Exact modifications on a vacuum spacetime due to a gradient bumblebee field at its vacuum expectation value

Abstract

This work belongs to the context of the standard-model extension, in which a Lorentz symmetry violation is induced by a bumblebee field as it acquires a nonzero vacuum expectation value. The mathematical formulation of a generic bumblebee model and its associated dynamical equations are presented. Then, these equations are considered for the vacuum and a substantial simplification is performed for the particular case of a gradient bumblebee field at its vacuum expectation value. After some further manipulation, a method to easily find solutions to the model is developed, in which the exact bumblebee field contributions to a vacuum metric from General Relativity is explicitly provided in terms of both of them. As some examples, the method was applied to determine the implications of the bumblebee field on the Schwarzschild solution and a rotating spacetime. A previously published solution was recovered and some new ones were obtained. In the rotating situation, a simple solution was found which contains both Kerr solution and the already published one as special cases. It is also shown that its distinguished surfaces are still given by the same corresponding expressions for the Kerr solution. As a conclusion, the mathematical improvement made is considered to be a significant contribution the theory as a powerful tool to investigate its many aspects and consequences.

Cosmology in the presence of diffeomorphism-violating, nondynamical background fields

“…One possibility of disregarding the very restrictive no-go results of Eqs. ( 37), ( 44) would be to elaborate modified-gravity theories based on the gravitational SME with diffeomorphism invariance violated spontaneously such as in bumblebee-type models [102][103][104][105][106][107][108][109][110][111][112][113][114][115]. By doing so, conflicts with the Bianchi identities of Riemannian geometry are neatly avoided.…”

Hubble tension as a guide for refining the early Universe: Cosmologies with explicit local Lorentz and diffeomorphism violation

“…Apart from strings, mechanisms that result in a breakdown of Lorentz symmetry at the fundamental level were also identified in loop quantum gravity [67,68], theories of noncommutative spacetimes [69][70][71], spacetime foam [72][73][74], nontrivial spacetime topologies [75][76][77][78], Einstein-aether gravity [79][80][81][82], bumblebee gravity [83][84][85][86][87][88][89][90][91][92], Hořava gravity [93], and covariant Hořava-like gravity [94][95][96]. Besides, in Refs.…”

Greybody factors of bosons and fermions emitted from higher dimensional dS/AdS black holes in Einstein-bumblebee gravity theory

“…The first physically accepted slowly rotating black hole solution in the EBGT was obtained by Ding and Chen [37]. Subsequently, Jaha et al [41] and Poulis and Soares [42] have recently managed to derive an arbitrarily spinning bumblebee black hole solution, which means crossing a difficult threshold in the EBGT. Another milestone in this regard was passed by [43], who achieved an exact higher dimensional anti-de Sitter (AdS) black hole solution in the EBGT.…”