scholarly journals Modeling Spacetime as a Branched Covering Space over 2-Knots

2019 ◽  
Author(s):  
Christopher Duston
Keyword(s):  
Gravitational Field ◽  
Partition Function ◽  
Thermodynamic Limit ◽  
Dimensional Reduction ◽  
Degrees Of Freedom ◽  
Covering Space ◽  
Topological Information ◽  
Spacetime Geometry ◽  
Branched Covering

In this paper we review a proposal to represent the geometric degrees of freedom of the gravitational field as a branched covering space, and introduce a new application of this in which the branch loci are 1- or 2-knots. This allows one to construct arbitrary smooth, closed 3- and 4-manifolds with enough geometric and topological information to write down a partition function and calculate statistical quantities in the thermodynamic limit. Further, we find clear evidence for a dimensional reduction of the spacetime geometry from four to two. As an example, we choose a family of smooth 4-manifolds presented in this way, and calculate the entropy of the system.

scholarly journals The statistical mechanics of near-extremal black holes

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Luca V. Iliesiu ◽  
Gustavo J. Turiaci
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Partition Function ◽  
Gauge Field ◽  
Dimensional Reduction ◽  
Degrees Of Freedom ◽  
Energy Scale ◽  
Fixed Charge ◽  
Extremal Black Hole ◽  
Extremal Black Holes

Abstract An important open question in black hole thermodynamics is about the existence of a “mass gap” between an extremal black hole and the lightest near-extremal state within a sector of fixed charge. In this paper, we reliably compute the partition function of Reissner-Nordström near-extremal black holes at temperature scales comparable to the conjectured gap. We find that the density of states at fixed charge does not exhibit a gap; rather, at the expected gap energy scale, we see a continuum of states. We compute the partition function in the canonical and grand canonical ensembles, keeping track of all the fields appearing through a dimensional reduction on S2 in the near-horizon region. Our calculation shows that the relevant degrees of freedom at low temperatures are those of 2d Jackiw-Teitelboim gravity coupled to the electromagnetic U(1) gauge field and to an SO(3) gauge field generated by the dimensional reduction.

scholarly journals WAVELESS APPROXIMATION THEORIES OF GRAVITY

2008 ◽  
Vol 17 (02) ◽  
pp. 265-273 ◽  
Author(s):  
JAMES A. ISENBERG
Keyword(s):  
Gravitational Field ◽  
Gravitational Radiation ◽  
Elliptic Equations ◽  
Degrees Of Freedom ◽  
Dynamic Instability ◽  
Accurate Approximation ◽  
Time Step ◽  
Einstein Theory ◽  
Physical Systems ◽  
Theories Of Gravity

The analysis of a general multibody physical system governed by Einstein's equations is quite difficult, even if numerical methods (on a computer) are used. Some of the difficulties — many coupled degrees of freedom, dynamic instability — are associated with the presence of gravitational waves. We have developed a number of "waveless approximation theories" (WAT's) which repress the gravitational radiation and thereby simplify the analysis. The matter, according to these theories, evolves dynamically. The gravitational field, however, is determined at each time step by a set of elliptic equations with matter sources. There is reason to believe that for many physical systems, the WAT-generated system evolution is a very accurate approximation to that generated by the full Einstein theory.

scholarly journals Nature does not play Dice at the Planck scale

2020 ◽  
Vol 29 (14) ◽  
pp. 2043012
Author(s):  
Tejinder P. Singh
Keyword(s):  
Degrees Of Freedom ◽  
Large Scale ◽  
Planck Scale ◽  
Coarse Graining ◽  
Lagrangian Dynamics ◽  
Time Intervals ◽  
Spacetime Geometry ◽  
The Status ◽  
Planck Time ◽  
Matter Fields

