Thermodynamics and weak cosmic censorship conjecture of the torus-like black hole

Abstract

After studying the energy-momentum relation of charged particles' Hamilton-Jacobi equations, we discuss the laws of thermodynamics and the weak cosmic censorship conjecture in torus-like black holes. We find that both the first law of thermodynamic as well as the weak cosmic censorship conjecture are valid in both the normal phase space and extended phase space. However, the second law of thermodynamics is only valid in the normal phase space. Our results show that the first law and weak cosmic censorship conjecture do not depend on the phase spaces while the second law depends. What's more, we find that the shift of the metric function that determines the event horizon take the same form in different phase spaces, indicating that the weak cosmic censorship conjecture is independent of the phase space.

No evidence for violation of the second law in extended black hole thermodynamics

“…It then follows that the second law could be violated. This is the argument in [10], which was then repeated in many subsequent follow-up works [11][12][13][14][15][16][17][18][19][20]. Our point of view is that this violation of the second law is not physical, and should be taken as a reductio ad absurdum of the assumption that the infalling particle changes the internal energy by E = dU .…”

“…Since the horizon area is interpreted as the entropy in black hole thermodynamics, this would mean that the second law has been violated. This result has received much attention lately and has been calculated to occur in a wide variety of black holes, going beyond general relativity and/or with various matter sources [11][12][13][14][15][16][17][18][19][20]. Notably, the case without electrical charge but with rotation, i.e.…”

Joule–Thomson expansion of the torus-like black hole

“…[82], the concept of the torus-like black hole was first introduced. This work has inspired many studies of the torus-like black hole, including the statistical entropy [83], the weak cosmic censorship conjecture [84,85], the tunneling radiation [86], heat engine [87], the dBB quantization [88], and other aspects [89][90][91]. Unlike previous studies, the topology of this space-time is S × S × M 2 .…”

Coalescence of Kerr Black Holes—Binary Systems from GW150914 to GW170814

“…The conjecture for a Reissner–Nordström (RN) black hole is valid when considering the back-reaction effect [ 21 , 22 ]. There are also various tests of the conjecture for anti-de Sitter (AdS) black holes [ 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 ]. In particular, from a thermodynamic point of view, since the second law of thermodynamics ensures an increase in the area of the black hole’s horizon, it can be a sufficient condition for the validity of the conjecture.…”