We study cosmological solutions of Einstein gravity with a positive cosmological constant and perfect fluid matter in diverse dimensions. These include big-bang models that re-collaspse, big-bang models that approach de Sitter acceleration at late times, and bounce models that are both past and future asymptotically de Sitter. The re-collapsing and the bounce geometries are all tall in the sens...

We study a generalisation of thermodynamic geometry to degenerate quantum ground states at zero temperatures exemplified by charged extremal black holes in type II string theories. Several examples of extremal charged black holes with non degenerate thermodynamic geometries and finite but non zero state space scalar curvatures are established. These include black holes described by D1-D5-P and ...

We construct the first smooth, horizonless “microstate geometries” that have the same charges, dipole charges and angular momenta as a BPS black ring whose horizon is macroscopic. These solutions have exactly the same geometry as black rings, except that the usual infinite throat is smoothly capped off at a very large depth. If the solutions preserve a U(1)×U(1) isometry, then this depth is lim...

We consider effective field theory around classical background geometries with a gauge theory dual, in the class of LLM geometries. These are dual to half-BPS states of N = 4 SYM. We find that the language of code subspaces is natural for discussing the set of nearby states, which are built by acting with effective fields on these backgrounds. This work extends our previous work by going beyond...

The main content of this review article is first to review the main inference tools using Bayes rule, the maximum entropy principle (MEP), information theory, relative entropy and the Kullback–Leibler (KL) divergence, Fisher information and its corresponding geometries. For each of these tools, the precise context of their use is described. The second part of the paper is focused on the ways th...

In recent years, a new paradigm in theoretical physics has emerged known as the holographic principle. This principle states that the number of degrees of freedom in a d-dimensional region of a (d + 1)-dimensional spacetime is proportional to the area of a suitably defined surface associated with the region of spacetime. This principle was motivated by the fact that the entropy of a black hole ...

Quantum entanglement entropy has a geometric character. This is illustrated by the interpretation of Rindler space or black hole entropy as entanglement entropy. In general, one can define a “geometric entropy”, associated with an event horizon as a boundary that concentrates a large number of quantum states. This allows one to connect with the “density matrix renormalization group” and to unve...

The Rényi entropy is a generalization of Shannon entropy to a one-parameter family of entropies. Tsallis entropy too is a generalization of Shannon entropy. The measure for Tsallis entropy is non-logarithmic. After the introduction of Shannon entropy , the conditional Shannon entropy was derived and its properties became known. Also, for Tsallis entropy, the conditional entropy was introduced a...

We study exponentially suppressed contributions to the degeneracies of extremal black holes. Within Sen’s quantum entropy function framework and focusing on extremal black holes with an intermediate AdS3 region, we identify an infinite family of semi-classical AdS2 geometries which can contribute effects of order exp(S0/c), where S0 is the Bekenstein-Hawking-Wald entropy and c is an integer gre...

For extremal black holes the fuzzball conjecture says that the throat of the geometry ends in a quantum ‘fuzz’, instead of being infinite in length with a horizon at the end. For the D1-D5 system we consider a family of sub-ensembles of states, and find that in each case the boundary area of the fuzzball satisfies a Bekenstein type relation with the entropy enclosed. We suggest a relation betwe...