We start from classical general relativity coupled to matter fields. Each configuration variable and its conjugate momentum, as also spacetime points are raised to the status of matrices [equivalently operators]. These matrices obey a deterministic Lagrangian dynamics at the Planck scale. By coarse-graining this matrix dynamics over time intervals much larger than Planck time, one derives quantum theory as a low energy emergent approximation. If a sufficiently large number of degrees of freedom get entangled, spontaneous localisation takes place, leading to the emergence of classical spacetime geometry and a classical universe. In our theory, dark energy is shown to be a large-scale quantum gravitational phenomenon. Quantum indeterminism is not fundamental, but results from our not probing physics at the Planck scale.

scholarly journals Dark Gravitational Field on Riemannian and Sasaki Spacetime

Universe ◽  
2020 ◽  
Vol 6 (9) ◽  
pp. 138
Author(s):  
Panayiotis Stavrinos ◽  
Christos Savvopoulos
Keyword(s):  
Dark Matter ◽  
Gravitational Field ◽  
Tangent Bundle ◽  
Degrees Of Freedom ◽  
Geometrical Structure ◽  
Geometric Model ◽  
Geodesic Motion ◽  
Tidal Forces ◽  
Geometric Methods ◽  
Raychaudhuri Equations

The aim of this paper is to provide the geometrical structure of a gravitational field that includes the addition of dark matter in the framework of a Riemannian and a Riemann–Sasaki spacetime. By means of the classical Riemannian geometric methods we arrive at modified geodesic equations, tidal forces, and Einstein and Raychaudhuri equations to account for extra dark gravity. We further examine an application of this approach in cosmology. Moreover, a possible extension of this model on the tangent bundle is studied in order to examine the behavior of dark matter in a unified geometric model of gravity with more degrees of freedom. Particular emphasis shall be laid on the problem of the geodesic motion under the influence of dark matter.

scholarly journals Partition Function in One, Two, and Three Spatial Dimensions from Effective Lagrangian Field Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Christoph P. Hofmann
Keyword(s):  
Partition Function ◽  
Degrees Of Freedom ◽  
Spatial Dimension ◽  
Lagrangian Method ◽  
Point Of View ◽  
Low Energy ◽  
Effective Theory ◽  
Goldstone Bosons ◽  
Effective Lagrangian ◽  
Spatial Dimensions

The systematic effective Lagrangian method was first formulated in the context of the strong interaction; chiral perturbation theory (CHPT) is the effective theory of quantum chromodynamics (QCD). It was then pointed out that the method can be transferred to the nonrelativistic domain—in particular, to describe the low-energy properties of ferromagnets. Interestingly, whereas for Lorentz-invariant systems the effective Lagrangian method fails in one spatial dimension (ds=1), it perfectly works for nonrelativistic systems in ds=1. In the present brief review, we give an outline of the method and then focus on the partition function for ferromagnetic spin chains, ferromagnetic films, and ferromagnetic crystals up to three loops in the perturbative expansion—an accuracy never achieved by conventional condensed matter methods. We then compare ferromagnets in ds=1, 2, 3 with the behavior of QCD at low temperatures by considering the pressure and the order parameter. The two apparently very different systems (ferromagnets and QCD) are related from a universal point of view based on the spontaneously broken symmetry. In either case, the low-energy dynamics is described by an effective theory containing Goldstone bosons as basic degrees of freedom.

scholarly journals The Spectrum of Teleparallel Gravity

Universe ◽  
2019 ◽  
Vol 5 (3) ◽  
pp. 80 ◽  
Author(s):  
Tomi Koivisto ◽  
Georgios Tsimperis
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Quadratic Form ◽  
Degrees Of Freedom ◽  
Arbitrary Dimension ◽  
Scalar Potential ◽  
Ultra Violet ◽  
Teleparallel Gravity ◽  
Frame Field ◽  
Covariant Derivation

The observer’s frame is the more elementary description of the gravitational field than the metric. The most general covariant, even-parity quadratic form for the frame field in arbitrary dimension generalises the New General Relativity by nine functions of the d’Alembertian operator. The degrees of freedom are clarified by a covariant derivation of the propagator. The consistent and viable models can incorporate an ultra-violet completion of the gravity theory, an additional polarisation of the gravitational wave, and the dynamics of a magnetic scalar potential.

