General bounds on holographic complexity

We prove a positive volume theorem for asymptotically AdS spacetimes: the maximal volume slice has nonnegative vacuum-subtracted volume, and the vacuum-subtracted volume vanishes if and only if the spacetime is identically pure AdS. Under the Complexity=Volume proposal, this constitutes a positive holographic complexity theorem. The result features a number of parallels with the positive energy theorem, including the assumption of an energy condition that excludes false vacuum decay (the AdS weak energy condition). Our proof is rigorously established in broad generality in four bulk dimensions, and we provide strong evidence in favor of a generalization to arbitrary dimensions. Our techniques also yield a holographic proof of Lloyd’s bound for a class of bulk spacetimes. We further establish a partial rigidity result for wormholes: wormholes with a given throat size are more complex than AdS-Schwarzschild with the same throat size.

Charged traversable wormholes in f(R) gravity

This work is focused on the study of charged wormholes in the following two aspects: (i) to obtain exotic matter free effective charged wormhole solutions and (ii) to determine deflection angle for gravitational lensing effect. We have defined a novel redshift function, obtained wormhole solutions using the background of [Formula: see text] theory of gravity and found the regions obeying the weak energy condition. Further, the gravitational lensing effect is analyzed by determining the deflection angle in terms of strong field limit coefficients.

Geometric properties of a certain class of compact dynamical horizons in locally rotationally symmetric class II spacetimes

In this paper, we study the geometry of a certain class of compact dynamical horizons with a time-dependent induced metric in locally rotationally symmetric class II spacetimes. We first obtain a compactness condition for embedded [Formula: see text]-manifolds in these spacetimes, satisfying the weak energy condition, with non-negative isotropic pressure [Formula: see text]. General conditions for a [Formula: see text]-manifold to be a dynamical horizon are imposed, as well as certain genericity conditions, which in the case of locally rotationally symmetric class II spacetimes reduces to the statement that “the weak energy condition is strictly satisfied or otherwise violated”. The compactness condition is presented as a spatial first-order partial differential equation in the sheet expansion [Formula: see text], in the form [Formula: see text], where [Formula: see text] is the Gaussian curvature of [Formula: see text]-surfaces in the spacetime and [Formula: see text] is a real number parametrizing the differential equation, where [Formula: see text] can take on only two values, [Formula: see text] and [Formula: see text]. Using geometric arguments, it is shown that the case [Formula: see text] can be ruled out and the [Formula: see text] ([Formula: see text]-dimensional sphere) geometry of compact dynamical horizons for the case [Formula: see text] is established. Finally, an invariant characterization of this class of compact dynamical horizons is also presented.

On the Energy of a Non-Singular Black Hole Solution Satisfying the Weak Energy Condition

The energy-momentum localization for a new four-dimensional and spherically symmetric, charged black hole solution that through a coupling of general relativity with non-linear electrodynamics is everywhere non-singular while it satisfies the weak energy condition, is investigated. The Einstein and Møller energy-momentum complexes have been employed in order to calculate the energy distribution and the momenta for the aforesaid solution. It is found that the energy distribution depends explicitly on the mass and the charge of the black hole, on two parameters arising from the space-time geometry considered, and on the radial coordinate. Further, in both prescriptions all the momenta vanish. In addition, a comparison of the results obtained by the two energy-momentum complexes is made, whereby some limiting and particular cases are pointed out.

Dark Matter Candidates with Dark Energy Interiors Determined by Energy Conditions

We outline the basic properties of regular black holes, their remnants and self-gravitating solitons G-lumps with the de Sitter and phantom interiors, which can be considered as heavy dark matter (DM) candidates generically related to a dark energy (DE). They are specified by the condition T t t = T r r and described by regular solutions of the Kerr-Shild class. Solutions for spinning objects can be obtained from spherical solutions by the Newman-Janis algorithm. Basic feature of all spinning objects is the existence of the equatorial de Sitter vacuum disk in their deep interiors. Energy conditions distinguish two types of their interiors, preserving or violating the weak energy condition dependently on violation or satisfaction of the energy dominance condition for original spherical solutions. For the 2-nd type the weak energy condition is violated and the interior contains the phantom energy confined by an additional de Sitter vacuum surface. For spinning solitons G-lumps a phantom energy is not screened by horizons and influences their observational signatures, providing a source of information about the scale and properties of a phantom energy. Regular BH remnants and G-lumps can form graviatoms binding electrically charged particles. Their observational signature is the electromagnetic radiation with the frequencies depending on the energy scale of the interior de Sitter vacuum within the range available for observations. A nontrivial observational signature of all DM candidates with de Sitter interiors predicted by analysis of dynamical equations is the induced proton decay in an underground detector like IceCUBE, due to non-conservation of baryon and lepton numbers in their GUT scale false vacuum interiors.

A regular scale-dependent black hole solution

In this work, we present a regular black hole solution, in the context of scale-dependent General Relativity, satisfying the weak energy condition. The source of this solution is an anisotropic effective energy–momentum tensor which appears when the scale dependence of the theory is turned-on. In this sense, the solution can be considered as a semiclassical extension of the Schwarzschild one.

Necessary conditions for having wormholes in f(R) gravity

For a generic f(R) which admits a polynomial expansion, we find the near-throat wormhole solution. Necessary conditions for the existence of wormholes in such f(R) theories are derived for both zero and nonzero matter sources. For vanishing external sources, we show that the energy conditions are violated. A particular choice of energy–momentum reveals that the wormhole geometry satisfies the weak energy condition (WEC). For a range of parameters, even the strong energy condition (SEC) is shown to be satisfied.