10 problems

Consider a system of energy $E$ and size $R$ falling into a black hole, and let $\Delta S_{BH}$ be the resulting change in black-hole entropy. Bekenstein bound conjecture. The seco…

A subextremal black hole is a black hole that is not extremal, and a continuous process is one in which the spacetime and matter fields remain regular and obey the weak energy cond…

The Bekenstein–Hawking entropy is the entropy associated with black holes in the quantum-gravity setting discussed here. Universality conjecture. The Bekenstein–Hawking entropy sho…

At fixed thermodynamic volume, consider Schwarzschild--AdS black holes and their entropy. Reverse isoperimetric conjecture. Schwarzschild--AdS black holes maximize entropy at fixed…

Let $S=A/(4G\hbar)$ be the Bekenstein–Hawking entropy of a black hole with mass $M$ and horizon area $A$. Entropy–mass bound conjecture. The entropy should satisfy … with equality…

Let $M$ be a spacetime, let $g \in [\mathrm{Lor}(M)/\mathrm{Diff}^{+}(M)]$ be an asymptotically flat and stationary black-hole solution, and let $\mathscr{E}_g$ be the differential…

Generalized entropy conjecture. The generalized entropy $\mathcal{S}_\text{gen}$ can only decrease when any type of matter is added. This conjecture proposes a generalized second l…

Let $A$ be a $(d-2)$-dimensional surface enclosing a $(d-1)$-dimensional volume in a $d$-dimensional spacetime, and let $S_A$ denote the entropy in the enclosed region. Higher-dime…

Sudarsky–Wald conjecture. A similar result to the converse statement relating the first law to stationarity should hold when an interior boundary is present; however, the precise f…

Ruppeiner's conjecture. The global correlations are expressed as follows: (a) zero state-space scalar curvature indicates bits of information on the event horizon fluctuating indep…