A Torsional Topological Invariant

Nieh, H. T.

doi:10.1142/s0217751x07038414

Cited by 98 publications

(67 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This boundary term was proposed in [17], and is proportional to the Nieh-Yan topological invariant, S NY . This topological term is related to the torsion T I := De I , and is of the form [38,39],…”

Section: B Holst and Nieh-yan Termsmentioning

confidence: 99%

Actions, topological terms and boundaries in first-order gravity: A review

Corichi

Rubalcava-Garcia

Vukašinac

2016

Int. J. Mod. Phys. D

View full text Add to dashboard Cite

In this review we consider first order gravity in four dimensions. In particular, we focus our attention in formulations where the fundamental variables are a tetrad e I a and a SO(3,1) connection ω aI J . We study the most general action principle compatible with diffeomorphism invariance. This implies, in particular, considering besides the standard Einstein-Hilbert-Palatini term, other terms that either do not change the equations of motion, or are topological in nature. Having a well defined action principle sometimes involves the need for additional boundary terms, whose detailed form may depend on the particular boundary conditions at hand. In this work, we consider spacetimes that include a boundary at infinity, satisfying asymptotically flat boundary conditions and/or an internal boundary satisfying isolated horizons boundary conditions. We focus on the covariant Hamiltonian formalism where the phase space Γ is given by solutions to the equations of motion. For each of the possible terms contributing to the action we consider the well posedness of the action, its finiteness, the contribution to the symplectic structure, and the Hamiltonian and Noether charges. For the chosen boundary conditions, standard boundary terms warrant a well posed theory. Furthermore, the boundary and topological terms do not contribute to the symplectic structure, nor the Hamiltonian conserved charges.The Noether conserved charges, on the other hand, do depend on such additional terms. The aim of this manuscript is to present a comprehensive and self-contained treatment of the subject, so the style is somewhat pedagogical. Furthermore, along the way we point out and clarify some issues that have not been clearly understood in the literature.

show abstract

Section: B Holst and Nieh-yan Termsmentioning

confidence: 99%

Actions, topological terms and boundaries in first-order gravity: A review

Corichi

Rubalcava-Garcia

Vukašinac

2016

Int. J. Mod. Phys. D

View full text Add to dashboard Cite

show abstract

“…The first is the Euler character of the Lorentz bundle over M (also known as the Gauss-Bonnet invariant), the second is the corresponding Pontryagin character, and the third is the Nieh-Yan character [65][66][67], which exists only for a connection with torsion. Each of these terms are exact forms L = dµ where the corresponding µ's can be computed to be 12…”

mentioning

confidence: 99%

The first law of black hole mechanics for fields with internal gauge freedom

Prabhu¹

2017

Class. Quantum Grav.

104

155

View full text Add to dashboard Cite

We derive the first law of black hole mechanics for physical theories based on a local, covariant and gauge-invariant Lagrangian where the dynamical fields transform non-trivially under the action of some internal gauge transformations. The theories of interest include General Relativity formulated in terms of tetrads, Einstein-Yang-Mills theory and Einstein-Dirac theory. Since the dynamical fields of these theories have some internal gauge freedom, we argue that there is no natural group action of diffeomorphisms of spacetime on such dynamical fields. In general, such fields cannot even be represented as smooth, globally well-defined tensor fields on spacetime. Consequently the derivation of the first law by Iyer and Wald cannot be used directly. Nevertheless, we show how such theories can be formulated on a principal bundle and that there is a natural action of automorphisms of the bundle on the fields. These bundle automorphisms encode both spacetime diffeomorphisms and internal gauge transformations. Using this reformulation we define the Noether charge associated to an infinitesimal automorphism and the corresponding notion of stationarity and axisymmetry of the dynamical fields. We first show that we can define certain potentials and charges at the horizon of a black hole so that the potentials are constant on the bifurcate Killing horizon, giving a generalised zeroth law for bifurcate Killing horizons. We further identify the gravitational potential and perturbed charge as the temperature and perturbed entropy of the black hole which gives an explicit formula for the perturbed entropy analogous to the Wald entropy formula. We then obtain a general first law of black hole mechanics for such theories. The first law relates the perturbed Hamiltonians at spatial infinity and the horizon, and

show abstract

“…When contracted by F αβ µ and F γδ ν , this term drops out from the general teleparallel Lagrangian. Moreover, one can reduce the number of independent terms in the Lagrangian by making use of the Nieh-Yan topological invariant [41,42,46].…”

Section: Parity Violating Termsmentioning

confidence: 99%

Premetric teleparallel theory of gravity and its local and linear constitutive law

et al. 2018

View full text Add to dashboard Cite

We continue to investigate the premetric teleparallel theory of gravity (TG) with the coframe (tetrad) as gravitational potential. We start from the field equations and a local and linear constitutive law. We create a Tonti diagram of TG in order to disclose the structure of TG. Subsequently we irreducibly decompose the 6th order constitutive tensor under the linear group. Moreover, we construct the most general constitutive tensors from the metric and the totally antisymmetric Levi-Civita symbol, and we demonstrate that they encompass nontrivial axion and skewon type pieces. Using these tools, we derive for TG in the geometric-optics approximation propagating massless spin 0, 1, and 2 waves, including the special case of Einstein's general relativity.

show abstract

A Torsional Topological Invariant

Cited by 98 publications

References 15 publications

Actions, topological terms and boundaries in first-order gravity: A review

Actions, topological terms and boundaries in first-order gravity: A review

The first law of black hole mechanics for fields with internal gauge freedom

Premetric teleparallel theory of gravity and its local and linear constitutive law

Contact Info

Product

Resources

About