R=0 spacetimes and self-dual Lorentzian wormholes

Abstract

A two-parameter family of spherically symmetric, static Lorentzian wormholes is obtained as the general solution of the equation $\rho ={\rho }_t=0$, where $\rho =T_{ij}{u}^i{u}^j$, ${\rho }_t=(T_{ij}-\frac{1}{2}T{g}_{ij})u^i{u}^j$, and $u^i{u}_i=-1$. This equation characterizes a class of spacetimes which are ``self dual'' (in the sense of electrogravity duality). The class includes the Schwarzschild black hole, a family of naked singularities, and a disjoint family of Lorentzian wormholes, all of which have vanishing scalar curvature (R=0). Properties of these spacetimes are discussed. Using isotropic coordinates we delineate clearly the domains of parameter space for which wormholes, nakedly singular spacetimes and the Schwarzschild black hole can be obtained. A model for the required ``exotic'' stress-energy is discussed, and the notion of traversability for the wormholes is also examined.

arXiv comment8 pages, RevTex two column, one figure

References in corpus (17)

• Dynamic wormholes, anti-trapped surfaces, and energy conditions
• The null energy condition in dynamic wormholes
• Natural Wormholes as Gravitational Lenses
• Scalar fields, energy conditions, and traversable wormholes
• Traversable wormholes from massless conformally coupled scalar fields
• Energy conditions and their cosmological implications
• Evolving Lorentzian Wormholes
• Microlensing by natural wormholes: theory and simulations
• Brane surgery: energy conditions, traversable wormholes, and voids
• Chromaticity effects in microlensing by wormholes
• Macrolensing signatures of large-scale violations of the weak energy condition
• In search for natural wormholes
• On Electrogravity Duality
• General Dynamic Wormholes and Violation of the Null Energy Condition
• Geometric wormhole throats
• Spherically symmetric empty space and its dual in general relativity
• A duality relation : global monopole and texture

Cited by in corpus (61)

• Traversable wormholes with arbitrarily small energy condition violations
• Morris-Thorne wormholes with a cosmological constant
• Possible wormholes in a brane world
• Gravitational Lensing by Wormholes
• Weak lensing in a plasma medium and gravitational deflection of massive particles using the Gauss-Bonnet theorem. A unified treatment
• Novel black-bounce spacetimes: wormholes, regularity, energy conditions, and causal structure
• Phenomenological aspects of black holes beyond general relativity
• Strong gravitational lensing by wormholes
• Gravitational lensing by scalar-tensor wormholes and the energy conditions
• Wormholes, the weak energy condition, and scalar-tensor gravity
• Higher-dimensional evolving wormholes satisfying the null energy condition
• Dynamic thin-shell black-bounce traversable wormholes
• Gravitational waves from quasinormal modes of a class of Lorentzian wormholes
• The exponential metric represents a traversable wormhole
• N-dimensional static and evolving Lorentzian wormholes with cosmological constant
• Evolving Lorentzian wormholes supported by phantom matter and cosmological constant
• On-brane data for braneworld stars
• Can extra dimensional effects allow wormholes without exotic matter?
• $f(R)$ gravity solutions for evolving wormholes
• Volume Integral Theorem for Exotic Matter
• Relativistic Bose--Einstein condensates thin-shell wormholes
• Traversable wormholes with charge and non-commutative geometry in the $f(Q)$ gravity
• Wormhole solutions in $f(R)$ Gravity
• Thin-shell wormholes in Rastall gravity
• Evolving Lorentzian wormholes supported by phantom matter with constant state parameters
• Thin-shell traversable wormhole crafted from a regular black hole with asymptotically Minkowski core
• Hunting extra dimensions in the shadow of Sgr A*
• Shadow of charged wormholes in Einstein-Maxwell-dilaton theory
• Two-fluid evolving Lorentzian wormholes
• Stability of charged thin-shell wormholes in (2 + 1) dimensions
• Exotic solutions in General Relativity: Traversable wormholes and 'warp drive' spacetimes
• Self--dual Lorentzian wormholes in n--dimensional Einstein gravity
• Wormholes with fluid sources: A no-go theorem and new examples
• Probing the existence of the ZTF Casimir wormholes in the framework of $f(\mathcal{R})$ gravity
• Static wormholes on the brane inspired by Kaluza-Klein gravity
• Evolving wormhole in the brane-world scenario
• Dynamic wormholes with particle creation mechanism
• Phantom Wormhole Solutions in a Generic Cosmological Constant Background
• Wormholes supported by pure ghost radiation
• Echoes from braneworld wormholes
• New Traversable Wormholes Solutions in $f(T)$ Gravity
• Spherically symmetric wormhole solutions in a general anisotropic matter field
• Electromagnetic Fields and Charged Particle Motion Around Magnetized Wormholes
• Galactic wormholes: Geometry, stability, and echoes
• Holography and trace anomaly: what is the fate of (brane-world) black holes?
• Phantom energy supported wormhole model in $f(R,T)$ gravity assuming conformal motion
• Traversable Wormholes in Higher Dimensional Theories of Gravity
• Gravitational lensing by a Bronnikov-Kim wormhole under a weak-field approximation and in a strong deflection limit
• Wormholes, naked singularities and universes of ghost radiation
• Schwarzschild-like Wormholes in Asymptotically Safe Gravity
• Black Holes and Wormholes Beyond Classical General Relativity
• Classical and semi-classical energy conditions
• Traversable wormholes in bi-metric gravity
• Circular light orbits of a general, static, and spherical symmetrical wormhole with $Z_2$ symmetry
• Thermodynamics of an Evolving Lorentzian Wormhole with Entropy Corrections
• New rotating Lorentzian wormhole spacetime
• Scalar Field Entropy in Brane World Black Holes
• Gravitational wave memory in wormhole spacetimes
• Cosmological Lorentzian Wormholes via Noether symmetry approach
• Decoding Horizonless Spacetime: Plasma-Induced Features in a Rotating Wormhole Shadow
• Trace anomaly contributions to semi-classical wormhole geometries