Cosmic branes and asymptotic structure

TL;DR

The paper extends the 4D link between superrotations and cosmic strings to higher dimensions by showing that only (d-3)-branes are locally flat near the brane; to include such branes piercing the celestial sphere, asymptotically locally flat boundary conditions are required. It constructs five-dimensional ALF solutions with polyhomogeneous, log-inclusive expansions and derives the corresponding Bondi-type framework, illustrating how the phase space enlarges relative to standard asymptotically flat spacetimes. The work highlights a structural parallel with asymptotically locally AdS spacetimes, where logarithmic terms are fixed by non-normalizable boundary data, and points toward extended asymptotic symmetries and potential connections to soft scattering, memory effects, and holography in higher dimensions.

Abstract

Superrotations of asymptotically flat spacetimes in four dimensions can be interpreted in terms of including cosmic strings within the phase space of allowed solutions. In this paper we explore the implications of the inclusion of cosmic branes on the asymptotic structure of vacuum spacetimes in dimension d > 4. We first show that only cosmic (d-3)-branes are Riemann flat in the neighbourhood of the brane, and therefore only branes of such dimension passing through the celestial sphere can respect asymptotic local flatness. We derive the asymptotically locally flat boundary conditions associated with including cosmic branes in the phase space of solutions. We find the asymptotic expansion of vacuum spacetimes in d=5 with such boundary conditions; the expansion is polyhomogenous, with logarithmic terms arising at subleading orders in the expansion. The asymptotically locally flat boundary conditions identified here are associated with an extended asymptotic symmetry group, which may be relevant to soft scattering theorems and memory effects.

Figures (7)

• Figure 1: Three cosmic strings: a string passing though the north pole of the sphere; a string rotated with respect to this axis and a third string (red) translated with respect to the first one.
• Figure 2: Cosmic string and membrane intersecting the celestial sphere.
• Figure 3: The blue line shows $F \left ( \frac{1}{2} (\frac{\pi}{2} - 2 x) | 2 \right )$, plotted over the range $(0,\pi/2)$. The red line shows $K^{\frac{1}{2}} F \left ( \frac{1}{2} (\frac{\pi}{2} - 2 x) | 2 \right )$, plotted over the same range, with $K^{\frac{1}{2}} = 0 .8$.
• Figure 4: $\Theta_{(0)}(\theta)$ for $K^{\frac{1}{2}} = 0.8$.
• Figure 5: The red line plots $f(\theta)$ and the blue line plots $\lambda f(\theta)$ for $\lambda = 0.8$. For any value of $\lambda < 1$ the blue curve will lie closer to the horizontal axis than the red curve.