Schwarzschild-like topological solitons

Abstract

We construct the first class of topological solitons in gravity that are supported by internal electromagnetic flux with vanishing net charges. The solutions are obtained in a six-dimensional Einstein-Maxwell theory with a three-form flux, and admit an uplift to type IIB supergravity on T4. They are asymptotic to a torus fibration over four-dimensional Minkowski spacetime. An interesting class corresponds to solitons with a BPS particle and its anti-BPS partner held apart by a vacuum bubble. In type IIB, they correspond to bound states of BPS and anti-BPS D1-D5 extremal black holes. These metrics are a particular limit of a larger class of axially symmetric metrics that we construct and that describe smooth horizonless topological solitons. They correspond to bound states of three non-BPS bubbles on a line. An important achievement is that the outer bubbles can carry arbitrary D1-D5 charges that we can tune to vanishing net charges. We discuss their properties and compare them to a four-dimensional Schwarzschild black hole of the same mass. We show that they have a long throat with a large redshift, and that they are ultra-compact with a characteristic size of 1.52 times the Schwarzschild radius.

Non-BPS bubbling geometries in AdS3

“…leads to the exact same equations as for the three Maxwell sectors (2.6). 6 The equations of motion of this system admit integrable structures that are well established from the Ernst formalism and inverse scattering. These integrable structures follow the fact that the ansatz in (2.7) admit an action from the Geroch group [39,40].…”

“…These integrable structures follow the fact that the ansatz in (2.7) admit an action from the Geroch group [39,40]. Our general system above will inherit all of these structures that can allow for a large phase 6 We have considered the four-dimensional Einstein-Maxwell action…”

“…An intriguing question in cosmological physics is the existence of gravitational solitons that can describe various dark and ultra-compact objects which, from afar, are indistinguishable from black holes in general relativity. Recently, the authors have developed a framework for constructing and studying large classes of gravitational solitons that are described by smooth horizonless solutions with arbitrary mass and charges in supergravity [1][2][3][4][5][6]. These are thought of as coherent states of quantum gravity that admit classical descriptions.…”

“…In the former case, only a few atypical sets of non-BPS smooth geometries [17][18][19][20][21][22][23] were known until recently. 2 Some promising breakthroughs have been achieved first from a consistent S 3 truncation of six-dimensional supergravity [26][27][28] and second from the "charged Weyl formalism" established by the authors [1][2][3][4][5][6]. In all of these solutions, only a small subset admits field theory descriptions in the context of AdS 3 /CFT 2 in type IIB supergravity: the JMaRT geometry [29] and the microstrata [30].…”

“…This article contributes to bridging the gap towards non-BPS holography. The initial goal is to adapt the formalism of [1][2][3][4][5][6] for a systematic construction of regular non-BPS geometries that are asymptotic to AdS D × C and that can be considered as non-BPS deformations on known BPS backgrounds. These deformations regularly backreact by inducing geometric transitions where compact directions in C degenerate in the spacetime.…”