Abstract
We demonstrate that all rigidly rotating strings with center of mass at the origin of the dS3 static patch satisfy the Higuchi bound. This extends the observation of Noumi et al. for the open GKP-like string to all solutions of the Larsen-Sanchez class. We argue that strings violating the bound end up expanding towards the horizon and provide a numerical example. Adding point masses to the open string only increases the mass/spin ratio. For segmented strings, we write the conserved quantities, invariant under Gubser’s algebraic evolution equation, in terms of discrete lightcone coordinates describing kink collisions. Randomly generated strings are found to have a tendency to escape through the horizon that is mostly determined by their energy. For rapidly rotating segmented strings with mass/spin < 1, the kink collisions eventually become causally disconnected. Finally we consider the scenario of cosmic strings captured by a black hole in dS and find that horizon friction can make the strings longer.
Highlights
With l being the de Sitter scale, led [2, 3] to conclude that for L > l2/α unitarity is violated unless the spectrum is modified
We demonstrate that all rigidly rotating strings with center of mass at the origin of the dS3 static patch satisfy the Higuchi bound
The result is that the string loses energy and angular momentum to the black hole,7 which happens on a timescale s3 tfr = R2
Summary
At this point we are interested in rigidly rotating strings in the static patch of dS3, for which we will demonstrate (1.2). Looking to solve the Polyakov equations of motion with constraints, we follow [5] and review their Ansatz in static patch coordinates, where the. The conformal flatness of the induced metric on the worldsheet in ensured by the constraints gμν XμX ν = 0 = gμν XμXν + gμν X μX ν. Where the constants c1, c2 are real and f , g are real functions of σ. Where k1, k2 are again real constants. The resulting surface that is traced out in spacetime will be the same but the timelike and spacelike worldsheet coordinates are interchanged.
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