Representation of compact stars using the black string set--up

Abstract

This work is devoted to provide a way of representing $4D$ spherically symmetric and static compact stellar configurations into a $5D$ space time, using the black string framework. We write the four and five dimensional line elements and the four and five dimensional energy momentum tensor such that the four and five dimensional quantities are related by a function $A(z)$, where $z$ represents to the extra dimension. Remarkably, one consequence of our chosen form for the line element, for the energy momentum tensor and for $A(z)$, is the fact that the $5D$ equations are reduced to the usual form of the four dimensional equations of motion. Also, the five dimensional conservation equation adopts the form of the four dimensional conservation equation. It is worth mentioning that, although our methodology is simple, this form of reduction could serve to represent other types of four dimensional objects into an extra dimension in future works. Furthermore, under our assumptions the sign of the pressure along the extra dimension is given by the trace of the four dimensional energy momentum tensor. Furthermore, our simple election for the function $A(z)$ modifies some features of the induced 4--dimensional compact stellar configuration, such as the mass--radius relation, the momentum of inertia, the central values of the thermodynamic variables, to name a few. Besides, the topology of this model is $S^2\times S^1$ and not the $S^3$ topology of the 5--dimensional structures.

References in corpus (29)

• Brane-World Gravity
• Physical Acceptability of Isolated, Static, Spherically Symmetric, Perfect Fluid Solutions of Einstein's Equations
• The Lovelock Black Holes
• Moments of inertia for neutron and strange stars: limits derived for the Crab pulsar
• The Phase Transition between Caged Black Holes and Black Strings - A Review
• Topology change in General Relativity and the black-hole black-string transition
• The Gravitational decoupling method: the higher dimensional case to find new analytic solutions
• Possibility of higher dimensional anisotropic compact star
• $\ell$-Boson stars
• New nonuniform black string solutions
• Black string solutions with negative cosmological constant
• Axionic black branes in the k-essence sector of the Horndeski model
• Regular black holes and its thermodynamics in Lovelock gravity
• LARGE EXTRA DIMENSIONS: Becoming acquainted with an alternative paradigm
• Compact objects in pure Lovelock theory
• Static and rotating black strings in dynamical Chern-Simons modified gravity
• Exact black strings and p-branes in general relativity
• Buchdahl-Vaidya-Tikekar model for stellar interior in pure Lovelock gravity - II
• Quasitopological electromagnetism: Reissner-Nordström black strings in Einstein and Lovelock gravities
• Rotating black strings in $f(R)$-Maxwell theory
• Phase transitions of black strings in dynamical Chern-Simons modified gravity
• Charged black strings and black branes in Lovelock theories
• Black String in Massive Gravity
• Stabilizing Homogeneous Black Strings in AdS
• Black string surrounded by a static anisotropic quintessence fluid
• Embedding of two de-Sitter branes in a generalized Randall Sundrum scenario
• Extensions of the generalized hedgehog ansatz for the Einstein-nonlinear $\sigma$-model system: black holes with NUT, black strings and time-dependent solutions
• A new exact solution of black-strings-like with a dS core
• Regular Schwarzschild-like spacetime embedded in a five dimensional bulk