Energy in topologically massive gravity

Abstract

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.

Mass and angular momentum of black holes in 3D gravity theories with first order formalism

“…The calculations of the right hand side of (A.2) are given by In order to get the charge variation (51) and (53), we consider the variations of frame fields, i.e. dreibein, connections 1-forms and auxiliary fields.…”

Black hole mass and angular momentum in topologically massive gravity

“…Following [24], we write for TMG 12) and compute separately the Einstein and Cotton contributions to the current K µ , neither of which is conserved alone. The computation of the Einstein contribution follows closely [23], taking care however that, to the difference of the background in [23], G µν = 0 for our background.…”

Gravitational Chern-Simons terms and black hole entropy. Global aspects

“…19) We see that conditions (4.17) and (4.19) are less restrictive then (4.15), a consequence of the additional reduction of the configuration space due to the requirement of the manifold being spin. A similar analysis may be performed with different choices in (4.7).…”

“…Again, there is no general closed form formula, so we list the first few terms of the expansion where in addition we used that n = 2 satisfies n = 2 (mod 4), so the left hand side in (D.16) is an even integer. In the case n = 4 from (D.16) and (D.17) follows P 2 (Z) = 7 4 P 2 1 (Z) (mod 1440) (D. 19) As P 2 1 , P 2 (Z) ∈ Z, this relation implies P 2 1 (Z) = 4 k , P 2 (Z) = 7 k (mod 1440) , k ∈ Z (D.20)…”

“…But, occasionally and for the purpose of comparison, we will analyze also the case D = 3 (for this case there is already a remarkably large literature, see [12][13][14][15][16][17][18][19][20][21][22][23][24][25]). …”