Related papers: Singularities From Entropy
The conditions for validity of the Causal Entropy Bound (CEB) are verified in the context of non-singular cosmologies with classical sources. It is shown that they are the same conditions that were previously found to guarantee validity of…
Spacetime singularity has always been of interest since the proof of the Penrose-Hawking singularity theorem. Naked singularity naturally emerges from reasonable initial conditions in the collapsing process. A recent interesting approach in…
Recently Bousso conjectured the entropy crossing a certain light-like hypersurface is bounded by the surface area. We point out a number of difficulties with this conjecture.
In a quantum gravity theory the entropy of entanglement $S$ between the fundamental degrees of freedom spatially divided by a surface is discussed. The classical gravity is considered as an emergent phenomenon and arguments are presented…
In the light of his recent (and fully deserved) Nobel Prize, this pedagogical paper draws attention to a fundamental tension that drove Penrose's work on general relativity. His 1965 singularity theorem (for which he got the prize) does not…
We present a review of the two prominent singularity theorems due to Penrose and Hawking, as well as their physical interpretation. Their usage is discussed in detail for the Schwarzschild spacetime with positive and negative mass. First,…
We establish mass lower bounds of Penrose-type in the setting of $3$-dimensional initial data sets for the Einstein equations satisfying the dominant energy condition, which are either asymptotically flat or asymptotically hyperboloidal.…
The various entropy bounds that exist in the literature suggest that spacetime is fundamentally discrete, and hint at an underlying relationship between geometry and "information". The foundation of this relationship is yet to be uncovered,…
For the power-law quantum wave packet in configuration space, the variance of the position observable may be divergent. Accordingly, the information-entropic formulation of the uncertainty principle becomes more appropriate than the…
Space-time singularities, viz. Big bang, Big crunch and black holes have been shown to follow from the singularity theorems of General relativity. Whether the entropy at such infinite proper-time objects can be other than zero has also been…
We present here an overview of our basic understanding and recent developments on spacetime singularities in the Einstein theory of gravity. Several issues related to physical significance and implications of singularities are discussed.…
Improving a singularity theorem in General Relativity by Galloway and Ling we show the following (cf.\ Theorem 1): If a globally hyperbolic spacetime $M$ satisfying the null energy condition contains a closed, spacelike Cauchy surface…
We propose new bounds on black hole entropy in terms of the specific heat at fixed charges. For special spherically-symmetric and static black holes ($g_{tt} g_{rr}=-1$), we prove the bounds with suitable sufficient energy conditions. For…
The holographic bound asserts that the entropy $S$ of a system is bounded from above by a quarter of the area ${\cal A}$ of a circumscribing surface measured in Planck areas: $S\leq {\cal A}/4{\ell^2_P}$. This bound is widely regarded a…
The original singularity theorems of Penrose and Hawking were proved for matter obeying the Null Energy Condition or Strong Energy Condition respectively. Various authors have proved versions of these results under weakened hypotheses, by…
We study the Penrose inequality and its rigidity for metrics with singular sets. Our result could be viewed as a complement of Theorem 1.1 of Lu and Miao (J. Funct. Anal. 281, 2021) and Theorem 1.2 of Shi, Wang and Yu (Math. Z. 291, 2019),…
The generalized covariant entropy bound is the conjecture that the entropy of the matter present on any non-expanding null hypersurface L will not exceed the difference between the areas, in Planck units, of the initial and final spatial…
In General Relativity, Birkhoff's theorem asserts that any spherically symmetric vacuum solution must be static and asymptotically flat. In this paper, we study the validity of Birkhoff's theorem for a broad class of modified gravity…
(abridged version) The separate universe conjecture states that in General Relativity a density perturbation behaves locally (i.e. on scales much smaller than the wavelength of the mode) as a separate universe with different background…
The von Neumann entropy of a generic quantum state is not unique unless the state can be uniquely decomposed as a sum of extremal or pure states. As pointed out to us by Sorkin, this happens if the GNS representation (of the algebra of…