Black holes with a cosmological constant in bumblebee gravity

Abstract

In this work, we present black hole solutions with a cosmological constant in the bumblebee gravity, which provides a mechanism for the Lorentz symmetry violation by assuming a nonzero vacuum expectation value for the bumblebee field. From the gravitational point of view, such solutions are spherically symmetric black holes with an effective cosmological constant and are supported by an anisotropic energy-momentum tensor, conceived of as the manifestation of the bumblebee field in the spacetime geometry. Then we calculate the shadow angular radius for the proposed black hole solution with a positive effective cosmological constant. In particular, our results are the very first relation between the bumblebee field and the shadow angular size.

Hamiltonian formulation of an effective modified gravity with nondynamical background fields

“…References [66][67][68] give an account of a scenario of an antisymmetric two-tensor acquiring a vacuum expectation value. Papers have also been written on black-hole solutions in the presence of bumblebee-type Lorentz violation [69][70][71][72][73]. Note that spontaneous Lorentz violation was demonstrated to occur in open-string field theory, too [7][8][9][10][11].…”

Bianchi type I cosmology with a Kalb-Ramond background field

“…Another useful simplification comes from the fact that p 2 = p 3 , according to the Kalb-Ramond energy-momentum tensor indicated in Eq. (28). Therefore, as we said, the directions x 2 and x 3 will be considered equivalent.…”

“…In particular, black hole solutions and anisotropies in the cosmic microwave background radiation were recently investigated by us in Refs. [28,33]. However, the description of that effects depends on the fields that are chosen to compose the mentioned coefficients.…”

“…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-Lemaîte-Robertson-Walker (FLRW) universe were studied in [31,32,38], and recently the impact of the Lorentz symmetry breaking on anisotropies of the cosmic microwave background radiation was examined by us in Ref.…”

Schwarzschild-like black hole with a topological defect in bumblebee gravity

“…On the other side, the Lorentz symmetry breaking is associated with the idea that the Quantum Gravity (QG) signals may emerge at low energy scales [4]. The naturelness and the possibility of Lorentz symmetry breaking is discussed in the context of string theory in [5][6][7][8][9][10][11][12][13][14][15]. The Lorentz symmety breaking arises in other theories like noncomutative field theories [16][17][18] and loop quantum gravity theory [19,20] among other scenarios [21][22][23][24].…”