Kinematical bound in asymptotically translationally invariant spacetimes

TL;DR

The paper addresses bound properties in non-asymptotically flat, asymptotically translationally invariant spacetimes such as black strings and branes. It employs a spinorial (Witten-type) approach with Nester tensors, extending methods to horizons and gauge fields. The main results are a positive energy theorem for black strings with horizon, and positive energy and positive tension theorems for charged branes in four dimensions, the latter showing that gauge fields do not contribute to tension; saturations lead to partial supersymmetry. These results provide kinematical constraints that could inform stability, end-states, and potential uniqueness properties of such spacetimes in the context of higher-dimensional gravity and string theory.

Abstract

We present positive energy theorems in asymptotically translationally invariant spacetimes which can be applicable to black strings and charged branes. We also address the bound property of the tension and charge of branes.

Figures (1)

• Figure 1: Full space-time $\cal{M}$ can be foliated by spacelike hypersurfaces $V_0$ normal to timelike vector field $n\propto\partial_t$ and timelike hypersurfaces $V_1$ normal to spacelike vector field $z\propto\partial_{x^1}$. We can define coordinate $\{x^i\}=(x_1,x_2,\cdots,x_n)$ in $V_0$, $\{x^I\}=(x_0,x_2,\cdots,x_n)$ in $V_1$ and $\{x^A\}=(x_2,\cdots,x_n)$ in $(n-2)-$dimensional spacelike surface $V_{01}$ normal to both vector fields $n$ and $z$. Furthermore, we set coordinate $\{x^a\}=(x_3,\cdots,x_n)$ in $(n-3)$-dimensional spacelike submanifold $V_{012}$ normal to $n,z$ and $\hat{r}\propto\partial_{x^2}$.