scholarly journals Total Conserved Charges of Kerr-Newman Spacetimes in Gravity Theory Using a Poincaré Gauge Version of the Teleparallel Equivalent of General Relativity

2013 ◽  
Vol 2013 ◽  
pp. 1-16
Author(s):  
Gamal G. L. Nashed
Keyword(s):  
General Relativity ◽  
Angular Momentum ◽  
Vector Field ◽  
Gravity Theory ◽  
Arbitrary Vector ◽  
Conserved Charges ◽  
Conserved Currents ◽  
Total Conserved Charges

The total conserved charges of several tetrad spacetimes, generating the Kerr-Newman (KN) metric, are calculated using the approach of invariant conserved currents generated by an arbitrary vector field that reproduces a diffeomorphism on the spacetime. The accompanying charges of some tetrads give the known value of energy and angular momentum, while those of other tetrads give, in addition to the unknown format charges, a divergent entity. Therefore, regularized expressions are considered also to get the commonly known form of conserved charges of KN.

scholarly journals Off-Shell Noether Currents and Potentials for First-Order General Relativity

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 348
Author(s):  
Merced Montesinos ◽  
Diego Gonzalez ◽  
Rodrigo Romero ◽  
Mariano Celada
Keyword(s):  
General Relativity ◽  
Vector Fields ◽  
Killing Vector ◽  
Spherically Symmetric ◽  
Killing Vector Fields ◽  
Arbitrary Vector ◽  
Four Dimensions ◽  
First Order ◽  
Direct Form ◽  
Definition Of

We report off-shell Noether currents obtained from off-shell Noether potentials for first-order general relativity described by n-dimensional Palatini and Holst Lagrangians including the cosmological constant. These off-shell currents and potentials are achieved by using the corresponding Lagrangian and the off-shell Noether identities satisfied by diffeomorphisms generated by arbitrary vector fields, local SO(n) or SO(n−1,1) transformations, ‘improved diffeomorphisms’, and the ‘generalization of local translations’ of the orthonormal frame and the connection. A remarkable aspect of our approach is that we do not use Noether’s theorem in its direct form. By construction, the currents are off-shell conserved and lead naturally to the definition of off-shell Noether charges. We also study what we call the ‘half off-shell’ case for both Palatini and Holst Lagrangians. In particular, we find that the resulting diffeomorphism and local SO(3,1) or SO(4) off-shell Noether currents and potentials for the Holst Lagrangian generically depend on the Immirzi parameter, which holds even in the ‘half off-shell’ and on-shell cases. We also study Killing vector fields in the ‘half off-shell’ and on-shell cases. The current theoretical framework is illustrated for the ‘half off-shell’ case in static spherically symmetric and Friedmann–Lemaitre–Robertson–Walker spacetimes in four dimensions.

scholarly journals A Conformal Field Theory of Extrinsic Geometry of 2-d Surfaces

1997 ◽  
Vol 52 (1-2) ◽  
pp. 97-104
Author(s):  
K.S. Viswanathan ◽  
R. Parthasarathy
Keyword(s):  
Extrinsic Curvature ◽  
Universality Class ◽  
Gravity Theory ◽  
World Sheet ◽  
Light Cone Gauge ◽  
Conformal Field ◽  
Extrinsic Geometry ◽  
Wznw Model ◽  
The Mean ◽  
Conserved Currents

Abstract In the description of the extrinsic geometry of the string world sheet regarded as a conformal immersion of a 2-d surface in R3 it was previously shown that, restricting to surfaces with h √ g = 1, where h is the mean scalar curvature and g is the determinant of the induced metric on the surface, leads to Virasaro symmetry. An explicit form of the effective action on such surfaces is constructed in this article, which is the extrinsic curvature analog of the WZNW action. This action turns our to be the gauge invariant combination of the actions encountered in 2-d intrinsic gravity theory in light-cone gauge and the geometric action appearing in the quantization of the Virasaro group. This action, besides exhibiting Virasaro symmetry in z-sector, has SL (2, C) conserved currents in the z̅-sector. This allows us to quantize this theory in the z̅-sector along the lines of the WZNW model. The quantum theory on h √ g = 1 surfaces in R3 is shown to be in the same universality class as the intrinsic 2-d gravity theory.

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