Modified black hole solution with a background Kalb–Ramond field

Abstract

We study the gravitation effects on a static and spherically symmetric spacetime due to the vacuum expectation value (VEV) of Kalb-Ramond field. The Kalb-Ramond VEV is a background tensor field which produces a local Lorentz symmetry breaking (LSB) of spacetime. Considering a non-minimal coupling between the Kalb-Ramond (vev) and the Ricci tensor we obtain an exact parameter-dependent power-law hairy black hole. For s = 1, the Lorentz violation produces a solution similar to the Reissner-Nordstrom, despite the absence of charge. The near horizon geometry is modified by including a new inner horizon and shifting the Schwarzchild horizon. Asymptotically, the usual Minkowski spacetime with a background tensor field is recover. By means of the mercury peherilion test, an upper bound to the local Lorentz violation (LV) is obtained and its corresponding effects on the black hole temperature is investigated.

Exact solution for a traversable wormhole in a curvature-coupled antisymmetric background field

“…In particular, the t-coefficient can only be expressed in terms of the field B µν when contracted with the Riemann curvature tensor from the ξ 1 coupling [32]. Second, the phenomenological role of the t-coefficient is an intriguing issue still little explored in the literature since previous investigations involving solutions of black holes [12] and wormholes [16] did not take into account this type of coupling present in (1). Hence, our main focus of this letter is to determine the existence of a wormhole solution modified by the ξ 1 coupling, responsible for producing a nonzero vacuum value for…”

“…Following the Refs. [12,16], we will restrict ourselves to the pseudo-electric configuration in which the field B µν is frozen in its vacuum expectation value b µν , whose explicit form is given by…”

“…In this context, it is of deep interest to explore the consequences of Lorentz violation in the gravitational scenario involving compact objects like black holes [11][12][13][14] and topologically non-trivial structures as wormholes [15,16] as well as in cosmology [17][18][19] . These objects originally were found as solutions for the field equations of general relativity, unraveling unexpected connections between two remote regions of the spacetime [20][21][22].…”

Bianchi type I cosmology with a Kalb–Ramond background field

“…A mechanism capable of overcoming these difficulties is the spontaneous Lorentz symmetry breaking [21], which works similarly to the Higgs mechanism, adding then a potential term to the Lagrange density constructed in such a way that its minimum lies at a nonzero vacuum expectation value (VEV) for either the background vector field or the background tensor field [22][23][24] (whether vector or tensor fields, such background fields are also called bumblebee fields). In this context, studying the behavior of gravity in the strong-field regime with the presence of spontaneous Lorentz violation is a tough task that has attracted attention in recent years, and several works involving solutions of compact objects like black holes [25][26][27][28] and topologically nontrivial structures like wormholes [29,30] have been carried out. In the cosmological scenario, effects of the Lorentz violation on the Friedmann-Lemaître-Robertson-Walker (FLRW) universe were studied in Refs.…”

“…From the phenomenological perspective, the role played by the t-coefficient is an interesting and few studied issue, since previous works like Refs. [26,30] did not take into account the coupling constant ξ 1 . 3 According to Refs.…”