Related papers: Note on the First Law with p-form potentials
We present a reduction theory for first order Lagrangian field theories which takes into account the conservation of momenta. The relation between the solutions of the original problem with a prescribed value of the momentum and the…
By introducing the divergence of a vector potential into the Lagrangian, a Lagrangian framework is developed to incorporate surface energy into elasticity. Besides the Euler-Lagrange equation and natural boundary condition, a new boundary…
Systems of coupled rate equations are ubiquitous in many areas of science, for example in the description of electronic transport through quantum dots and molecules. They can be understood as a continuity equation expressing the…
Supergravity provides the effective field theories for string compactifications. The deformation of the maximal supergravities by non-abelian gauge interactions is only possible for a restricted class of charges. Generically these…
We analyze the constraints of gauge theories on Kerr and Kerr-de Sitter spacetimes, which contain one or more horizons. We find that the constraints are modified on such backgrounds through the presence of additional surface terms at the…
We propose a first-order geometric Lagrangian for four-dimensional conformal gravity within the Cartan formulation, which yields, dynamically, the standard constraints on the fields, expected for conformal gravity. Upon imposing the…
We provide the canonical formulation of double field theory. It is shown that this dynamics is subject to primary and secondary constraints. The Poisson bracket algebra of secondary constraints is shown to close on-shell according to the…
We introduce a Lagrangian-space Effective Field Theory (LEFT) formalism for the study of cosmological large scale structures. Unlike the previous Eulerian-space construction, it is naturally formulated as an effective field theory of…
A powerful mechanism for constructing gauge theories is to start from a theory with a global symmetry, then apply the "gauge principle," which demands that this symmetry hold locally. For example, the global phase rotation of a system of…
We briefly outline several main results concerning various new physically relevant features found in gravity -- both ordinary Einstein or $f(R)=R+R^2$ gravity in the first-order formalism, coupled to a special kind of nonlinear…
General charged black ring solution with two angular momenta, a charge and a dipole charge is found by the inverse scattering method. The solution is presented in a relatively concise form in which its symmetries are manifest. The…
In this short review we compare the rigid Noether charges to topological gauge charges. One important extension is that one should consider each boundary component of spacetime independently. The argument that relates bulk charges to…
A general definition of a black hole is given, and general `laws of black-hole dynamics' derived. The definition involves something similar to an apparent horizon, a trapping horizon, defined as a hypersurface foliated by marginal surfaces…
Using well known Lagrangean techniques for uncovering the gauge symmetries of a Lagrangean, we derive the transformation laws for the phase space variables corresponding to local symmetries of the Hamilton equations of motion. These…
In this work we revisit the study of the gravitational interaction in the context of the Special Theory of Relativity. It is found that, as long as the equivalence principle is respected, a relativistic non-linear energy conservation…
These notes have been triggered by physicist's considerations on (1)'Pre-quantized wave equations' for matter fields, (2) Conservation laws, (3) Gauge Field extensions. All starting from variational principles. These notes do not contain…
A property well known as the first law of black hole is a relation among infinitesimal variations of parameters of stationary black holes. We consider a dynamical version of the first law, which may be called the first law of black hole…
In this paper we consider second-order field theories in a variational setting. From the variational principle the Euler-Lagrange equations follow in an unambiguous way, but it is well known that this is not true for the Cartan form. This…
Augmented variational principles are introduced in order to provide a definition of relative conservation laws. As it is physically reasonable, relative conservation laws define in turn relative conserved quantities which measure, for…
Theory of gravity is considered in the Regge-Teitelboim approach in which the pseudo-Riemannian space is treated as a surface isometrically embedded in an ambient Minkowski space of higher dimension. This approach is formulated in terms of…