Related papers: Holographic Lattices and Numerical Techniques
Shape dynamics is a classical theory of gravity which agrees with general relativity in many important aspects, but which possesses different gauge symmetries and can present some fundamental global differences with respect to Einstein…
Noncommutative black holes in higher dimensions are investigated in the context of holographic principle. Quantization rules for the discrete mass spectrum are derived and compared with the continuous spectrum in the literature. Because of…
I review recent developments in numerical relativity, focussing on progress made in 3D black hole evolution. Progress in development of black hole initial data, apparent horizon boundary conditions, adaptive mesh refinement, and…
We study functional analytic aspects of two types of correction terms to the Heisenberg algebra. One type is known to induce a finite lower bound $\Delta x_0$ to the resolution of distances, a short distance cutoff which is motivated from…
Isolated and Dynamical horizons are used to generate boundary conditions upon the lapse and shift vectors. Numerous results involving the Hamiltonian of General relativity are derived, including a self-contained derivation of the…
Focusing on the connection between the Landau theory of second order phase transitions and the holographic approach to critical phenomena, we study diverse field theories in an anti-de Sitter black hole background. Through simple analytical…
We study the scalar modes of linear perturbations in loop quantum cosmology. This is done on a lattice where each cell is taken to be homogeneous and isotropic and can be quantized via standard homogeneous loop quantum cosmology techniques.…
We provide a general algorithm to construct a Hamiltonian, such that its dynamical flow covariantly defines any given spherically symmetric and static metric. This Hamiltonian is defined as a linear combination of the standard (general…
We propose a universal formula of dc electrical conductivity in rotational- and translational- symmetries breaking systems via the holographic duality. This formula states that the ratio of the determinant of the dc electrical…
We use solution-generating techniques to construct interpolating geometries between general asymptotically flat, charged, rotating, non-extremal black holes in four and five dimensions and their subtracted geometries. In the…
Through an illuminating thought experiment we demonstrate that the nonsingular "continued collapse" picture of a black hole is the only consistent and physical one. We provide a class exact solutions on the boundary of the space of physical…
We study black hole solutions in an extension of General Relativity (GR) with an explicit non-minimal coupling between matter and curvature. General black hole solutions satisfying the known energy conditions are derived including the ones…
General relativity can describe various gravitational systems of astrophysical relevance, like black holes and neutron stars, or even strongly coupled systems through the holographic duality. The characteristic initial (boundary) value…
In this paper we discuss about properties of lattices and its application in theoretical and algorithmic number theory. This result of Minkowski regarding the lattices initiated the subject of Geometry of Numbers, which uses geometry to…
We show that the algebraic aspects of Lie symmetries and generalized symmetries in nonrelativistic and relativistic quantum mechanics can be preserved in linear lattice theories. The mathematical tool for symmetry preserving discretizations…
Black hole configurations offer insights on the non-linear aspects of gravitational theories, and can suggest testable predictions for modifications of General Relativity. In this work, we examine exact black hole configurations in…
In recent papers we had developed a unified picture of black hole entropy and curvature which was shown to lead to Hawking radiation. It was shown that for any black hole mass, holography implies a phase space of just one quantum associated…
We provide a geometric framework for the construction of non-vacuum black holes whose metrics are stationary and axisymmetric. Under suitable assumptions we show that the Einstein equations reduce to an Einstein-harmonic map type system and…
The recent detections of gravitational waves from binary systems of black holes are in remarkable agreement with the predictions of General Relativity. In this pedagogical mini-review, I will go through the physics of the different phases…
We propose a holographic dictionary which comes from reducing the bulk theories in an asymptotically flat spacetime to its null infinity. A general boundary theory is characterized by a fundamental field, an infinite tower of descendant…