SIGNATURES OF AN EMERGENT GRAVITY FROM BLACK HOLE ENTROPY

2009 ◽  
Vol 18 (14) ◽  
pp. 2323-2327
Author(s):  
CENALO VAZ
Keyword(s):  
Phase Transition ◽  
Black Hole ◽  
Mass Spectrum ◽  
Partition Function ◽  
Ground State ◽  
Degrees Of Freedom ◽  
Thermodynamic Description ◽  
Black Hole Entropy ◽  
Fundamental Particle ◽  
Horizon Radius

The existence of a thermodynamic description of horizons indicates that space–time has a microstructure. While the "fundamental" degrees of freedom remain elusive, quantizing Einstein's gravity provides some clues about their properties. A quantum AdS black hole possesses an equispaced mass spectrum, independent of Newton's constant, G, when its horizon radius is large compared to the AdS length. Moreover, the black hole's thermodynamics in this limit is inextricably connected with its thermodynamics in the opposite (Schwarzschild) limit by a duality of the Bose partition function. G, absent in the mass spectrum, re-emerges in the thermodynamic description through the Schwarzschild limit, which should be viewed as a natural "ground state." It seems that the Hawking–Page phase transition separates fundamental, "particle-like" degrees of freedom from effective, "geometric" ones.

scholarly journals 3+1DMassless Weyl Spinors from Bosonic Scalar-Tensor Duality

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Andrea Amoretti ◽  
Alessandro Braggio ◽  
Giacomo Caruso ◽  
Nicola Maggiore ◽  
Nicodemo Magnoli
Keyword(s):  
Dirac Equation ◽  
Charge Density ◽  
Dimensional Reduction ◽  
Degrees Of Freedom ◽  
Planar Boundary ◽  
Weyl Spinor ◽  
Bf Theory ◽  
Free Theory ◽  
Tomographic Representation

We consider the fermionization of a bosonic-free theory characterized by the3+1Dscalar-tensor duality. This duality can be interpreted as the dimensional reduction, via a planar boundary, of the4+1Dtopological BF theory. In this model, adopting the Sommerfield tomographic representation of quantized bosonic fields, we explicitly build a fermionic operator and its associated Klein factor such that it satisfies the correct anticommutation relations. Interestingly, we demonstrate that this operator satisfies the massless Dirac equation and that it can be identified with a3+1DWeyl spinor. Finally, as an explicit example, we write the integrated charge density in terms of the tomographic transformed bosonic degrees of freedom.

Symplectic geometry of radiative modes and conserved quantities at null infinity

1981 ◽  
Vol 376 (1767) ◽  
pp. 585-607 ◽  
Keyword(s):  
Angular Momentum ◽  
Gravitational Field ◽  
Phase Space ◽  
Degrees Of Freedom ◽  
Symplectic Geometry ◽  
Conserved Quantities ◽  
Null Infinity ◽  
Hamiltonian Description ◽  
Infinite Dimensional ◽  
Massless Spin

The Hamiltonian description of massless spin zero- and one-fields in Minkowski space is first recast in a way that refers only to null infinity and fields thereon representing radiative modes. With this framework as a guide, the phase space of the radiative degrees of freedom of the gravitational field (in exact general relativity) is introduced. It has the structure of an infinite-dimensional affine manifold (modelled on a Fréchet space) and is equipped with a continuous, weakly non-degenerate symplectic tensor field. The action of the Bondi-Metzner-Sachs group on null infinity is shown to induce canonical transformations on this phase space. The corresponding Hamiltonians – i. e. generating functions – are computed and interpreted as fluxes of supermomentum and angular momentum carried away by gravitational waves. The discussion serves three purposes: it brings out, via symplectic methods, the universality of the interplay between symmetries and conserved quantities; it sheds new light on the issue of angular momentum of gravitational radiation; and, it suggests a new approach to the quantization of the ‘true’ degrees of freedom of the gravitational field.

Sign in / Sign up

Export Citation Format

Share Document