Birkhoff for Lovelock Redux
We show succinctly that all metric theories with second order field equations obey Birkhoff's theorem: their spherically symmetric solutions are static.
gr-qc↗
arXiv subjects
S. Deser
Publications and source records attributed to S. Deser.
Curvature invariants of static spherically symmetric geometries
We construct all independent local scalar monomials in the Riemann tensor at arbitrary dimension, for the special regime of static, spherically symmetric geometries. Compared to general spaces, their number is significantly reduced: the extreme example is the collapse of all invariants ~ Weyl^k, to a single term at each k. The latter is equivalent to the Lovelock invariant L_k. Depopulation is less extreme for invariants involving rising numbers of Ricci tensors, and also depends on the dimension. The corresponding local gravitational actions and their solution spaces are discussed.
gr-qc↗
Free Spin 2 Duality Invariance Cannot be Extended to GR
We show by explicit computation that the recently discovered duality invariance of D=4 linearized gravity fails, already at first self-interacting, cubic, approximation of GR. In contrast, the cubic Yang-Mills correction to Maxwell does admit a simple deformed duality.
hep-th↗
How Special Relativity Determines the Signs of the Nonrelativistic, Coulomb and Newtonian, Forces
We show that the empirical signs of the fundamental {\it static} Coulomb/Newton forces are dictated by the seemingly unrelated requirement that the photons/gravitons in the respective underlying Maxwell/Einstein physics be stable. This linkage, which is imposed by special relativity, is manifested upon decomposing the corresponding fields and sources in a gauge-invariant way, and without appeal to static limits. The signs of these free field excitation energies determine those of the instantaneous forces between sources; opposite Coulomb/Newton signs are direct consequences of the Maxwell/Einstein free excitations' odd/even spins.
gr-qc↗
Duality invariance of all free bosonic and fermionic gauge fields
We give a simple general extension to all free bosonic and fermionic massless gauge fields of a recent proof that spin 2 is duality invariant in flat space. We also discuss its validity in (A)dS backgrounds and the relevance of supersymmetry.
hep-th↗
Shortcuts to Spherically Symmetric Solutions: A Cautionary Note
Spherically symmetric solutions of generic gravitational models are optimally, and legitimately, obtained by expressing the action in terms of the two surviving metric components. This shortcut is not to be overdone, however: a one-function ansatz invalidates it, as illustrated by the incorrect solutions of [1].
gr-qc↗
Schwarzschild and Birkhoff a la Weyl
We provide a simple derivation of the Schwarzschild solution in General Relativity, generalizing an early approach by Weyl, to include Birkhoff's theorem: constancy of the mass; its deeper, Hamiltonian, basis is also given. Our procedure is illustrated by a parallel derivation of the Coulomb field and constancy of electric charge, in electrodynamics.
gr-qc↗
Cotton Blend Gravity $pp$ Waves
We study conformal gravity in d=2+1, where the Cotton tensor is equated to a--necessarily traceless--matter stress tensor, for us that of the improved scalar field. We first solve this system exactly in the $pp$ wave regime, then show it to be equivalent to topologically massive gravity.
gr-qc↗
Conformal Invariance of Partially Massless Higher Spins
We show that there exist conformally invariant theories for all spins in d=4 de Sitter space, namely the partially massless models with higher derivative gauge invariance under a scalar gauge parameter. This extends the catalog from the two known gauge models -- Maxwell and partially massless spin 2 -- to all spins.
hep-th↗
The Dynamics of General Relativity
This article--summarizing the authors' then novel formulation of General Relativity--appeared as Chapter 7 of an often cited compendium edited by L. Witten in 1962, which is now long out of print. Intentionally unretouched, this posting is intended to provide contemporary accessibility to the flavor of the original ideas. Some typographical corrections have been made: footnote and page numbering have changed--but not section nor equation numbering etc. The authors' current institutional affiliations are encoded in: arnowitt@physics.tamu.edu, deser@brandeis.edu, misner@physics.umd.edu .
