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We propose new concepts, a dynamically transversely trapping surface (DTTS) and a marginally DTTS, as indicators for a strong gravity region. A DTTS is defined as a two-dimensional closed surface on a spacelike hypersurface such that photons emitted from arbitrary points on it in transverse directions are acceleratedly contracted in time, and a marginally DTTS is reduced to the photon sphere in spherically symmetric cases. (Marginally) DTTSs have a close analogy with (marginally) trapped surfaces in many aspects. After preparing the method of solving for a marginally DTTS in the time-symmetric initial data and the momentarily stationary axisymmetric initial data, some examples of marginally DTTSs are numerically constructed for systems of two black holes in the Brill-Lindquist initial data and in the Majumdar-Papapetrou spacetimes. Furthermore, the area of a DTTS is proved to satisfy the Penrose-like inequality, $A_0le 4pi (3GM)^2$, under some assumptions. Differences and connections between a DTTS and the other two concepts proposed by us previously, a loosely trapped surface [arXiv:1701.00564] and a static/stationary transversely trapping surface [arXiv:1704.04637], are also discussed. A (marginally) DTTS provides us with a theoretical tool to significantly advance our understanding of strong gravity fields. Also, since DTTSs are located outside the event horizon, they could possibly be related with future observations of strong gravity regions in dynamical evolutions.
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A dynamically transversely trapping surface (DTTS) is a new concept of an extension of a photon sphere that appropriately represents a strong gravity region and has close analogy with a trapped surface. We study formation of a marginally DTTS in time-symmetric, conformally flat initial data with two black holes, with a spindle-shaped source, and with a ring-shaped source, and clarify that $mathcal{C}lesssim 6pi GM$ describes the condition for the DTTS formation well, where $mathcal{C}$ is the circumference and $M$ is the mass of the system. This indicates that an understanding analogous to the hoop conjecture for the horizon formation is possible. Exploring the ring system further, we find configurations where a marginally DTTS with the torus topology forms inside a marginally DTTS with the spherical topology, without being hidden by an apparent horizon. There also exist configurations where a marginally trapped surface with the torus topology forms inside a marginally trapped surface with the spherical topology, showing a further similarity between DTTSs and trapped surfaces.
We study the properties of the loosely trapped surface (LTS) and the dynamically transversely trapping surface (DTTS) in Einstein-Maxwell systems. These concepts of surfaces were proposed by the four of the present authors in order to characterize strong gravity regions. We prove the Penrose-like inequalities for the area of LTSs/DTTSs. Interestingly, although the naively expected upper bound for the area is that of the photon sphere of a Reissner-Nordstroem black hole with the same mass and charge, the obtained inequalities include corrections represented by the energy density or pressure/tension of electromagnetic fields. Due to this correction, the Penrose-like inequality for the area of LTSs is tighter than the naively expected one. We also evaluate the correction term numerically in the Majumdar-Papapetrou two-black-hole spacetimes.
We present a framework for nonlinearly coupled scalar-tensor theory of gravity to address both inflation and core-collapse supernova problems. The unified approach is based on a novel dynamical trapping and relaxation of scalar gravity in highly energetic regimes. The new model provides a viable alternative mechanism of inflation free from various issues known to affect previous proposals. Furthermore, it could be related to observable violent astronomical events, specifically by releasing a significant amount of additional gravitational energy during core-collapse supernovae. A recent experiment at CERN relevant for testing this new model is briefly outlined.
Bialynicki-Birula and Charzynski [1] argued that the gravitational wave emitted during the merger of a black hole binary may trap particles. In this Letter we amplify their statement by describing particle motion in the wave proposed by Lukash [2] to study anisotropic cosmological models. Bounded geodesics (found both analytically and numerically) arise when the wave is of Bianchi type VI. Their symmetries are identified.
We show that it is possible to locate the event horizons of a black hole (in arbitrary dimensions) as the zeros of certain Cartan invariants. This approach accounts for the recent results on the detection of stationary horizons using scalar polynomial curvature invariants, and improves upon them since the proposed method is computationally less expensive. As an application, we produce Cartan invariants that locate the event horizons for various exact four-dimensional and five-dimensional stationary, asymptotically flat (or (anti) de Sitter) black hole solutions and compare the Cartan invariants with the corresponding scalar curvature invariants that detect the event horizon. In particular, for each of the four-dimensional examples we express the scalar polynomial curvature invariants introduced by Abdelqader and Lake in terms of the Cartan invariants and show a direct relationship between the scalar polynomial curvature invariants and the Cartan invariants that detect the horizon.
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