We investigate both the "physical process" version of the first law and the second law of black hole thermodynamics for charged and rotating black holes. We begin by deriving general formulas for the first order variation in ADM mass and angular momentum for linear perturbations off a stationary, electrovac background in terms of the perturbed non-electromagnetic stress-energy, δT ab , and the perturbed charge current density, δj a . Using these formulas, we prove the "physical process version" of the first law for charged, stationary black holes. We then investigate the generalized second law of thermodynamics (GSL) for charged, stationary black holes for processes in which a box containing charged matter is lowered toward the black hole and then released (at which point the box and its contents fall into the black hole and/or thermalize with the "thermal atmosphere" surrounding the black hole). Assuming that the thermal atmosphere admits a local, thermodynamic description with respect to observers following orbits of the horizon Killing field, and assuming that the combined black hole/thermal atmosphere system is in a state of maximum entropy at fixed mass, angular momentum, and charge, we show 1 that the total generalized entropy cannot decrease during the lowering process or in the "release process". Consequently, the GSL always holds in such processes. No entropy bounds on matter are assumed to hold in any of our arguments.
It has been shown that a nearly extremal black hole can be overcharged or
overspun by a test particle if radiative and self-force effects are neglected,
indicating that the cosmic censorship might fail. In contrast, the existing
evidence in literature suggests that an extremal black hole cannot be
overcharged or overspun in a similar process. In this paper, we show explicitly
that even an exactly extremal black hole can be destroyed by a test particle,
leading to a possible violation of the cosmic censorship. By considering higher
order terms, which were neglected in previous analysis, we show that the
violation is generic for any extremal Kerr-Newman black hole with nonvanishing
charge and angular momentum. We also find that the allowed parameter range for
the particle is very narrow, indicating that radiative and self-force effects
should be considered and may prevent violation of the cosmic censorship.Comment: 9 pages, 2 figur
The first law of black hole mechanics is derived from the Einstein-Maxwell Lagrangian by comparing two infinitesimally nearby stationary black holes. With similar arguments, the first law of black hole mechanics in Einstein-Yang-Mills theory is also derived.
It has been shown that ultraenergetic collisions can occur near the horizon
of an extremal Kerr black hole. Previous studies mainly focused on geodesic
motions of particles. In this paper, we consider spinning test particles whose
orbits are non-geodesic. By employing the Mathisson-Papapetrou-Dixon equation,
we find the critical angular momentum satisfies $J=2E$ for extremal Kerr black
holes. Although the conserved angular momentum $J$ and energy $E$ have been
redefined in the presence of spin, the critical condition remains the same
form. If a particle with this angular momentum collides with another particle
arbitrarily close to the horizon of the black hole, the center-of-mass energy
can be arbitrarily high. We also prove that arbitrarily high energies cannot be
obtained for spinning particles near the horizons of non-extremal Kerr black
holes.Comment: 11 pages, no figure; matches version published in PR
We show that for any perfect fluid in a static spacetime, if the Einstein constraint equation is satisfied and the temperature of the fluid obeys Tolman's law, then the other components of Einstein's equation are implied by the assumption that the total entropy of the fluid achieves an extremum for fixed total particle number and for all variations of metric with certain boundary conditions. Conversely, one can show that the extrema of the total entropy of the fluid are implied by Einstein's equation. Compared to previous works on this issue, we do not require spherical symmetry for the spacetime. Our results suggest a general and solid connection between thermodynamics and general relativity. PACS number(s): 04
The problem of a spherically symmetric charged thin shell of dust collapsing gravitationally into a charged Reissner-Nordström black hole in d spacetime dimensions is studied within the theory of general relativity. Static charged shells in such a background are also analyzed. First a derivation of the equation of motion of such a shell in a d-dimensional spacetime is given. Then a proof of the cosmic censorship conjecture in a charged collapsing framework is presented, and a useful constraint which leads to an upper bound for the rest mass of a charged shell with an empty interior is derived. It is also proved that a shell with total mass equal to charge, i.e., an extremal shell, in an empty interior, can only stay in neutral equilibrium outside its gravitational radius. This implies that it is not possible to generate a regular extremal black hole by placing an extremal dust thin shell within its own gravitational radius. Moreover, it is shown, for an empty interior, that the rest mass of the shell is limited from above. Then several types of behavior of oscillatory charged shells are studied. In the presence of a horizon, it is shown that an oscillatory shell always enters the horizon and reemerges in a new asymptotically flat region of the extended Reissner-Nordström spacetime. On the other hand, for an overcharged interior, i.e., a shell with no horizons, an example showing that the shell can achieve a stable equilibrium position is presented. The results presented have applications in brane scenarios with extra large dimensions, where the creation of tiny higher dimensional charged black holes in current particle accelerators might be a real possibility, and generalize to higher dimensions previous calculations on the dynamics of charged shells in four dimensions.
The tunneling effect near a weakly isolated horizon (WIH) has been studied. By applying the null geodesic method of Parikh and Wilczek and Hamilton-Jacibi method of Angheben et al. to a weakly isolated horizon, we recover the semiclassical emission rate in the tunneling process. We show that the tunneling effect exists in a wide class of spacetimes admitting weakly isolated horizons. The general thermodynamic nature of WIH is then confirmed.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.