Gravitational double layers turn out to be feasible in quadratic theories of gravity. New physics arises.

Double layers (DL) may be found in several disciplines: in biology separating two different forms of matter, in chemistry as interfaces between different phases (liquid and solid), or in physics when two laminar parallel shells with opposite electric charges are found next to each other. DL are especially important in plasma and cellular physics, representing abrupt drops in the electric potential by which the cell, or plasma, “protects” itself from the environment.

However, gravitational DL were nowhere to be found in gravitational physics, until now.

In this paper I have demonstrated that DL are possible in gravity theories with a quadratic Lagrangian. This comes as a surprise because an analogy with electrostatics may seem to indicate a dipolar distribution of matter on DL. At first sight, this sounds strange because only positive masses exist. See, however, CQG 11 (1994) 1483, CQG 24 (2007) 3529 and 3541. Thus, the potential consequences are tremendous, and new physical behaviors can be described.

Tensor distribution techniques have been used, so that DL are described in an idealized manner by hypersurfaces supporting Dirac-delta and Dirac-delta-prime type terms. A comparison with the same techniques in electrostatics suggests that the former represents a localized energy–momentum content while the latter provides the dipolar contribution, which arises due to an abrupt change in the scalar curvature across the DL. The gravitational DL thus constructed can be thought of as “protecting” a given scalar curvature (or a cosmological constant) from a different neighbor one.

These DL are described not only by the dipolar part and a standard energy–momentum tensor; in addition they also carry a new flux vector and a new scalar tension, both representing terms concerning the mixing with the surrounding bulk. The field equations for these quantities are presented in the paper and they show that the energy–momentum tensor supported on DL is no longer divergence-free the novel quantities act as sources or currents leading to unexpected physical behaviors. The full energy–momentum tensor is, of course, divergence-free.

The paper presents the explicit solution for 4-dimensional DL separating two portions of a 5-dimensional bulk space-time with different scalar curvatures (or cosmological constants). These DL represent standard Robertson–Walker geometries with unexpected properties, including big-bang eras with radiation dominated matter followed by accelerating expansion epochs. Interestingly, the generalized continuity equation allows for violations of the standard behavior of the energy density (ρ ~ a^{-3(1+w)}) for linear equations of state p = wρ.

Several doors are open, and various checks are in order. One should try to find actual, regular, solutions that approach the idealized version given in the paper. The stability of the solutions must also be analyzed. Most importantly, a clear interpretation of the dipolar term is elusive. Finally, the question of how these solutions fit in a general gravitational theory must be addressed, to examine if DL arise generically in regimes dominated by quadratic terms in the curvature.

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