gr-qc↗
The Many Dimensions of Dimension
Some aspects of the history and impact of the dimension revolution are briefly surveyed, starting with Nordstrom's D=5 scalar gravity-electromagnetism unification.
physics.hist-ph↗
Stress and Strain: T^{μν} of Higher Spin Gauge Fields
We present some results concerning local currents, particularly the stress tensors T^{μν}, of free higher (>1) spin gauge fields. While the T^{μν} are known to be gauge variant, we can express them, at the cost of manifest Lorentz invariance, solely in terms of (spatially nonlocal) gauge-invariant field components, where the "scalar" and "spin" aspects of the systems can be clearly separated. Using the fundamental commutators of these transverse-traceless variables we verify the Poincare algebra among its generators, constructed from the T^0_μand their moments. The relevance to the interaction difficulties of higher spin systems is mentioned.
hep-th↗
A Note on Stress-Tensors, Conservation and Equations of Motion
Some unusual relations between stress tensors, conservation and equations of motion are briefly reviewed.
gr-qc↗
Energy in Topologically Massive Gravity
We define conserved gravitational charges in -cosmologically extended- topologically massive gravity, exhibit them in surface integral form about their de-Sitter or flat vacua and verify their correctness in terms of two basic types of solution.
gr-qc↗
Shortcuts to high symmetry solutions in gravitational theories
We apply the Weyl method, as sanctioned by Palais' symmetric criticality theorems, to obtain those -highly symmetric -geometries amenable to explicit solution, in generic gravitational models and dimension. The technique consists of judiciously violating the rules of variational principles by inserting highly symmetric, and seemingly gauge fixed, metrics into the action, then varying it directly to arrive at a small number of transparent, indexless, field equations. Illustrations include spherically and axially symmetric solutions in a wide range of models beyond D=4 Einstein theory; already at D=4, novel results emerge such as exclusion of Schwarzschild solutions in cubic curvature models and restrictions on ``independent'' integration parameters in quadratic ones. Another application of Weyl's method is an easy derivation of Birkhoff's theorem in systems with only tensor modes. Other uses are also suggested.
gr-qc↗
Novel Properties of Massive Higher Spin Fields
I outline a series of results obtained in collaboration with A. Waldron on the properties of massive higher (s>1) spin fields in cosmological, constant curvature, backgrounds and the resulting unexpected qualitative effects on their degrees of freedom and unitarity properties. The dimensional parameter $Ł$ extends the flat space m-line to a $(m^2,Ł)$ "phase" plane in which these novel phenomena unfold. In this light, I discuss a possible partial resurrection of deSitter supergravity. I will also exhibit the well-known causality problems of coupling these systems to gravity and, for complex fields, to electromagnetism, systematizing some of the occasionally misunderstood obstacles to interactions, particularly for s = 3/2 and 2.
gr-qc↗
A Note on Matter Superenergy Tensors
We consider Bel-Robinson-like higher derivative conserved two-index tensors $H_\mn$ in simple matter models, following a recently suggested Maxwell field version. In flat space, we show that they are essentially equivalent to the true stress-tensors. In curved Ricci-flat backgrounds it is possible to redefine $H_\mn$ so as to overcome non-commutativity of covariant derivatives, and maintain conservation, but they become model- and dimension- dependent, and generally lose their simple "BR" form.
gr-qc↗
Arbitrary Spin Representations in de Sitter from dS/CFT with Applications to dS Supergravity
We present a simple group representation analysis of massive, and particularly ``partially massless'', fields of arbitrary spin in de Sitter spaces of any dimension. The method uses bulk to boundary propagators to relate these fields to Euclidean conformal ones at one dimension lower. These results are then used to revisit an old question: can a consistent de Sitter supergravity be constructed, at least within its intrinsic horizon?
hep-th↗