“Physical process version” of the first law and the generalized second law for charged and rotating black holes

Abstract

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.

Mass, charge, and motion in covariant gravity theories

“…In a series of papers spanning more than a decade [8][9][10][11][12][13][14][15][16][17], Wald and coauthors developed a systematic and mathematically rigorous approach to Lagrangian and Hamiltonian field theory of a general n-dimensional covariant theory, with applications to (e.g.) black hole thermodynamics, conserved quantities, and stability.…”

Perfect mirrors and the self-accelerating box paradox

“…In opposition to any such scenario, reference [14] points out that if the black hole system can be described as a standard state of thermal equilibrium then no violation of the second law can occur, regardless of the detailed behavior of any perfect mirrors. However, this begs the question of whether the posited description is appropriate and, if it is, of whether the usual expressions for black hole entropy are consistent with this description in the absence of novel entropy bounds.…”

“…A final question is whether the results of Section II above might not be germane in analyzing some of the "time machines" that people have tried to imagine. While we know of no direct application, many of the "materials science" 14 Most of these uncertainties relate to "finite size effects" in the broad sense of the term. See for example the comments in [11] about the effects of finite wavelength on the scattering of thermal radiation.…”

A Second Law for higher curvature gravity

“…5 For higher curvature gravity theories, this was shown explicitly in [20], and is implied by the Appendix of [8] or section 2 of [21].…”

“…Not yet, because the Second Law requires the entropy to be increasing at every instant of time: dS/dv ≥ 0. At intermediate times, you must fix the JKM ambiguity (up to higher order terms like K 4 which vanish at linear order).4 Some special cases are given in [11][12][13][14][15][16], while progress for actions with derivatives of Riemann is in [17][18][19].5 For higher curvature gravity theories, this was shown explicitly in [20], and is implied by the Appendix of [8] or section 2 of [21]. …”