Related papers: Singularity theory and heat equation
We establish a one-to-one mapping between entanglement entropy, energy, and temperature (quantum entanglement mechanics) with black hole entropy, Komar energy, and Hawking temperature, respectively. We show this explicitly for 4-D…
We formulate Euler-Poincar\'e and Lagrange-Poincar\'e equations for systems with broken symmetry. We specialize the general theory to present explicit equations of motion for nematic systems, ranging from single nematic molecules to biaxial…
It has been argued that the entanglement spectrum of a static patch of de Sitter space must be flat, or what is equivalent, the temperature parameter in the Boltzmann distribution must be infinite. This seems absurd: quantum fields in de…
We consider the ill-posed Cauchy problem for the polyharmonic heat equation on recovering a function, satisfying the equation $(\partial _t + (- \Delta)^m) u=0$ in a cylindrical domain in the half-space ${\mathbb R}^n \times [0,+\infty)$,…
The Euler equation (EE) is one of the basic equations in many physical fields such as fluids, plasmas, condensed matter, astrophysics, oceanic and atmospheric dynamics. A symmetry group theorem of the (2+1)-dimensional EE is obtained via a…
A number of boundary problems in multidimensional elasticity theory are solved. The solutions can be treated as the simplest cosmological models. Some specific properties of the solutions and experimental consequences of the theory are…
We explore the thermodynamics of a black-hole solution in improved holographic QCD with a simple dilaton potential having two parameters. By applying techniques of singular perturbation theory, we get uniform approximations for the metric…
Two novel topological black hole exact solutions with unusual shapes of horizons in the simplest holographic axions model, the four-dimensional Einstein-Maxwell-axions theory, are constructed. We draw embedding diagrams in various…
In this work, we develop a generalisation of the thermal entropy to complex inverse temperatures, which we call the thermal pseudo-entropy. We show that this quantity represents the pseudo-entropy of the transition matrix between…
The Eigenstate Thermalization Hypothesis (ETH) provides a way to understand how an isolated quantum mechanical system can be approximated by a thermal density matrix. We find a class of operators in (1+1)-$d$ conformal field theories,…
A general approach to anomaly in quantum field theory is newly formulated by use of the propagator theory in solving the heat-kernel equation. We regard the heat-kernel as a sort of the point-splitting regularization in the space(-time)…
Based on the conformal energy theorem we prove the uniqueness theorem for static higher dimensional electrically and magnetically charged black holes being the solution of Einstein (n-2)-gauge forms equations of motion. Black hole spacetime…
We consider a gauge symmetry in a quantum Hilbert space. The symmetry leads to that of the heat-kernel and of the anomaly formulae which were previously obtained by the authors. This greatly simplifies and clarifies the structure of the…
We construct a class of charged, rotating solutions of (n+1)-dimensional Einstein-Maxwell-dilaton gravity with Liouville-type potentials and investigate their properties. These solutions are neither asymptotically flat nor (anti)-de Sitter.…
Topological solutions in the (2+1)-dimensional Einstein theory of gravity are studied within the ADM canonical formalism. It is found that a conical singularity appears in the closed de Sitter universe solution as a topological defect in…
We consider a perturbed Hermitian-Einstein equation, which we call the Donaldson-Thomas equation, on compact K\"ahler threefolds. In arXiv:0805.2195, we analysed some analytic properties of solutions to the equation, in particular, we…
In this article we inspect the dynamics of classical field theories with a local conformal behavior. Our interest in the multisymplectic setting comes from its suitable description of field theories, and the conformal character has been…
We introduce Riemann-Hilbert problems determined by refined Donaldson-Thomas theory. They involve piecewise holomorphic maps from the complex plane to the group of automorphisms of a quantum torus algebra. We study the simplest case in…
The complete form of the high-temperature expansion of the one-loop contribution to the free energy of a scalar field on a stationary gravitational background is derived. The explicit expressions for the divergent and finite parts of the…
We investigate consistent charged black hole solutions to the Einstein-Maxwell-Dilaton (EMD) equations that are asymptotically AdS. The solutions are gravity duals to phases of a non-conformal plasma at finite temperature and density. For…