Asymptotic symmetries of Rindler space at the horizon and null infinity

We investigate the asymptotic symmetries of Rindler space at null infinity and at the event horizon using both systematic and ad hoc methods. We find that the approaches that yield infinite-dimensional asymptotic symmetry algebras in the case of anti–de Sitter and flat spaces only give a finite-dimensional algebra for Rindler space at null infinity. We calculate the charges corresponding to these symmetries and confirm that they are finite, conserved, and integrable, and that the algebra of charges gives a representation of the asymptotic symmetry algebra. We also use relaxed boundary conditions to find infinite-dimensional asymptotic symmetry algebras for Rindler space at null infinity and at the event horizon. We compute the charges corresponding to these symmetries and confirm that they are finite and integrable. We also determine sufficient conditions for the charges to be conserved on-shell, and for the charge algebra to give a representation of the asymptotic symmetry algebra. In all cases, we find that the central extension of the charge algebra is trivial.

Figure 1

Lines of constant $\eta =x/t$ (red lines) and constant $\zeta =x^2-t^2$ (blue lines) in Rindler space.

Figure 2

Lines of constant $u=a(x-t)$ (red lines) and constant $r=a(x+t)$ (blue lines) in Rindler space.

Figure 3

The division of flat space into the right Rindler wedge (R), the left Rindler wedge (L), and the future (F) and past (P) regions.

Figure 4

The Penrose diagram of Minkowski space, showing the regions R, L, F, and P. The conformal infinity of the right Rindler wedge is a subset of the conformal infinity of Minkowski space, intersecting ${\mathcal{J}}^{+}$ and ${\mathcal{J}}^{-}$.