test particles with sufficient charge and angular momentum, which can overcharge the black hole get repelled and does not enter the event horizon. Similar analysis has been done on various scenarios, and it is always found that the formation of a naked singularity by overcharging is not possible [12][13][14][15][16][17][18][19][20][21]. On the other hand, Hubeny has shown that if the initial configuration is near extremal, it is possible to overcharge a Reissner-Nordstrom (RN) black hole using test particle absorption [22].…”

“…This is first attempted in the seminal work of Wald [6], and he proved that it is impossible to overcharge or overspin an extremal Kerr-Newman black hole via the process of test particle absorption. In followup works, the validity of WCC for several class of black hole spacetimes has been extensively studied [10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Also, Hubeny showed that it is possible to overcharge a near extremal black hole to create a naked singularity in the final state via charged particle absorption as long as back-reaction effects can be neglected [24].…”